POCKET NOTE STRATEGIC FINANCIAL MANAGEMENT ICAN NOV 2019 DIET

TABLE OF CONTENTS
TABLE OF CONTENTS ------------------------------------------------------------------------------------------- 1

SESSION 1: INTRODUCTION TO FINANCIAL MANAGEMENT ------------------------------------- 5

CHAPTER ONE; REGULATORY BACKGROUND -------------------------------------------------------20

CHAPTER 1; THE FINANCIAL MANAGEMENT ENVIRONMENT ---------------------------------25

ILLUSTRATIONS ON INTRODUCTION---------------------------------------------------------------------32

CHAPTER TWO; COST OF CAPITAL -----------------------------------------------------------------------42

ILLUSTRATION ON COST OF CAPITAL -------------------------------------------------------------------46

CHAPTER THREE: BETA FACTOR --------------------------------------------------------------------------53

ILLUSTRATIONS ON BETA ISSUE ---------------------------------------------------------------------------54

SOLUTION TO ILLUSTRATION 1 ON BETA ISSUE -----------------------------------------------------54

SOLUTION TO ILLUSTRATION 2 ----------------------------------------------------------------------------55

CHAPTER 4: CAPITAL BUDGETING ------------------------------------------------------------------------57

ILLUSTRATIONS ON CAPITAL BUDGETING BASICS -------------------------------------------------67

CHAPTER 5; ADJUSTED PRESENT VALUE ---------------------------------------------------------------81

ILLUSTRATIONS ON ADJUSTED PRESENT VALUE ---------------------------------------------------81

SESSION 6: CAPITAL RATIONING AND REPLACEMENT -------------------------------------------90

ILLUSTRATIONS ON CAPITAL RATIONING AND REPLACEMENT ------------------------------94

SOLUTION TO QUESTION 5 --------------------------------------------------------------------------------- 106

SESSION 7: LEASING ------------------------------------------------------------------------------------------ 108

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ILLUSTRATIONS ON LEASING ----------------------------------------------------------------------------- 112

SESSION 8: RISK AND UNCERTAINTY ------------------------------------------------------------------- 118

ILLUSTRATIONS ON RISK AND UNCERTAINTY ----------------------------------------------------- 121

CHAPTER NINE: CAPITAL STRUCTURE---------------------------------------------------------------- 133

ILLUSTRATIONS ON CAPITAL STRUCTURE ---------------------------------------------------------- 139

CHAPTER 10: CAPM AND PORTFOLIO THEORY ---------------------------------------------------- 144

ILLUSTRATIONS ON CAPM AND PORTFOLIO THEORY------------------------------------------- 147

CHAPTER ELEVEN: CURRENCY HEDGING METHODS------------------------------------------- 153

ILLUSTRATIONS ON CURRENCY HEDGING METHODS ------------------------------------------- 154

ILLUSTRATION ON CONVERSION OF CURRENCY-------------------------------------------------- 160

CHAPTER 12: INTERNATIONAL INVESTMENT DECISIONS ------------------------------------- 169

ILLUSTRATIONS ON INTERNATIONAL INVESTMENT DECISIONS---------------------------- 170

CHAPTER 13: OPTION VALUATION ---------------------------------------------------------------------- 173

ILLUSTRATION ON OPTION VALUATION-------------------------------------------------------------- 175

CHAPTER 14: INTEREST RATE HEDGING------------------------------------------------------------- 179

ILLUSTRATIONS ON INTEREST RATE HEDGING---------------------------------------------------- 182

CHAPTER 15: BUSINESS VALUATION ------------------------------------------------------------------- 188

ILLUSTRATIONS ON BUSINESS VALUATION --------------------------------------------------------- 188

SESSION 16: FREECASH FLOW MODEL ---------------------------------------------------------------- 192

ILLUSTRATIONS ON FREECASH FLOW MODEL ----------------------------------------------------- 193

CHAPTER 17: ECONOMIC VALUE ADDED, MARKET VALUE ADDED AND

SHAREHOLDERS VALUE ANALYSIS --------------------------------------------------------------------- 198

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ILLUSTRATIONS ON ECONOMIC VALUE ADDED, MARKET VALUE ADDED AND

SHAREHOLDERS VALUE ANALYSIS --------------------------------------------------------------------- 198

SESSION 18; MERGER AND ACQUISITION ------------------------------------------------------------- 207

ILLUSTRATIONS ON MERGER AND ACQUISITION ------------------------------------------------- 217

A) -------------------------------------------------------------------------------------------------------------------------- 218
PRE-ACQUISITION VALUE:--------------------------------------------------------------------------------------------- 218
A. RAYMOND PIC N4-90 X 150M = 735 --------------------------------------------------------------------------------- 218
B. HAROLD N15M/0.08 — = 250 ------------------------------------------------------------------------------------ 218
LIMITED ------------------------------------------------------------------------------------------------------------------ 218
985 ------------------------------------------------------------------------------------------------------------------------ 218
C. POST-ACQUISITION VALUE: -------------------------------------------------------------------------------------- 218
HAROLD LIMITED N15MXL.05 = --------------------------------------------------------------------------------- 315.00
218
/0.08 - 0.03 --------------------------------------------------------------------------------------------------------------- 219
RAYMOND PIC. ---------------------------------------------------------------------------------------------------------- 219
735.00 -------------------------------------------------------------------------------------------------------------------- 219
TRANSACTION COSTS (8.00) (1.85) ---------------------------------------------------------------------------- 219
PRE-ACQUISITION TOTAL VALUE ----------------------------------------------------------------------------- (985.00)
219
INCREMENTAL VALUE ------------------------------------------------------------------------------------------------- 219
55.15 ---------------------------------------------------------------------------------------------------------------------- 219

CHAPTER 19: CORPORATE RESTRUCTURING ------------------------------------------------------ 229

ILLUSTRATIONS ON CORPORATE RESTRUCTURING --------------------------------------------- 231

SESSION 20: CORPORATE FAILURE --------------------------------------------------------------------- 236

ILLUSTRATIONS ON CORPORATE FAILURE --------------------------------------------------------- 236

SOLUTION TO ILLUSTRATION 2 ON CORPORATE FAILURE ------------------------------------ 238
LIMITATION OF CORPORATE FAILURE MODELS -------------------------------------------------- 239

SESSION 21: BOND PRICING -------------------------------------------------------------------------------- 240

ILLUSTRATIONS ON BOND PRICING -------------------------------------------------------------------- 242

SOLUTION TO ILLUSTRATION 1 -------------------------------------------------------------------------- 243
B PART OF THE QUESTION IS ON ZERO COUPON BOND ------------------------------------------ 243
SOLUTION TO ILLUSTRATION 2 ON BOND VALUATION USING YIELD CURVE ---------- 243
SOLUTION TO ILLUSTRATION 3 ON YIELD CURVE DERIVATION ---------------------------- 244
SOLUTION TO ILLUSTRATION 4 ON BOND PRICING (DURATION AND MACAU LAY
DURATION) ------------------------------------------------------------------------------------------------------- 245
SOLUTION TO ILLUSTRATION 5 ON JULIUS BERGER --------------------------------------------- 246

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SOLUTION TO ILLUSTRATION 6 ON GNT -------------------------------------------------------------- 247

SOLUTION TO ILLUSTRATION 7 --------------------------------------------------------------------------------- 250

SESSION 22: DIVIDEND POLICY --------------------------------------------------------------------------- 254

ILLUSTRATION ON DIVIDEND POLICY ----------------------------------------------------------------- 263

SOLUTION TO ILLUSTRATION 1 -------------------------------------------------------------------------- 264

SOLUTION TO ILLUSTRATION 2 -------------------------------------------------------------------------- 265

CHAPTER 23: SOURCE OF FINANCE --------------------------------------------------------------------- 267

ILLUSTRATIONS ON SOURCE OF FINANCE ----------------------------------------------------------- 276

FINANCE FOR SMALL AND MEDIUM SIZED ENTITIES ------------------------------------------- 277

ILLUSTRATION ON FINANCE FOR SMALL AND MEDIUM SIZED ENTITIES ---------------- 279

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SESSION 1: INTRODUCTION TO FINANCIAL

MANAGEMENT
This aspect of this Manual covers stakeholder theory, agency theory, financial markets, financial
environments, money laundering, corporate social responsibility, treasury management and emerging issues.
LESSON 1: Financial Environment and Role of Financial Managers
This aspect of the syllabus covers;

▪ Financial objectives within the strategic planning process

▪ Impact of macroeconomics and the role of international financial institutions in strategic financial
management
▪ Corporate social responsibility
▪ Agency theory
▪ Professional, regulatory and legal framework relevant to financial management including stock
exchange requirement, money laundering and director’s responsibilities
▪ Treasury management
1.1 STRATEGIC PROCESS
Steps in the strategic process
1. Identify the corporate objective (usually a financial objective)
2. Establish targets for the financial objective
3. Develop business strategies for achieving the financial objectives
4. Convert strategies into action plans
5. Monitor performance
The PRIMARY CORPORATE OBJECTIVE
The identification of a primary objective is a starting point for the formulation of a strategy to achieve that
objective. The primary objective is often stated as maximizing the wealth of the owners (maximizing the
market value of the company). In reality, the wealth maximization objective must be pursued within the
boundaries of the needs of other stakeholders.
Corporate Social Responsibility (CSR) is a term to describe the view that a company should pursue
objectives that are in the interest of stakeholder groups other than shareholders such as employees and
society as a whole.
Wealth Maximization; shareholder wealth is increased by dividend payments and a higher share price or
both. The practical problems with wealth maximization are
▪ What should be the time period for setting targets for wealth maximisation
▪ How will wealth creation be measured; how can targets be divided into share price growth and
dividend payments targets
▪ Share prices are often affected by general stock market sentiment (investor attitudes) rather than
any real success or falling of the company itself

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OTHER FINANCIAL OBJECTIVES

▪ Maximising profit
▪ Achieving growth in earnings per share
Measuring the achievement of financial objectives
When a financial objective is established, actual performance should be measured against the objective.
This can be done by financial ratios comparing trend, industry average and with similar companies.
▪ ROCE = profit before interest and taxation/ (share capital & reserves + long term debt capital +
preference share capital) x 100%
▪ Return on shareholder capital = profit after taxation and preference dividend / share capital and
reserves x 100%
▪ EPS = profit attributable to ordinary shareholders / weighted average number of shares
▪ Total shareholders return = (share price at end – share price at start) + dividends / share price at
the start x 100%
Other objectives which are non-financial include paying staff competitive salaries, invest in staff training,
invest in new product development and considering the needs of the society and preserving environment.
Role of Financial Managers
Financial managers provide advice concerned with three fundamental decisions
1. Investment decisions; concerned with what projects to undertake with available resources
2. Financing decisions; concerned with how finance should be raised in order to minimise cost of capital
3. Dividend decisions; concerned with what the balance should be between the amount of profit
distributed and that retained for reinvestment in the business.

1.2 DEFINITION, MEANING AND SCOPE OF FINANCIAL MANAGEMENT

Financial Management is that managerial activity which is concerned with the planning and controlling of the
firm’s financial resources. It can also be defined as the management of the finances of an organization in order
to achieve their financial objectives. It is basically about the identification of the possible strategies capable of
maximizing an organization’s market value which involves the allocation of scarce resources among
competing opportunities.

Financial planning ensures that enough funding is available at the right time to meet the needs of the
organization for short, medium and long term capital while financial control is the process of comparing data
on actual performance with expected performance.

NATURE OF CORPORATE FINANCE

Finance can be regarded as the management of money which is very vital to the management of any
organization as the functional activities of companies such as marketing, production; personnel etc. require the
use of money.

There is an inseparable relationship between finance and the real resources of an organization as almost all
business activities directly or indirectly involve the acquisition and use of funds. Corporate Finance functions
to make money available to meet the cost of production, advertising or marketing. The functions of raising

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funds, investing them in assets and distributing returns earned from assets to Shareholders are respectively
known as the Financing, Investing and Dividend decision.

The nature of corporate finance stems from the fact that it is holistic, long term and involves agents acting on
behalf of the principal towards attaining organizational goals.

SCOPE OF CORPORATE FINANCE

The scope of Finance lies in the fact that firms raise and secure whatever capital they need (financing
decision), they use the funds to generate appropriate returns (investment decisions) and the profits or returns
are distributed to the owners of the business (dividend decision). These decisions are inter-related and have
impact on the share price of the company with full consideration of risk management techniques.

FINANCING DECISION: This is concerned with when, how and where funds needed will be acquired. It
considers the sources of finance available, their cost and the accessibility while taking into consideration the
mix of debt and equity finance in the capital structure and its effect on the company’s leverage. (Financial
risk).

It is concerned with the cost of capital, sources of finance, capital structure decisions, leverage and other ways
of raising and managing funds such as working capital, merger and acquisition and so on.
Financing decision considers the amount of funds needed, the various sources of finance available, the
flexibility of the sources, the commitments, legal implications and the impact of such on the control, earnings
and capital structure in general.

INVESTMENT DECISION: This is concerned with how the funds acquired should be utilized so as to add
value to shareholder’s wealth. It is mainly concerned with how long term assets (capital budgeting) and short
term assets (working capital) are managed to ensure that providers of fund get their funds back and
shareholders wealth is maximized.
It is concerned with ways of appraising various investments available measuring the risk and uncertainty
associated with them, measuring the impact of taxation and inflation on the available cash flow and how funds
should be allocated when there is capital restriction, how and when to replace assets, also considering leasing
and hire purchase options of acquiring long term assets and also the valuation of bonds. It looks at the various
ways in which funds raised can be effectively and efficiently utilized at minimum risk using CAPM, Portfolio
analysis and other cost benefit analysis techniques. It also takes into consideration the various ways a business
can be valued and all other relevant issues as regards the capital market.

DIVIDEND DECISIONS; this is concerned with what portion of the company’s profit at the end of a period
should be given as compensation to ordinary shareholders after settling other stakeholders. It considers the
factors that govern how and when to pay dividend and their likely effect on shareholder’s wealth. It looks at
the various responses or reactions that might arise as a result of non-payment of dividend based on the
composition of shareholders and their preferences.

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A Firm attempt to balance cash-inflows and outflows while the above decisions are performed and this
balance is known as the liquidity decision. To save a firm against the risk of illiquidity the current assets of the
firm should be well managed.

A conflict exists between profitability and illiquidity while managing current assets. If enough funds are not
invested in current assets the firm may become illiquid but it would lose profitability if too much fund is
invested as a result of idle current assets and so should be balanced always.

1.3 OBJECTIVES OF THE FIRM

The starting point for developing good financial management for any company is the definition of workable
objectives which are concerned with the firm as a whole and should be explicit, quantifiable and capable of
being achieved. Objectives should relate to the key factors for business success which are typically as follows;
1. Profitability (return on investment) 2. Market share
3. Growth 4. Cash-flow
5. Value added 6. Industrial relations
7. Quality of firm’s product 8. Customer satisfaction

Frequently encountered financial objectives of the firm are:

1. PROFIT MAXIMISATION; is an easily understood and measurable rationale objective for any business since
it focuses the firm’s effort towards making money. Although profits are so important they are not considered as
the best measure of a company’s achievements for the following reasons;
a. profit maximization ignores timing of returns
b. it does not take account of risk
c. It can be manipulated by the choice of accounting policies
d. It assumes perfect competition
e. It is ambiguous as the profit is not defined whether short term or long term, after tax or
before tax etc.
f. Profits on their own take no account of the volume of investment undertaken to make
such profit
g. Whose profit is the firm maximizing since stakeholders are much
h. Profits are usually measures of short term performance whereas a company should be
appraised over a longer term

2. SATISFICING OBJECTIVES: States that a business is a coalition of shareholders, creditors,

management, employees, suppliers and customers with none of the participants having prominence over
the others meaning that the interest of all participants in the coalition share the same risk and profit

The limitation of this is that in reality the risk position and attitude of all stakeholders are different so
also their objectives. It also ignores the timing of returns.

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3. MAXIMISATION OF SHAREHOLDERS WEALTH: This simply means maximizing the net

present value of a course of action to shareholders (net present value of a course of action is the
difference between the present value of benefits and cost associated).

This objective considers the timing and risk of expected returns by selecting an appropriate discount rate
and uses cash flows which are objective for all measurements.

The wealth created by a company through its actions is reflected in the market value of the company’s
shares which is represented by the share price (serving as a performance indicator)

OTHER NON FINANCIAL OBJECTIVES

1. Welfare of employees; is an attempt to provide good working conditions, training and career
development and good pension plan
2. Welfare of management; must be ensured as managers will often take decisions to improve their
positions at the expense of shareholders
3. Welfare of society as a whole; the company’s corporate responsibility towards the wellbeing of the
society
4. Fulfillment of responsibility towards customer and suppliers; fair and honest dealing with customers
providing products and services of their desired quality and also meeting payments and other obligations
of suppliers.

1.4. ROLE OF THE SENIOR FINANCIAL EXECUTIVE

The principal role of the senior financial executive when setting financial goals is the maximization of
shareholder’s wealth (which is equivalent to the maximization of the market value of the company’s ordinary
shares.
A large part of the senior financial manager’s role is advisory, providing advice on financial strategies and
policies. Strategies must be developed in order to achieve its corporate objectives. Financial strategies should
be formulated by the board of directors to achieve its objective of maximizing shareholder’s wealth.
The actions of stakeholder groups in pursuit of their various goals can exert influence on strategy. The greater
the power of the stakeholder, the greater his influence will be.
STRATEGIES FOR ACHIEVING FINANCIAL GOALS
Strategy may be defined as a course of action, including the specification of resources required to achieve a
specific objective. It can be short term or long term depending on the time horizon of the objective to be
achieved.
CHARACTERISTICS OF STRATEGIC DECISIONS
Johnson, Scholes and Whittington (2008) have summarized the characteristics of strategic decisions for an
organization as follows;
▪ Strategic decisions will be concerned with the scope of the organization’s activities.
▪ Strategy involves the matching of an organization’s activities to the environment in which it operates
▪ Strategy also involves the matching of an organization’s activities to its resource capability
▪ Strategic decisions therefore involve major decisions about the allocation or re-allocation of resources
▪ Strategic decisions will affect operational decisions because they will set off a chain of lesser
decisions and operational activities, involving the use of resources

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▪ Strategic decisions will be affected by environmental considerations, resources capability and the
values & expectations of the people in power within the organization.
▪ Strategic decisions are likely to affect the long term direction that the organization takes
▪ Strategic decisions have implications for change throughout the organization, and so are likely to be
complex in nature.
LEVELS OF STRATEGY
There are three main levels of strategy.
CORPORATE STRATEGY; is concerned with the broader issues such as “what business are we in”?
Financial aspects of this level include the choice of method entering a market or business, whether entry
should be accomplished through an acquisition or through organic growth.
BUSINESS OR COMPETITIVE STRATEGY; covers the question of how strategic business units (SBU)
compete in individual markets and therefore of the resources which should be allocated to them. It relates to
individual strategic business units (parts of the organization where there are distinct external markets for goods
or services). Competitive strategy examines the threat on the performance of the company of factors such as
▪ The potential changes in the industry in which the firm operates (new competitors)
▪ Competition between existing firms in terms of costs, pricing and product quality
▪ Development of substitute products that may affect the industry as a whole
▪ Monopolistic power of individual companies in the input markets and companies in the various
product markets
OPERATIONAL STRATEGY; has to do with how different functions within the business (finance function
included) contribute to corporate and business strategies. The successful implementation of business strategies
relates to a great extent on decisions taken at the operational level.
The advice of the Finance manager to management or board of directors include;
▪ Investment selection and capital resource allocation
▪ Minimizing the cost of capital
▪ Distribution and retention policy
▪ Financial planning and control
▪ The management of risk
▪ Communicating financial policy and corporate goals to stakeholders

1. INVESTMENT SELECTION AND CAPITAL RESOURCE ALLOCATION

This would be dealt more under capital budgeting. The finance manager needs to incorporate
corporate policy issues such as pollution control, refusal to trade and others into investment decisions,
which method of appraisal should be used, the extent of information required for project appraisal, the
basis for evaluating competing projects when there is capital rationing and other investment decision
issues
2. MINIMISING THE COST OF CAPITAL
The Finance manager needs to have a good understanding of the various sources of finance existing
and available to the organization. He should be able to choose an optimal mix of capital structure
taking into consideration the tax implications, risk profile of investors & management, restrictions of
any kind and the impact on key ratios.
3. DISTRIBUTION AND RETENTION POLICY

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The finance manager should have a good understanding that retained earnings is a significant source
of finance and so should ensure that there is a balance between paying too much dividend or too low
dividend.
Dividend policy should be based on investor’s preference for cash dividend now or capital gains in the
future from enhanced share value resulting from reinvestment into projects with positive net present
value (NPV).
The dividend policy could be stable dividend policy, constant dividend policy, zero dividend policy or
a residual dividend policy.
4. FINANCIAL PLANNING AND CONTROL
This covers the monitoring of the company’s financial position, the evaluation of its productive capacity needs
and the financing requirements of the company.
STRATEGIC CASH FLOW PLANNING; businesses require adequate net inflow of cash to survive. A
company should avoid running out of cash and having too much cash

When a company is cash rich; the company may

▪ Plan to use the cash for investment
▪ Pay out the cash to shareholders as dividend
▪ Re-purchase its own shares (share buyback)
Strategic fund management is an extension of cash flow planning, which takes into consideration the ability
of a business to overcome unforeseen problems with cash flows. Where cash flow has become a problem, the
company may choose to sell off some of its assets. It is important to recognize that there are some assets that a
company can survive without and those that are essential for the company’s continued operation.
Assets can be divided into three categories.
▪ Those that are needed to carry out the core activities of the business (plant & machinery)
▪ Those that are essential for carrying out the main activities of the business and can be sold off at fairly
short notice (short term marketable instruments)
▪ Those that are not essential for carrying out the main activities of the business and can be sold off to
raise cash, but may take some time to sell (subsidiary companies, long term investment)
FINANCIAL CONTROLS include strategic planning & control, tactical control and operational controls.
Strategic control looks at deciding the objectives of the organization, changes in these objectives, resources
used to attain these objectives and the policies that are to govern the acquisition, use and disposition of these
resources.
Tactical control is the process by which managers assure that resources are obtained and used effectively &
efficiently in the accomplishment of the objectives
Operational control is the process of assuring that specific tasks are carried out effectively and efficiently.
5. RISK MANAGEMENT
Investors must be compensated in the form of higher returns for any extra risk they take. All businesses face
some sort of risk, although the extent of the risk will vary. In a risk free investment (treasury bills, gilts)
investors will only be compensated for the fact that they are postponing consumption in favour of investment.
As investors take extra risk, they would require a return that compensates them for delayed consumption and
also the additional risk.

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The level of risk that a company is willing to expose itself to will depend on the risk appetite of its
shareholders. Conservative shareholders would be risk-averse (preferring less risk with lower returns) while
aggressive shareholders would be risk-takers (preferring more risk in exchange for a chance of higher returns).
RISK PREFERENCES
Shareholders tend to invest in those companies that have a risk profile similar to their own portfolio. Financial
managers must be aware of the risk preferences of their company shareholders and invest funds accordingly.
They should avoid trying to change the risk profile of the company without the approval of the shareholders as
this could lead to existing shareholders selling their shares (share price reduction). They should also avoid
imposing their own risk preferences on their business decisions.
METHODS OF RISK MANAGEMENT
Risk can be managed in several ways;
▪ Hedging; involves actions taken to make an outcome more certain
▪ Diversifying; is the process of spreading the risk amongst several investments and sectors
▪ Risk mitigation; involves putting procedures in place to avoid investments in projects whose risk is
above the shareholders required level

6. MANAGEMENT OF FINANCIAL RESOURCES

This is part of the overall financial strategy and consists of the management of the items in the statement of
financial position to achieve the desired balance between risk and return. The financial management process
provides the framework for coordinating and controlling the firm’s actions to achieve the financial objectives.
The goal of short term financial management is to manage each of the firm’s current assets and liabilities in
order to achieve a balance between profitability and risk, which enhances shareholders value. The efficient
management of financial resources of a company is achieved through the construction of annual cash budgets
which reflect the firm’s planned inflows and outflows of cash. The cash budget presents a useful tool for the
estimation of short term cash requirement or surplus of a company. If a surplus is predicted, an appropriate
investment in short term money market instruments should be considered; but for a deficit, the most efficient
method of financing should be sought.

1.5. TREASURY FUNCTION

TREASURY FUNCTION; the treasury department is responsible for making sure that cash is available in the
right amounts, at the right time and in the right place. Its roles include
▪ Produce regular cash flow forecasts to predict surpluses and short falls
▪ Arrange short term borrowing and investment when necessary
▪ Deal with entity’s banks
▪ Finance the business on a day to day basis
▪ Advise senior managers on long term financing requirements
▪ Advise on foreign exchange transactions
▪ Risk management such as foreign exchange or currency risk, interest rate risk, credit risk or market
risk. (credit risk is a risk that a debt will not be paid when due while market risk is the risk of adverse
movement in the market price of assets)

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Cash Management Function; this involves managing cash receipts, cash payments and net cash balances.
This can be done by pooling and netting of cash flows to avoid interest charges on deficit accounts.

Advantages of centralized treasury management

▪ Cash is managed by specialist staff
▪ It allows for easy pooling of all cash deficits and surpluses from different accounts into a central bank
account
▪ Cash can easily be channeled to where it is needed and overdraft interest minimized
▪ It lowers the total amount of cash kept aside for precautionary purposes
▪ It increases the negotiating power of the treasury department with banks and third parties
Treasury Department as a Profit Centre; this is with the aim of motivating management and has the
following benefits such as potential for additional profits, efficient operation and a realistic transfer of cost to
business units at the market value.
The challenges with running the department as a profit Centre include potential for huge losses due to
speculative deals, additional administrative cost and additional cost of management time in terms of
negotiating transfer prices.
The possible risks of operating a treasury department include
▪ The risk that the treasury department will raise finance for the entity in an efficient or inappropriate
way
▪ It may fail to manage the financial risks of the entity sufficiently
▪ It may employ dealers for foreign exchange or investing surplus funds. The dealers may exceed their
trading limits or make mistakes when dealing.
▪ The treasury department may earn only a low return on their investment or surplus funds

1.6. STAKEHOLDERS THEORY

Stakeholders are individuals or groups who are affected by the activities of the firm. They are classified as
internal (employees & managers), connected (shareholders, customers, suppliers, competitors, debt holders &
banks) and external (local communities, pressure groups, government, professional and regulatory bodies).
They could be classified as primary stakeholders whose participation is needed for the business continuity
(customers, suppliers) and secondary stakeholders whose failing to participate in the business has no effect on
the going concern of the business (government, managers).
OBJECTIVES OF THE VARIOUS STAKEHOLDERS
Directors/managers Maximizing their rewards
Employees Maximizing their rewards & continuity of employment
Suppliers Receiving full payment as at when due
Banks Receiving full payment as at when due & minimizing default
Ordinary shareholders Maximize wealth as business Owners
Customers Satisfaction in terms of goods, Service, quality, price
Government Tax payments, high level of Employment & sustained growth

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Professional & regulatory bodies Ensure strict adherence to rules & regulations & dues payment

The actions of stakeholders group in pursuit of their various goals can exert influence on strategy. The greater
the power of the stakeholder, the greater the influence. The expectations of the various groups may conflict
thereby influencing strategic decision making and emphasizing the importance of corporate governance.

STAKEHOLDER THEORY AND CORPORATE GOVERNANCE

Stakeholder theory states that organizations have responsibilities to a wide range of stakeholders that they just
can’t be responsible to shareholders only. Corporate governance is the system by which organizations are
directed and controlled. The directors with the power to direct and control the organization have the duty of
Accountability to the organization’s stakeholders. Corporate governance regulations aim to control the ability
of the directors to promote their own interest and ensure adequate disclosure of their activities.
STAKEHOLDERS refer to every individual or group that is affected directly or indirectly by the decisions of
the organization. The main categories of stakeholder group in a company are
▪ Shareholders
▪ Directors and senior managers
▪ Other employees
▪ Lenders
▪ The Government
▪ Customers
▪ Suppliers
▪ Society as a whole
▪ Professional bodies
Stakeholders could be categorized as internal, external or connected and can be classified as primary and
secondary stakeholders. Companies might therefore state their objectives in terms of seeking to increase the
wealth of shareholders but subject to the need to satisfy other stakeholders showing due concern for social and
environmental issues.
The ability of stakeholders to influence what a company does will depend on a large extent on the;
▪ Extent to which interest can be accommodated without conflict
▪ Power of each group of stakeholders to influence or determine the objectives and strategies

The above situation can be explained using Mendelow’s stakeholder matrix.

POWER/INFLUENCE
HIGH LOW
INTEREST HIGH KEY PLAYERS; manage closely, KEEP INFORMED; make use of
involve in projects and decisions. their interest through involved
Engage on regular basis and work to consulting in their area of interest as
maintain the relationship. a supporter. EDUCATION &

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PARTICIPATION COMMUNICATION
LOW MEET THEIR NEEDS; engage and LOW PRIORITY; monitor and
consult, increase and maintain level communicate generally to keep
of interest as they may be a risk to the updated. Regular minimal contact.
idea. INTERVENTION DIRECTION

Conflicts between different stakeholder objectives

Different stakeholders have different interest in a company which might be incompatible and in conflict with
each other. When a conflict arises, a compromise may be reached where all stakeholders are satisfied partially
or the company will act in the interest of the most powerful stakeholders.

THOMAS KILMANN
Kenneth Thomas and Ralph Kilmann based their conflict style inventory on the managerial grid developed by
Blake and Murton. They arranged 5 conflict resolution approaches on the scale of two individual
characteristics (assertiveness and cooperativeness). It is used to identify an individual’s natural tendencies
when dealing with conflict.
ASSERTIVE COMPETITION COLLABORATION
COMPROMISE
UNASSERTIVE AVOIDANCE ACCOMODATION

UNCOPERATIVE COOPERATIVE
Assertiveness refers to the desire to satisfy one’s own concerns while cooperativeness has to do with the desire
to satisfy the concerns of others.
COMPETITION; this is used when you are in a position of power because they are confident. It is useful
when the conflict needs to be resolved urgently, solution is unpopular or the other party is trying to exploit a
situation to their own advantage.
COLLABORATION; this is an approach to meet the needs of everyone involved and acknowledge
everyone’s views as equally important. It brings together many viewpoints to arrive at the best solution and is
highly acceptable
COMPROMISING; all parties feel partially satisfied. It means everyone has to give up something but is
useful when the impact of the conflict objectives outweigh the effects of breaking the impasse amongst the
parties involved.
AVOIDANCE; this is an approach that tries to evade the conflict or pass it on to another. It is only acceptable
when there is someone trustworthy to resolve the conflict.
ACCOMODATING; an approach that is prepared to meet the needs of others at the expense of their own
needs. This is unacceptable from a business point of view.

Conflicts between different stakeholder objectives

Different stakeholders have different interest in a company which might be incompatible and in conflict with
each other. When a conflict arises, a compromise may be reached where all stakeholders are satisfied partially
or the company will act in the interest of the most powerful stakeholders.
1.7. AGENCY THEORY

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AGENCY THEORY was developed by Jensen and Meckling (1976) who defined it as a form of contract
between a company’s owners and its managers, where the owners appoint an agent (the managers) to manage
the company on their behalf.
Agency conflicts are differences in the interests of a company’s owners and managers. They arise in several
ways
S ACRONY METHOD DESCRIPTION
N M
1 M MORAL HAZARD Refers to the managers personal interest such as status,
car, lunch, allowances
2 T TIME HORIZON Shareholders are interested in long term while managers
may be concerned with short term
3 R RISK AVERSION Management may be risk averse due to stability of the
company while shareholders may want bigger risks as
long as returns are high
4 E EFFORT LEVEL Managers may work less hard than they would if they
were the owners of the company
5 E EARNINGS Management are more likely to want to reinvest profits in
RETENTION order to make the company bigger rather than pay out the
profit as dividend because their remuneration is linked to
company size

Agency costs are the costs that the shareholders incur when professional managers are employed to run the
company. There are three different aspects to agency cost
1. Costs of monitoring such as cost of preparing and presenting annual reports and audited accounts to
shareholders (monitoring cost)
2. Losses that arise when managers take decisions that are not in the best interest of the shareholders
(opportunity cost)
3. Costs incurred to provide incentives to managers to act in the best interest of the shareholders
(bonding costs).
REDUCING THE AGENCY PROBLEM
▪ Devising a remuneration package for senior managers
▪ Ensuring that the board consists largely of independent non-executive directors who play no executive
role.
▪ Independent non-executive directors should take decisions where there is a conflict of interest between
executive directors and best interests of the company.
INCENTIVE SCHEME (management reward scheme)
A controversial issue is evaluating if the agency problem can be reduced and managers persuaded to focus
on returns to shareholders as the main objective of the company. It is believed that this can be done if their
remuneration is linked to profits, earnings, share price or total shareholder return’
The remuneration package should be structured as follows;
▪ A high basic salary with pension entitlements
▪ Annual performance incentives for exceeding annual targets
▪ Long term performance incentives which are linked to share price growth or TSR. They are
usually provided in the form of share awards or share options in the company. Share awards refers
to the situation where a company purchases a quantity of its own shares and offers it to executive

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directors and senior managers on the condition that certain long term financial targets are met
while share options grants the holder the right to purchase new shares in the company on or after a
specified date in the future.
AGENCY RELATIONSHIP
Agency is acting on behalf of another (principal) in dealing with others. Directors (agents) run the company on
behalf of shareholders (principal) in the interest of shareholders.
However, whenever there is an agency relationship there arises an agency problem concerned with preventing
directors from rewarding themselves excessively or underperforming while all monies and resources expended
by the principal in monitoring the agent is referred to as agency cost.
SHAREHOLDERS AND MANAGERS
The cost of optimal decisions as regards value of shareholder’s wealth to a manager depends on his share of
total equity. If managers believe that they will not have a fair share of the company’s benefit, there would be
little incentive to undertake creative activities and they might engage in self-promoting activities such as;
1. they might not work industriously to maximize shareholder’s wealth
2. give themselves high salaries and perks
3. provide themselves with larger empires through merger and organic growth enhancing promotion
opportunity
4. take a short term view of the company’s performance (short termism)
5. reduce risk through diversification which improves their security and status but may not necessarily
benefit shareholders

SOLUTIONS TO AGENCY PROBLEM

It has been argued that the best remedy to agency problem between the managers and shareholders is to link
the reward to company performance. Some methods used are:

1. PROFIT RELATED PAY; relating pay or bonus to profit size or other performance. This is an
incentive to achieve a good performance level which attracts and keeps valuable employees in the
organization. It explicitly communicates to all employees what creates organization’s success and
focuses everyone towards continuous improvement aimed at motivating employees to act in the long
term interest of the organization as more profit is an increase in value of shareholders’ wealth.

PROBLEMS ASSOCIATED WITH REWARD SCHEME

a. It can encourage dysfunctional behavior such as budget padding
b. Makes managers only short term conscious (bonus focused)
c. Managers make decisions contrary to the wider purpose of the organization
d. Self-interested performance at the expense of team work
e. High level of output at the expense of quality
f. Standards and targets may have to be lowered to get the bonus
g. It makes managers value extrinsic rewards (bonus & allowance) over intrinsic rewards (satisfaction from
job experience and career prospects)

2. REWARDING MANAGERS WITH SHARES; is the giving of shares to managers at an attractive

offer price when the company goes public. It is believed that as managers and shareholders the
temptation of underperforming will be reduced.

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3. EMPLOYEES SHARE OPTION SCHEME; selected employees under the scheme are given the
option after a certain date to subscribe for the company’s shares at a fixed price. This will be beneficial
only if the company does well and the share price goes up.

CREDITORS AND SHAREHOLDERS

Creditors provide funds for a company based on the company’s assets, gearing level and cash flow. If the
managers take on riskier projects than expected by the creditors the burden of the extra risk will fall largely on
the creditors but if the investments are successful, the extra benefits accrue to the shareholders.
Management acting on behalf of shareholders might reduce the wealth or increase the risk of creditors by
selling off assets of the company & paying large dividends. When a company is in financial difficulties and in
danger of closing up shareholders believes they have little to, lose by undertaking risky projects at the expense
of creditors.
When corporate failure occurs most of the firm’s value is transferred to debt holders who bear the bulk of the
liquidity cost and so restricts managers acting on behalf of shareholders using bond covenants such as;

1. ASSET CONVENANT; which governs the company’s acquisition, use and disposal of assets (specific
or general)
2. FINANCING CONVENANT; defines the type and amount of additional debt that the company can
issue, its ranking and potential claim in case of default
3. DIVIDEND CONVENANT; restricts the amount of dividend the company is able to pay
4. FINANCIAL RATIO CONVENANT; fixes the limit of key ratios such as gearing level, interest cover,
net working capital etc.
5. MERGER CONVENANT; restricting future merger activity of the company
6. INVESTMENT CONVENANT; regulates the future investment policy of the organization.
7. SINKING FUND INVESTMENT; whereby the company makes payments especially to the bond
trustees who might gradually repurchase bonds or build up funds to redeem loans.
8. EMPLOYEES CONVENANT; regulates the employment and dismissal of key employees

CORPORATE SOCIAL RESPONSIBILITY (CSR)

This refers to the responsibilities that a company has towards society. It can be described as decisions made by
a business that is linked to ethical values, respect for individuals, society and environment all in compliance
with legal requirement. CSR is based on the concept that a company is a citizen of the society in which it exists
and operates. It has two key areas of responsibilities
▪ General responsibilities needed for industry success and regulatory duties
▪ Duties beyond the general responsibilities
PRINCIPLES OF CSR; there are five main aspects
1. A company should operate in an ethical way, and with integrity (recognized code of ethical behavior)
2. Employees should be treated fairly and with respect (employment policies, training & condition)
3. Respect for basic human rights must be demonstrated
4. Company should be responsible citizen in its community. (investing in local communities)
5. Company should ensure environment is sustained for future generations (reducing air or water
pollution, recycling of waste materials, cutting down on use of non-renewable energy resources such
as oil and coal, using renewable energy sources such as water and wind)

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CSR AND STAKEHOLDERS IN THE COMPANY

The concept of corporate citizenship and CSR is consistent with the stakeholder view on how a company
should be governed with responsibilities not only to its shareholders but also to employees, customers,
suppliers and the society as a whole. A company should consider these responsibilities in developing a
strategy for the future as it is exposed to reputation risk. Reputation risk is the risk that its reputation with
the general public and customers will be damaged by an unexpected event or disclosure.
CORPORATE SOCIAL RESPONSIBILITY (CSR)
This refers to the idea that the company should be sensitive to the needs of all stakeholders in its business
operations and not just shareholders. It emphasizes that company’s reputation can be improved and its long
term future secured by aligning its core value with that of the society.
BENEFITS OF A GOOD CSR STRATEGY
▪ Differentiation: it stands the company out making it unique
▪ It attracts and retains high caliber staff
▪ Brand strengthening due to the firm’s honest approach
▪ Lower cost because it is in the plan
▪ Identification of new market opportunities and of changing social expectations
▪ Overall increase in profitability due to lower risk, lower cost and increased sales
ARGUMENTS AGAINST CSR
▪ The primary purpose of the business is to make profit
▪ The prime stakeholders are the shareholders and so their wealth should be maximized
▪ It allows Directors feel generous and righteous at the expense of shareholders
▪ What is the democratic basis of choosing between CSR projects?
NOTE: all CSR project results should be measured for effectiveness and efficiency.

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CHAPTER ONE; REGULATORY BACKGROUND

REGULATORY BACKGROUND looks at Money laundering, directors’ responsibilities and the
roles of SEC & NSE
2.1. MONEY LAUNDERING
MONEY LAUNDERING covers any activity by which the apparent source and ownership of money or
property representing proceeds of crime are changed, so they appear to have been obtained legitimately.
THREE MAJOR STEPS OF MONEY LAUNDERING;
1. Cash is introduced into the financial system by some means (placement)
2. Complex financial transactions hide the illegal source (layering)
3. Wealth appears to have been generated from legal sources (integration)
FORMS OF MONEY LAUNDERING
▪ Structuring/smurfing is a method of placement by which cash is deposited with banks in smaller
amounts to avoid suspicion
▪ Bulk cash smuggling to jurisdictions with greater bank secrecy or less rigorous money laundering
enforcement
▪ Cash intensive businesses that simply deposit both legitimate and criminally derived cash as
legitimate earnings
▪ Real estate may be purchased with illegal proceeds and then sold. The sale proceeds appear to
outsiders to be legitimate income.
FINANCIAL ACTION TASK FORCE (FATF) against money laundering
FATF was formed in 1989 by the G7 countries as an inter-governmental body whose purpose is to develop and
promote an international response to combat money laundering and financing of terrorism. It is a policy body
which brings together legal, financial and law enforcement experts to achieve national legislation and
regulatory reforms.
FATF RECOMMENDATIONS
1. Countries should criminalize money laundering on the basis of UN conventions
2. Countries should ensure that financial institution secrecy laws do not inhibit implementation of the
recommendations
3. Financial institutions should not keep anonymous accounts or accounts in obviously fictitious names
4. Financial institutions should undertake customer due diligence measures (identifying and verifying the
identity of customers) when establishing business relations, carrying out occasional transactions,
suspicion of money laundering or terrorist financing or when there is doubts as regards the veracity or
adequacy of previously obtained customer data.
5. Financial institutions should pay special attention to all complex, unusual large transactions and
unusual pattern of transactions which have no apparent economic or visible lawful purpose
6. All suspicions on reasonable grounds of proceeds of criminal activities should be reported promptly to
the financial intelligence unit.
7. Financial institutions should develop programmes (such as developing internal policies, procedures,
controls, compliance management arrangement, ongoing employee training programme, audit
function to test the system) against money laundering and terrorist financing
8. FATF assesses each member country against these recommendations in published reports and all
violations or non-compliant countries are subjected to financial sanctions

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MONEY LAUNDERING IN NIGERIA

Nigeria has a comprehensive anti-money laundering legislation which is contained in the money
laundering (prohibition) act 2011 (as amended in 2012). The act requires businesses within the regulated
sector (banking, investment, money transmission, certain professions) to report to the authorities’
suspicions of money laundering by customers or others.
Money laundering is widely defined in Nigeria to include any handling or involvement with the proceeds
of any crime as well as activities which would fall within the traditional definition.
It is an offence to conceal or disguise the origin of, convert or transfer, remove from the jurisdiction or
acquire, use, retain or take possession or control of any fund or property which is reasonably known as
proceeds of an unlawful act.
SPECIFIC RULES ON CASH TRANSFERS
Cash payments exceeding N5, 000,000 in the case of an individual or N10,000,000 for corporate body are
illegal unless made through a financial institution.
Any cash transfer to a foreign country exceeding $10,000 transfer must be reported to CBN within 7 days
from the date of the transaction.
Transportation of cash or negotiable instruments in excess of $10,000 or its equivalent by individuals in
and out of the country must be declared to the Nigerian’s Custom Service.
SPECIFIC RULES FOR FINANCIAL INSTITUTIONS AND DESIGNATED NON FINANCIAL
INSTITUTIONS (REGULATED ENTITIES)
Designated non-financial institutions includes dealers in jewelry, cars & luxury goods, chartered
accountants, audit firms, tax consultants, clearing and settlement companies, legal practitioners, hotels,
casinos, supermarkets, or such other businesses as the Federal Ministry of Commerce or appropriate
regulatory authorities may from time to time designate.
1. Identification of customers; they must identify customers and verify their data using reliable
independent source documents.
2. Due diligence; they must conduct ongoing due diligence on a business relationship, scrutinize
transactions undertaken in the course of the relationship for compliance with risk profile, and ensure
that documents, data or information are updated and reviewed continuously.
3. Internal procedures, policies and controls; they must develop programs to combat the laundering of
crime proceeds or other illegal act through designation of compliance officers at management level at
all branches, regular training programmes for employees, centralization of information collected and
establishment of internal audit unit to ensure compliance with and effectiveness of measures put in
place.
4. Sundry issues; where an amount is less than the threshold under regulation, a regulated entity can
require for the identification of the customer and if the customer is a politically exposed person,
appropriate risk management systems and management approval must be in place before and during
any business relationship with such persons.
Suspicious transactions refer to transactions that involve unreasonable frequency, surrounded by
conditions of unusual or unjustified complexity or may involve terrorist financing or be inconsistent with

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the known transaction of the business relationship. Suspicious transactions should be reported to EFCC
immediately.
Designated non-financial institutions must submit to the ministry a declaration of activities before
commencement of the business, ensure that customers fill a standard data form that warrants presentation
of international passport, driving license, national identity card for transactions exceeding $1,000 or its
equivalent
Financial institutions must report to EFCC within 7 and 30 days respectively any single transaction in
excess of N5,000,000 or its equivalent for individual and N10,000,000 or its equivalent for corporate
bodies. Anonymous account maintaining is prohibited neither should a person operate shell account.
Permission can be sought by Nigerian Regulatory Authorities from the Federal High Court to place any
bank account under surveillance, obtain access to any suspected computer system or to obtain confidential
information.

2.2. DIRECTORS RESPONSIBILITIES

DUTIES OF DIRECTORS
▪ A director of a company stands in a fiduciary relationship towards the company and must act in
utmost good faith towards the company in any transaction with it or on its behalf. A fiduciary is
an individual in whom another has placed the utmost trust and confidence to manage and protect
property or money. Fiduciary relationship is where one person has an obligation to act for
another’s benefit.
▪ A director must act at all times in what he believes to be the best interest of the company as a
whole so as to preserve its assets, further its business and promote the purpose for which it was
formed.
▪ A director must exercise his powers for the purpose for which he is specified and must not do so
for a collateral purpose.
▪ A director is allowed to delegate his powers but not in a manner that would amount to an
abdication of duty.
▪ Directors responsibilities under law cannot be relieved in any way by provisions contained in the
articles or resolutions of a company or in any contract
▪ A director is an agent of a company, trustees for the company’s assets and powers (legal position
of directors) and so must account for all moneys over which they have control, refund any monies
improperly paid away, exercise their powers honestly in the interest of the company and all the
shareholders
CONFLICT OF DUTIES AND INTEREST
▪ Personal interest of a director must not conflict with his duties as a director
▪ A director must not make any secret profit when performing his duties
▪ Directors must not misuse confidential/insider information

DUTY OF CARE AND SKILL; both for executive and non-executive directors
▪ The director of a company must exercise the powers and discharge the duties of his office honestly, in
good faith and in the best interest of the company
▪ Director must exercise that degree of care, diligence and skill which a reasonable prudent director
would exercise in comparable circumstances

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▪ Failure to take reasonable care may be grounds for an action for negligence and breach of duty
▪ Each director is individually responsible for the actions of the board in which he participated

2.3. NIGERIAN STOCK EXCHANGE (NSE)

NSE is regulated by the Securities and Exchange Commission (SEC) subject to its regulations.
ROLES OF SEC
▪ Registers all securities to be offered for sale to, or for subscription by, the public
▪ Approves timing of new issues
▪ Maintains surveillance over dealings in securities
▪ Registers all stock exchanges including their branches and capital market operators
▪ Protects the securities market against any manipulations including insider trading
Companies wishing to be admitted to the official list of the Nigerian Stock Exchange must comply with the
Exchange’s listing rules, CAMA 90 provisions, rules and regulations of Investment and Securities Act 2007
ROLES OF NSE
▪ Provides a platform for buying and selling of existing securities
▪ Provides liquidity for investors
▪ Regulates the activities of stockbrokers
▪ Encourages transactions in the new issue market
▪ Helps to spread promoters ‘risks
The detailed listing requirements of NSE are set out in 10 chapters in the green book.
GENERAL REQUIREMENTS OF THE LISTING RULES
▪ An application for listing will only be entertained if sponsored by a dealing member of the exchange
▪ The company must be a public company, which will issue or has issued an invitation to the public to
subscribe for its shares or has satisfied council that the public is sufficiently interested in the
company’s shares to warrant listing
▪ All securities for which listing is sought must first be registered with SEC
▪ All applications and documents to be considered or approved by council should be submitted to the
exchange at the earliest possible date
▪ The final prospectus for approval must be forwarded to the exchange at least 7 working days before
the date of the completion board meeting
▪ All applicant companies must sign a general undertaking that they will provide promptly certain
information about their operations and follow certain administrative procedures before listing is
granted
▪ Directors must state in explanatory circular or other documents accompanying the notice of meeting
where it is desired to increase the authorized share capital
▪ The company must comply with the minimum public float requirement prescribed by the listing
standard criteria chosen by the issuer
▪ Subscription list must remain open for a maximum period of 28 working days
▪ A maximum of 10% of an offering will be allowed to staff of the company (subsidiary or associate
companies) on special application forms. It may be placed in trust for the employees
▪ The company must provide the general undertaking, list of members of staff who have been allotted
shares, the number of such shares, the capacity they work for the company and their number of years

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of service to Nigerian Stock Exchange for any shares in a placement or public offer reserved for
employees.
▪ The specified listing fee must be paid by all companies listed
▪ All clauses in the company’s memorandum and articles of association that restrict the transfer of fully
paid up shares must be expunged
▪ All listed companies must advertise the notice of their AGM in at least two widely read newspapers
(conspicuously placed) at least 21 days before the AGM
▪ The subscription monies pending allotment and return of funds to subscribers must be deposited in a
designated bank account appointed by the issuing house and the company
▪ All accrued interests in respect of cleared allotments must be paid to the company to offset the cost of
the issue
▪ Returned monies arising from an unsuccessful application or abortion of an offer or issue will attract
interest at a rate determined by the commission.

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CHAPTER 1; THE FINANCIAL MANAGEMENT

ENVIRONMENT
This chapter looks at the Economic environment, financial management framework, financial markets,
money markets and money market instrument
3.1. GOVERNMENT ECONOMY POLICY AND MACRO-ECONOMIC POLICY TARGETS
MACRO-ECONOMICS is concerned with the economy at large (national or international level) and with the
behavior of large aggregates such as national income, money supply and level of employment. A government
is concerned with how the economy is behaving as a whole and macro-economic variable
Macroeconomic policy objectives refer to the ultimate aims of the economic policy such as
▪ Economic growth (national income/standard of living) /real growth in the national economy
▪ Control price inflation or price level stability
▪ Full employment (low unemployment/ short term involuntary employment)
▪ Balance of payments stability/ equilibrium (is the wealth of a country in relative to others)
▪ Income redistribution
Policy targets are the quantified levels or range which the policy is intended to achieve
Policy instruments are the tools used to achieve these objectives such as monetary policy, fiscal policy,
exchange rate policy and external trade policy.

POLICY EXPLANATION
MONETARY POLICY This is the regulation of the economy through the control of
CONFLICT
money supply, level of interest rate and availability of credit
FISCAL POLICY Refers to government spending and taxation. It controls S IN
demand in an economy POLICY
EXCHANGE RATE It could be managed by government (fixed policy), determined OBJECTIV
POLICY by the forces of demand and supply (fluctuating policy) or a ES AND
policy where government only intervenes to manipulate the INSTRUM
forces of demand and supply to its favour (managed or dirty ENTS
exchange policy)
EXTERNAL TRADE This involves policies that stimulating exports, import controls Macro-
POLICY to protect domestic industries. economic
policy aims
cannot necessarily all be sustained together for a long period of time, attempts to achieve one objective will
often have adverse effects on the other sooner or later.

CONFLICT BETWEEN STEADY BALANCED GROWTH AND FULL EMPLOYMENT

Economic growth is measured by the rate of growth in economic activity annually. GDP can be measured by
the volume of output of goods and services, and other economic activity (output approach), or by the amount
of income earned each year by individuals and organizations annually (income approach) or by the amount of
spending in the economy annually (expenditure approach). The total GDP should be same using any of the
three approaches, but the expenditure approach seems to be the most useful for analysis purpose.
GDP = C + G + I + (X – M)

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C is total annual consumption on goods and services other than capital investment and government
consumption
G is spending by the government (consumption and investment)
I is investment spending (other than government investment)
X is the value of exports of goods and services
M is the value of imports of goods and services
X-M is the annual balance of trade in the country in international trade

The formula shows that growth in GDP annually can be achieved through higher spending on consumption,
higher government spending, more investment and an improvement in the balance of trade. However, growth
is only achievable if an increase in C, G or I does not result in a matching fall in one of the other elements in
the formula.

A growing economy should be able to provide more jobs, modern technology. As growth is achieved, the
modern technology might reduce the new jobs anticipated thereby increasing unemployment.
To create jobs and growth, there must be increase in aggregate demand (government increased spending or
reduced taxation), imports will increase creating a balance of payment deficit which weakens the company’s
currency value and raise the cost of imports giving rise to inflation (price rises). The country may increase its
interest rate to correct inflation, which will deter investment creating unemployment.
GDP AND INFLATION
The formula for GDP is a money measurement that ignores inflation. There is a difference between growth of
GDP in money terms and growth of GDP in real terms. GDP growth in real terms means growth after the
effect of inflation has been removed.
Government would be concerned about inflation because it wants to achieve real growth in national income
each year and also because a high rate of inflation will have harmful effects on the economy which may lead to
a fall in the rate of economic growth.
Inflation creates pressure for general cost increases and results in transfer of wealth within the economy in
unfair ways.
HOW DO THE ECONOMIC POLICIES AFFECT BUSINESSES?
Government uses economic policy to try to influence economic conditions with the objective of achieving
sustained growth and full employment and restricting the rate of inflation.
Business planning should take account of the likely effect of changes in demand for sales growth. Business
planning will be easier if government policy is relatively stable.
FISCAL POLICY AND BUSINESS
Companies might transfer business operations to low tax countries to minimize their tax payments. Tax has
impact on the investment decisions, customers spending decisions. Tax changes brought about by fiscal policy
affects businesses in terms of additional cost, labour cost etc.
MONETARY POLICY AND INFLATION
The CBN uses monetary policy rate (interest rate it charges to banks when it lends to banks) as a major
instrument for controlling inflation. In order to reduce inflation, the CBN may raise the monetary policy rate
(central bank base rate) which leads to transmission effect in the economy.
Transmission effect in the economy is the netting or offsetting effect where the banks who borrow at a higher
rate from the CBN also charge borrowers a high rate which reduces the demand from customers to borrow and

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in turn reducing consumption spending. When spending is rising too fast (risk of inflation), the interest rates
should be increased to discourage borrowing and credit thereby restricting spending and vice versa.
Monetary policy affects the borrowing cost of business as fewer investments show positive returns deterring
companies from borrowing to finance expansion. It makes it difficult to raise monies from share issues.
Businesses will be affected negatively by low demand from insufficient money in circulation and increased
rate.
MONETARY POLICIES AND EXCHANGE RATE
Monetary policy can also affect the value of a country’s currency. Higher interest rates are likely to attract
more investors into buying investments in the currency while lower interests are likely to persuade investors to
sell their investments in the currency. Changes in interest rates, by affecting supply and demand for the
currency can therefore alter its exchange rate value.
CBN could use exchange rate as a key economic policy target but where interest rates are used to manage the
value of a country’s currency in the foreign exchange markets, it cannot be used at same time as a tool for
controlling inflation.
In Nigeria’s case where a significant proportion of foreign exchange receipts come from oil, the exchange rate
is a function of the oil price in the international market. A rise in oil price leads to appreciation of the naira and
vice versa.
Exchange rate policy will affect the international competitiveness of companies as well as the amount they pay
for goods and services (transactional and economic risk)
IMPACT OF GOVERNMENT POLICIES on business
Government policies influence performance of businesses through affecting their policy areas such as taxation
levels, interest rates, exchange rates, incentive schemes, public expenditure levels, environment protection,
consumers and worker protection, restrictive practices and others.
The government policy could encourage firms to locate in particular areas, regulate monopolies and also the
activity of firms which are not in public best interest.

PORTER’S VIEW ON THE INFLUENCE OF GOVERNMENT ON AN INDUSTRY

▪ Capacity expansion through capital allowance, regional incentives, supply of infrastructure and
subsidies
▪ Demand can be influenced by government at all times, since they are the major customer of business
in all areas
▪ Divestment and exit is controlled by Government based on its impact on public interest. Sectors such
as health, defense, transport, education, telecommunication, electricity and agriculture can be
controlled by government.
▪ Emerging industries may be controlled by the government through license control
▪ Entry barriers as the government may restrict competition or make it harder for foreign firms to
compete.
▪ Competition policy may prevent too much market share
▪ New product adoption may be influenced by government policies.
OTHER GOVERNMENT POLICIES THAT AFFECT BUSINESS
COMPETITION POLICY

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The government might have laws or regulations for preventing anti-competitive actions by companies, rules
preventing the creation of monopolies. Government might try to control monopolies and other anti-competitive
behavior by companies in the following ways
1. Establishing a government body with the power to investigate and if necessary prevent proposed
mergers or takeovers. (security and exchange commission
2. Ordering that a company that has over-grown be broken down to several smaller companies

GOVERNMENT ASSISTANCE FOR BUSINESS

This involves government providing aids to companies in particular industries or geographical locations in
forms of cash grants.
GREEN POLICIES
The economic cost of business includes both the direct cost of business activities but also social costs. Social
costs include the cost of damage to the environment, cost of cleaning up waste and pollution created by
business activities (externalities).
Many of these social costs are paid for by the government (tax payers money) but recognition of these costs is
on the increase through the creation of Green policies aimed at reducing the amount of social cost or
externalities or making companies pay for the social costs they incur.
Green policies could be created for prevention or reduction of air, land or water pollution, protection of natural
resources and development of cleaner and environmentally-friendly energy resources.
With the Green policies spread, companies might react by investing in technology that reduces pollution from
factories and other manufacturing Centre’s, developing products or packaging that are more environmentally
friendly, trading in carbon credits to reduce or avoid fines and penalties.
CORPORATE GOVERNANCE REGULATIONS
There may be more regulation and restriction on corporate activity to check serious financial mismanagement.
There is a call for more supervision of corporate activity in Nigeria to improve investor confidence and avoid
scandals.
3.2. FINANCIAL MANAGEMENT FRAMEWORK
A Financial intermediary is an institution that links lenders with borrowers by obtaining deposits from lenders
and then re- lending to borrowers. It can also be defined as a party bringing together providers and users of
finance either as broker or as principal. Examples of financial intermediaries include commercial banks,
finance houses, building societies, government national savings department, insurance companies, pension
funds, unit trust companies, investment trust companies.
Financial intermediation is the process by which financial intermediaries provide a linkage between surplus
and deficit units in the economy. Surplus units are firms/individuals which/who have excess funds above their
immediate needs. Those who need the funds for immediate investment programmes are referred to as deficit
units. The financial intermediaries develop the facilities and instruments that make lending and borrowing
possible.
There are four aspects of the intermediation functions
➢ Maturity intermediation: a large portion of the deposits mobilized by banks have a short term maturity
since most customers withdraw on demand while the banks will lend the money for a longer period.
The satisfaction of these two contradictory objectives (of depositors and borrowers) is what is referred

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to as maturity transformation. A lot of expertise is required from the banks to avoid mismatch as it is
the long term loans which sustain the development of the economy.
➢ Liquidity intermediation: banks need to ensure the liquidity of the economy (they have no excuse for
not meeting the demand of their customers when they come to withdraw) despite the short duration of
the deposits they mobilize and the tenor of the loans they give. The confidence which depositors have
in the banking system is crucial to the functioning of the system or market.
➢ Size /Denomination intermediation: banks accept both small and large deposits and make them
available as loans to the deficit sector.
➢ Risk intermediation: banks spread out deposit risk by accepting deposits from heterogeneous
depositors (individuals and companies in various industries) of various sizes and minimize lending
risks by making loans available to diverse borrowers of various sizes. Banks have different kinds of
loans and deposits in their portfolios.

BENEFITS OF FINANCIAL INTERMEDIATION

1. REDUCTION OF RISK THROUGH POOLING- since financial intermediaries lend to a large
number of individuals and organizations, any losses suffered through default by borrowers or capital
losses are effectively pooled and borne as cost by the intermediary.
2. MATURITY TRANSFORMATION – financial intermediaries bridge the gap between lenders wish
for liquidity and borrowers desire for long term loans using the continual turnover of cash between
borrowers and investors.
3. CONVENIENCE: they provide a simple way for the lender to invest without personally looking for a
borrower.
4. REGULATION: investors are protected against negligence or malpractice by the comprehensive
system of regulation in place in the financial markets.
5. Financial intermediaries also provide a ready source of fund for borrowers.
6. They can aggregate or package the amounts lent by savers and lend on to borrowers in different
amounts
7. They give investors access to diversified portfolios covering a varied range of different securities.
8. INFORMATION: they offer a wide range of specialist expert advice on the various investment
opportunities that is not directly available to the private investor.

MONEY MARKETS AND CAPITAL MARKETS

MONEY MARKETS are markets for short term capital. They are markets for trading short term financial
instruments and short term lending or borrowing. Money markets are operated by the banks and other
financial institutions. The primary market is known as the official market while other markets are known
as the parallel or wholesale market.
MARKET TYPE DEALINGS
PRIMARY MARKET Approved institutions deal in financial instruments with the central bank.
Central bank controls short term interest rate through trading
INTERBANK MARKET Banks lend short term funds to each other
EUROCURRENCY Banks lend and borrow in foreign currencies
MARKET
CERTIFICATE OF Trading in certificate of deposits
DEPOSIT MARKET

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LOCAL AUTHORITY Local authorities issue and sell short term debt instruments as a means of
MARKET borrowing short term funds
FINANCE HOUSE Dealing in short term loans raised from money markets by finance houses
MARKET
INTER COMPANY Direct short term lending between treasury departments of large
MARKET companies

CAPITAL MARKETS are markets for trading in long term finance, in the form of long term financial
instruments such as equities and corporate bonds. In UK the principal capital markets are:
a. The stock exchange “main market” and
b. The more loosely regulated second tier Alternative Investment Market (AIM)
Firms obtain long term or medium term capital either through raising of share capital (ordinary shares) and
loan capital (loan notes, corporate bonds, debentures, unsecured and convertible bonds).
The stock market serves two main purposes
a. AS PRIMARY MARKETS they enable organizations to raise new finance by issuing new shares or
bonds.
b. AS SECONDARY MARKETS they enable existing investors to sell their investments if they wish.
Marketability of securities is a key feature of a capital market.
c. It also allows a company to take over another by issuing shares to finance the takeover.
INSTITUTIONAL INVESTORS are institutions which have large amount of funds which they want to invest,
and they will invest in stocks, shares or any other assets which offer satisfactory returns and security or lend
money to companies directly. The major institutional investors in the UK are pension funds, insurance
companies, investment trusts, unit trusts and venture capital organizations’.
INTERNATIONAL MONEY AND CAPITAL MARKETS are available for larger companies wishing to
raise larger amounts of finance. Larger companies are able to borrow funds on the Eurocurrency markets
(international money markets) and on the markets for Eurobonds (international capital markets).
EUROCURRENCY MARKETS
Eurocurrency is currency which is held by individuals and institutions outside the country of issue of that
currency. When a company borrows in a foreign currency, the loan is known as a Eurocurrency loan. The
Eurocurrency markets involving the depositing of funds with a bank outside the country of the currency in
which the funds are denominated and re-lending these funds for a fairly short term (usually three months).
Most euro currency transactions take place between banks of different countries and take the form of
negotiable certificates of deposit.
INTERNATIONAL CAPITAL MARKET involves a company issuing bonds to investors with the bank
merely arranging the transaction by finding investors who will take up the bonds while interest is payable to
the investors themselves not the bank. Eurobond is a bond denominated in a currency which often differs from
that of the country of issue.
Eurobonds are long term loans raised by international companies or other institutions and sold to investors in
several countries at the same time. Its issue term is typically ten to fifteen years. Eurobond may be the most
suitable source of finance for a large organization with an excellent credit rating such as a large successful
multinational company which requires a long term loan to finance a big expansion programme (as the
borrowing is not subject to the national exchange controls of any government.

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POCKET NOTE STRATEGIC FINANCIAL MANAGEMENT ICAN NOV 2019 DIET

Eurobond issues can be made whenever market condition seems favorable unlike domestic capital issues that
may be regulated by the government or central bank with a long queue for issues.
FACTORS TO BE CONSIDERED WHEN SUBSCRIBING TO A BOND ISSUE
1. Security: borrower must be of high quality
2. Marketability: available market in which bonds can be bought and sold.
3. Anonymity: the confidentiality of the issue as it is generally issued to bearer
4. Return on investment: is tax free
PATTERN OF INTEREST RATES
This refers to the variety of interest rates on different financial assets and the margin between interest rates on
lending and deposits that are set by banks.
FACTORS THAT INFLUENCE THE PATTERN OF INTEREST RATES ON FINANCIAL ASSETS
a. RISK: there is a tradeoff between risk and return. Higher risk borrowers must pay higher yields on
their borrowing to compensate lenders for the greater risk involved. Banks would set an interest rate
on its loan at a markup above its base rate based on the credit worthiness of the borrower.
b. NEED TO MAKE PROFIT ON RE-LENDING- financial intermediaries make their profits from
re-lending at a higher rate of interest than the cost of their borrowing.
c. DURATION OF THE LENDING: the term of the loan or asset will affect the rate of interest
charged on it. In general, the longer dated assets will earn a higher yield than similar short dated assets
but this is not always the case. The differences are referred to as the term structure of interest rate.
d. SIZE OF THE LOAN OR DEPOSIT: the yield on assets might vary with the size of the loan or
deposit. Administrative costs savings help to allow lower rates of interest to be charged by banks on
larger loans and higher rates of interest to be paid on larger deposits
e. DIFFERENT TYPES OF FINANCIAL ASSET: attract different rates of interest partly because
different types of financial assets attract different sorts of lender or investor.
The rates of interest paid on government borrowing (treasury bill rate for short term borrowing and the gilt
edged rate for long dated government bonds) provide benchmarks for other interest rates. LIBOR or the
London interbank offered rate is the rate of interest applying to wholesale money market lending between
London banks.
RISK RETURN TRADE OFF
There is a tradeoff between risk and return. Investors in riskier assets expect to be compensated for the
risk. In the case of ordinary shares, investors hope to achieve their return in the form of an increase in the
share price (capital gain) as well as from dividends. In general, the higher the risk of the security, the more
important is the capital gain component of the expected yield.
In the same way higher risk borrowers must pay higher yields on their borrowing to compensate lenders
for the greater risk involved. The higher the risk, the higher the interest rate.
An investor has the choice between different forms of investment. The investor may earn interest by
depositing funds with a financial intermediary or invest in corporate bonds or invest directly in a company
by purchasing shares in it. The current market price of a security is found by discounting the future
expected earnings stream at a rate suitably adjusted for risk. This means that the higher the degree of risk
associated with an investment, the higher the rate of return. The rate of return has two components: annual
income (dividend or interest) and expected capital gain. The higher the risk of a security, the more
important is the capital gain component of the expected yield.
INVESTMENTS ACCORDING TO THEIR RISK IN ASCENDING ORDER

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a. GOVERNMENT BONDS has a negligible risk of default and tends to form the base level for returns
in the market.
b. COMPANY BONDS has some risk of default usually secured against corporate assets.
c. PREFERENCE SHARES are generally riskier than bonds since they rank behind debt in the event of
a liquidation.
d. ORDINARY SHARES carry a high level of risk. Dividends are paid out of distributable profit after
all other liabilities have been paid and can be subject to large fluctuations annually. In general, the
level of risk will vary with the operational and financial gearing of the company and the nature of the
markets in which it operates.

REVERSE YIELD GAP

It is expected that debt on yield should be lower than the yield on shares because debt involves lower risk
than equity investment, but this is not the case as yield on shares are lower than that on debt: and this
situation is called reverse yield gap. A reverse yield gap can occur because shareholders may be willing to
accept lower returns on their investment in the short term, in anticipation that they will make capital gains
in the future.
INTEREST RATES AND SHAREHOLDERS REQUIRED RATE OF RETURN
Given that equity shares and interest earning investments are alternatives from the investor’s point of
view, changes in the general level of interest rate can be expected to have an effect on the rates of return
which shareholders will expect. increase in the shareholders’ required rate of return will lead to a fall in
the market value of the share.

ILLUSTRATIONS ON INTRODUCTION
ILLUSTRATION 1 (ICAN NOVEMBER 2017)
Private sector companies have multiple stakeholders who are likely to have divergent interests.
Required:
a. Identify FIVE stakeholder groups and briefly discuss their financial objectives (10 marks)
b. Explain ways in which companies’ directors can be encouraged to achieve the objective of
maximization of shareholder’s wealth (5 marks)
SOLUTION TO ILLUSTRATION 1
a) Stakeholders in a company include amongst others: shareholders; directors /managers; lenders;
employees; suppliers; customers; and government. These groups are likely to share in the wealth and
risk generated by a company in different ways and thus conflicts of interest are likely to exist.
Conflicts also exist not just between groups but within stakeholder groups. This might be because
sub-groups exist, for example preference shareholders and equity shareholders within the overall
category of shareholders.
Alternatively, individuals within a stakeholder group might have different preferences (e.g. to risk
and return, short term and long term returns). Good corporate governance is partly about the
resolution of such conflicts. Financial and other objectives of stakeholder groups may be identified as
follows:

Shareholders

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Shareholders are normally assumed to be interested in wealth maximisation. This, however, involves
consideration of potential return and risk. For a listed company, this can be viewed in terms of the
changes in the share price and other market-based ratios using share price (e.g. price/earnings ratio,
dividend yield, earnings yield etc).
Where a company is not listed, financial objectives need to be set in terms of other financial
measures, such as return on capital employed, earnings per share, gearing, growth, profit margin,
asset utilisation and market share. Many other measures also exist which may collectively capture the
objectives of return and risk.
Shareholders may have other objectives for the company and these can be identified in terms of the
interests of other stakeholder groups. Thus, shareholders as a group may be interested in profit
maximisation. They may also be interested in the welfare of their employees, or the environmental
impact of the company's operations. Management
While executive directors and managers should attempt to promote and balance the interests of
shareholders and other stakeholder groups, it has been argued that they also promote their own
individual interests and should be seen as a separate stakeholder group.
This problem arises from the divorce between ownership and control. The behaviour of managers
cannot be fully observed by the shareholders, giving them the capacity to take decisions which are
consistent with their own reward structures and risk preferences. Directors may therefore be
interested in their own remuneration package.
They may also be interested in building empires, exercising greater control, or positioning
themselves for their next promotion. Non-financial objectives of managers are sometimes
inconsistent with what the financial objectives of the company ought to be.

Lenders
Lenders are concerned to receive payment of interest and eventually re-payment of the capital at
maturity. Unlike the ordinary shareholders, they do not share in the upside (profitability) of
successful organisational strategies. They are therefore likely to be more risk averse than
shareholders, with an emphasis on financial objectives that promote liquidity and solvency with low
risk (e.g. low gearing, high interest cover, security, strong cash flow).

Employees
The primary interests of employees are their salary/wage and the security of their employment. To an
extent there is a direct conflict between employees and shareholders as wages are a cost to the
company and income to employees.

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Performance-related pay, based on financial or other quantitative objectives may, however, go some
way toward drawing the divergent interests together.

Suppliers and Customers

Suppliers and Customers are external stakeholders with their own set of objectives (profit for the
supplier and, possibly, customer satisfaction with the goods or services) that, within a portfolio of
businesses, are only partly dependent on the company in question. Nevertheless, it is important to
consider and measure the relationship in term of financial objectives relating to quality, lead times,
volume of business, price and a range of other variables in considering any organisational strategy.
Government - Interested in payments of tax for planning purposes and the operating environment.
b) The directors of companies can be encouraged to achieve the objective of maximising
shareholders" wealth through managerial reward schemes and through regulatory requirements. 101

Managerial reward schemes

As agents of the company"s shareholders, the directors may not always act in ways which increase
the wealth of shareholders, a phenomenon called the agency problem. They can be encouraged to
increase or maximise shareholders" wealth by managerial reward schemes such as performance-
related pay and share option schemes. Through these methods, the goals of shareholders and
directors may increase in congruence.

Performance-related pay, links part of the remuneration of directors to some aspect of corporate
performance, such as levels of profit or earnings per share. One problem here is that it is difficult to
choose an aspect of corporate performance which is not influenced by the actions of the directors,
leading to the possibility of managers influencing corporate affairs for their own benefit rather than
the benefit of shareholders, for example, focusing on short-term performance while neglecting the
longer term.

Share option schemes bring the goals of shareholders and directors closer together to the extent that
directors become shareholders themselves. Share options allow directors to purchase shares at a
specified price on a specified future date, encouraging them to make decisions which exert an
upward pressure on share prices. Unfortunately, a general increase in share prices can lead to
directors being rewarded for poor performance, while a general decrease in share prices can lead to
managers not being rewarded for good performance. However, share option schemes can lead to a
culture of performance improvement and so can bring continuing benefit to stakeholders.

Regulatory Requirements/ Corporate Governance

Regulatory Requirements can be imposed through Corporate Governance codes of best practice and
stock market listing regulations.

Corporate Governance codes of best practice seek to reduce corporate risk and increase corporate
accountability. Responsibility is placed on directors to identify, access and manage risk within an
organisation. An independent perspective is brought to directors" decisions by appointing
nonexecutive directors to create a balanced board of directors, and by appointing non-executive
directors to remuneration committees and audit committees.

ILLUSTRATION 2

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Financial managers need only concentrate on meeting the needs of shareholders by maximizing earnings per
share - no other group matters. Discuss (10 marks)
SOLUTION TO ILLUSTRATION 2
PROFIT MAXIMISATION; one of the principles of the market economy is that if the owners of businesses
attempt to achieve maximum profitability and earnings this will help to increase the wealth of the society. As a
result, it is usually assumed that a proper objective for private sector organizations is profit maximization. The
view I s substantially correct. In general, the market economy has out-performed planned economies in most
places of the world. Two key objectives of financial managers must therefore be effective management of
shareholders fund and the provision of financial information which will help to increase shareholders wealth.
Problems with profit maximization
Profit seeking organizations could be a problem to the society for instance, the monopolists are able to earn
large returns which are disproportionate to the benefits they bring to the society. The cost of pollution falls on
the society rather than on the company which is causing it. A company can increase profit by making some of
its workers redundant but the cost of the unemployed people fall on the society through social security system.
The question that then follows is "should individual companies be concerned with these market imperfections?
GOVERNMENT'S ROLE
There are two opposing view points. On the one hand it can be argued that companies should only be
concerned with maximization of shareholders wealth. It is the role of government to pick up the problems of
market imperfections (example by breaking up monopolies, by fining polluters and by paying social security
benefits)
STAKEHOLDER INTERESTS
An alternative view point is that a company is a coalition of different stakeholder groups: shareholders,
lenders, directors, employees, customers, suppliers, government and society as a whole. The objectives of all
these groups which are often in conflict, need to be considered by company managers when making decisions.
From this view point, financial managers cannot be content with meeting the needs of shareholders only.
CONSIDERATION OF STAKEHOLDERS
The truth is somewhere in between. The over-riding objective of companies is to create long term wealth for
shareholders. However, this can only be achieved, if the likely behaviour of other stakeholders is concerned.
for example, if we create extra short-term profits by cutting employer benefits or delaying payments to
creditors there are likely to be repercussions which reduce longer term shareholders wealth or if we fail to
motivate managers and employees adequately, the costs of the resulting inefficiencies will ultimately be borne
by shareholders.
CONCLUSION
In summary the financial manager is concerned with managing the company’s funds on behalf of shareholders,
and producing information which shows the likely effect of management decisions on shareholder wealth.
However, management decisions will be made after also considering other stakeholder groups and a good
financial manager will be aware that the financial information is only one input to the final decision

ILLUSTRATION 3 (ICAN MAY 2017 ADJUSTED)

Many decisions in financial management are taken in a framework of conflicting stakeholder viewpoints.
Identify the stakeholders and some of the financial management issues involved in the following situations:

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a. A private company converting into a public company

b. A highly geared company attempting to restructure its capital
c. A large conglomerate ‘spinning off its numerous divisions by selling them, or setting them up as
separate companies
d. Japanese car-makers, such as Nissan and Honda, building new car plants in other countries
(10 marks)

SOLUTION TO ILLUSTRATION 3
(a) A large conglomerate spinning off its Divisions
Large conglomerates may sometimes have a market capitalisation which is less than the total realisable value
of the subsidiaries ('conglomerate discount'). This arises because more synergy could occur by the combination
of the group's businesses with competitors than by running a diversified group where there is no obvious
benefit from remaining together. The stakeholders involved in potential conflicts include.
i. Shareholders
They will see the chance of immediate gains in share price if subsidiaries are sold. ii. Subsidiary company
Directors and employees
They may either gain opportunities (e.g. if their company becomes independent) or suffer the threat of job loss
(e.g. if their company is sold to a competitor). (b) A private company converting into a public company
When a —private company converts into a public company, some of the existing shareholders/managers will
sell their shares to outside investors. In addition, new shares may be issued. The dilution of ownership might
cause loss of control by the existing management. Stakeholders involved in potential conflicts include:

a. Existing shareholders/managers
They will want to sell some of their shareholding at a price as high as possible. This may motivate them to
overstate their company's prospects. Those shareholders/managers who wish to retire from the business may be
in conflict with those who wish to stay in control - the latter may oppose the conversion into a public company.

b. New outside shareholders

Most of these will hold minority stakes in the company and will receive their rewards as dividends only. This
may put them in conflict with the existing shareholders who receive dividends. On conversion to a public
company, there should be clear policies on dividends and Directors' remuneration.

c. Employees, including managers who are not shareholders

The success of the company depends partly on the efforts put in by employees.
They may feel that they should benefit when the company goes public. One way of organising this is to create
employee share options or other bonus schemes. iv. Regulatory agencies
(c) Japanese car manufacturer building new car plants in other countries The stakeholders involved in potential
conflicts include:
i. The shareholders and management of the Japanese company

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They will be able to gain from the combination of advanced technology with a cheaper workforce. ii. Local
employees and managers engaged by the Japanese company They will gain enhanced skills and better work
prospects.
iii. The government of the local country, representing the tax payers
The reduction in unemployment will ease the taxpayers' burden and increase the government's popularity
(provided that subsidies offered by the government do not outweigh the benefits!). iv. Shareholders, managers
and employees of local car-making firms
These will be in conflict with the other stakeholders above as existing manufacturers lose market share.
v. Employees of car plants based in Japan
These are likely to lose their jobs if car-making is relocated to lower wage areas. They will need to compete on
the basis of higher efficiency.

ILLUSTRATION 4
A company is considering improving the methods of remuneration for its senior employees. As a member of
the executive board, you are asked to give opinions on the following suggestions:
a. A high basic salary with usual perks such as company car, pension scheme etc. but no performance
related bonuses
b. A lower basic salary with usual perks plus a bonus related to their division’s profit before tax
c. A lower basic salary with usual perks plus a share option scheme which allows senior employees to
buy a given number of shares in the company at a fixed price at the end of each financial year.
Requirement
Discuss the arguments for and against each of the three options from the point of view of both the company
and its employees. Detailed comments on the taxation implications are not required. (10 marks)

SOLUTION 4
FACTORS AFFECTING REMUNERATION POLICY
a. Cost: the extent to which the package provides value for money
b. Motivation: the extent to which the package motivates employees both to stay with the company and
to work with the company to their full potential
c. Fiscal effects; government tax incentives may promote different types of pay. At present there are tax
benefits in offering some types of share option schemes. At times of wage control and high taxation, this can
act as an incentive to make the perks a more significant part of the package
d. Goal congruence; the extent to which the package encourages employees to work in such a way as to
achieve the objectives of the firm; perhaps to maximise rather than to satisfice.
OPTION A; in this context, this option is relatively expensive with no playback to the firm in terms of low
profitability. It is unlikely to encourage staff to maximize their efforts although the
I extent to which it acts as a motivator is dependent on the individual psychological make up of the employees
concerned. Many still prefer this type of package and the company is able to budget accurately for its staff cost

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OPTION B; the cost of this scheme will be lower, though not proportionately so, during a time of low profits.
The effect on motivation will vary with the individual concerned and also depend on I whether it is an
individual or a group performance calculation. There is a further risk that figures and performance may be
manipulated by managers in such a way as to maximize their bonus to the detriment of the overall longer-term
company benefit.
OPTION C; a share option scheme carries fiscal benefits in the same way as the performance related pay
above. it also minimizes the cost of the firm since it it is effectively borne by the existing shareholders through
dilution of their shareholding. Depending on how pricing is done, it may achieve goal congruence. It is
possible for the scheme to behave in a way which is unrelated to the individual's performance as the share
price depends also on many external factors to the firm. Staff will continue to obtain vast majority of their
income through salary and perks and are thus likely to be more concerned with maximizing these elements of
their income rather than working to raise share prices.

ILLUSTRATION 5 (ICAN NOVEMBER 2015 ADJUSTED)

Assume you are Finance Director of a large multinational company, listed on many international stock
markets. The company is reviewing its corporate plan. At present, the company focuses on maximizing
shareholder wealth as its major goal. The Managing Director thinks this single goal is inappropriate and asks
his co-directors for their views on giving greater emphasis to the following:
I. Cash flow generation
II. Profitability as measured by profits after tax and return on investment
III. Risk adjusted return to shareholders
IV. Performance improvement in a number of areas such as concern for the environment, employees’
remuneration and quality of working conditions and customer satisfaction
Requirement
Provide the Managing Director with a report for presentation at the next board meeting which:
a. Discusses the argument that maximization of shareholder wealth should be the only true objective of a
firm, and
b. Discuss the advantages and disadvantages of the MD’s suggestions about alternative goals (10
marks)
SOLUTION 5
(a)
To: The Managing Director
From: The Finance Director
ARGUMENT ON SHAREHOLDERS" WEALTH MAXIMISATION OBJECTIVE OF A COMPANY
The memorandum is meant to educate you on the debate on shareholders" wealth maximization objective as
the only true objective of a company.

What is shareholdersu wealth maximization? Shareholders" wealth maximization objective concept means
maximizing the return to ordinary shareholders as measured by the sum of dividends and capital appreciation.
It means maximizing the net present value of a course of action t. shareholders, that is, the difference between
the present value of its benefits and the present value of its costs. A financial action that has a positive Net

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Present Value (NPV) creates wealth for shareholders. It also seeks to maximize the value of a firm or its share
price. Though, the share price is determined by a general consensus among market operators, regarding the
value of companies and mirrors its expectation concerning the current and anticipated future profits of the
firms, it reflects the time value of money to them and the risk attached to those profits.
Shareholders" wealth maximization may have some practical difficulties in selecting a suitable measurement
for growth in shareholders' wealth, financial targets such as profit maximization and growth in earnings per
share might be used but no financial target on its own is ideal.
Financial performance may be assessed in a variety of ways by the actual or expected increase in the share
price, growth in profits, growth in earnings per share and so on. Companies may also adopt profit
maximization (accounting profit), profitability maximization (Return on Capital Employed (ROCE), Return on
Equity(ROE), Return On Investment (ROI), growth, long-term stability and so on as their objective, but all
these objectives ignore risk and time value of money which are taking care of in the shareholders" wealth
maximization objective. In practice, however, companies might have other stated objectives, but these can
usually be justified in terms of the pursuit of wealth maximization. Therefore, the shareholders wealth
maximization objective is an appropriate and operationally feasible criterion to choose among the alternative
objectives.
However, shareholders" wealth maximization objective should not be adopted in isolation without considering
other objectives such as, profit maximization and earnings growth, in the expectation that if these objectives
are achieved shareholders" wealth maximization will be increased by an optimal amount.
It is therefore recommended that companies should assume and follow this objective in their financial decision
making, but they should balance it with those of other stakeholders in the firm. It is theoretically logical and
operationally feasible normative goal for guiding financial decision-making. It is also all embracing, that is, it
takes care, in the long run, all other company objectives including maximization of profits, sales revenue,
market share, level of employee turnover, satisfaction of management staff and so on.
Signed
Finance Director
(b) i) Cash flow generation
Cash flow generation is one of the main sources of liquidity; it is a short-term objective which should be
pursued only in a period of economic meltdown. During this period, it is the „survival instinct" that is critical.
Shareholders are not likely to put their funds in a company whose management lacks the required
aggressiveness for long-term profitability and growth. However, if the aim of the firm"s management is to
maximize the net present value of the cash flows generated in the medium to long term, then this objective will
effectively be the same as maximizing shareholders" wealth.
ii) Profitability as measured by profit after tax and return on investment
This is a better objective than profit maximization (accounting profit) as it takes into account both profits and
the assets utilized in generating such profits.
Measures Of profitability include return on capital employed (ROCE) or return on investment (ROI) or return
on equity (ROE) and earnings per share (EPS) and so on. This objective has something short coming namely:

1. Problem of definition, that is, which profits and capital are to be used.

2. The uncertainty that goes with the earning of the profits (risk) is ignored; iii) Time value of money is
also ignored and

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iv) It fails to provide an operational feasible measure for ranking alternative courses of action in terms of their
economic efficiency.
However, companies use it to assess performance and control in their organisations. It is useful for the
comparison of widely differing divisions within a diverse multinational company and can provide something
approaching a „level playing field" when setting targets for the different branches of the organisation. It is
important, however, that the measurement techniques to be used in respect of both profits and the asset base
are very clearly defined and that there is a clear and consistent approach to accounting for inflation to be able
to solve the problem of definition, The selection of the time frame is also important in ensuring that the
selected objectives work for the long-term health of the business.

3. Risk adjusted returns to shareholders

It is assumed that the use of risk adjusted returns in this question relates to the criteria used for investment
appraisal rather than to the performance of the firm. As such, it cannot be pursued solely as an organizational
objective, but used as a tool in achieving it.
It provides a useful input to the goal setting process as it focuses attention on the company’s policy on making
risky investments. Since investment decisions usually affect the value of the firm if the investments are
profitable and add to shareholders"
wealth, it is important that they are evaluated on a criteria which is compatible with the objective of the
shareholders" wealth maximization.
However, it is fundamental that a company uses the right technique to avoid wrong decisions, bearing in mind
the financial implication such decisions can bring to the company. It should also be noted that an investment
must firstly be properly evaluated before selection. It is the acceptable investments that should be included in
the capital expenditure programme of the company. Thus, investments should be evaluated on the basis of a
criterion, which is compatible with the objective of the shareholders" wealth maximization bearing in mind
that an investment will add to the shareholders" wealth if it yields benefits in excess of the minimum benefits
as per the opportunity cost of capital.

4. Performance improvement in non-financial areas

Aside from the financial objectives which firms pursue, there are other objectives which are critical to the
achievement of the shareholders" wealth maximization and which should also be of concern to corporate
organizations. These are the non-financial objectives. A company as an

ILLUSTRATION 6 (ICAN MAY 2015)

Globalization has created more opportunities for money laundering with its associated risks, which
government and international bodies are trying to combat through legislations
Required
a. Explain the term money laundering and identify two major perpetrators (3 marks)
b. State 4 steps involved in assessing the risk associated with money laundering (4 marks)
c. State 3 necessary steps in curbing the spread of money laundering (3 marks)

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CHAPTER TWO; COST OF CAPITAL

This session evaluates the cost of raising finance, calculations on WACC, optimum capital structure, marginal
cost of capital.
DEFINITION
COST OF CAPITAL is the cost of funds raised by a company, which is the minimum return, expected by
investors that put funds into the company and the minimum return that a company ought to make on its own
investments so as to be able to pay back the fund providers.
Cost of capital is an opportunity cost of finance as it is the cost foregone for capital to be raised. A bank would
not offer you a loan except you are interested in foregoing interest so also investors would not invest in a
company that would not give them good returns.
FACTORS DETERMINING COST OF CAPITAL
1. Business Risk: is defined as the potential variability of earnings before interest and tax (EBIT) of an
investment. The level of business risk is determined by management policies. If the risk level of the
company is altered, the investors will change their return and cost of capital. The higher the business
risk the higher the cost of capital.
2. Financial risk: is described as the increased variability in returns on ordinary shares resulting from
introduction of debt finance. It is the risk of the company being able to pay an interest on debt and still
pay investors their dividend. The higher the financial risk the higher the compensation required and the
cost of capital.
3. Level of Inflation: inflation is described as the persistent increase in the price of goods and services or
the fall in the value of money which compels investors to demand for a compensation for the loss, the
higher the level of inflation the higher the cost of capital.
4. Marketability of a company’s security: as a Security’s marketability increases so also does the
investor’s confidence thereby lowering their returns and cost of capital as well.
5. Amount of financing: the larger the financing requirements of a company the higher the cost of capital
as a result of increased floatation cost, increased risk associated with large sum and additional cost of
reducing the security’s price.
6. General Economic Conditions which determines demand and supply of capital within the economy.
An increase in demand with no corresponding increase in supply compels the lender to raise their
required return and vice versa

COMPONENTS OF COST OF CAPITAL

COSTOF CAPITAL= RISK FREE RATE + RISK PREMIUM/COMPENSATION
1. RISK FREE RATE OF RETURN: which is the return required from a security with no risk i.e. a return
that is certain such as government bonds, treasury bills and certificates etc.
2. PREMIUM FOR BUSINESS RISK: refers to the compensation required for investing in the inherent
risk of that sector of business. It is the compensation required for the risk that the expected earnings will
be different from actual earnings as a result of increased fixed cost in the operating cost of the business
3. PREMIUM FOR FINANCIAL RISK: refers to the compensation that debt holder’s interest might
reduce or eliminate any surplus that would have been available as dividend or compensation that the
company might be liquidated.

SIGNIFICANCE OF COST OF CAPITAL

1. It is used as a standard for evaluating investment decisions i.e. as a cut off or hurdle rate for screening
investments.

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2. It assists in determining a company’s debt policy

3. It helps in appraising the performance of top management
4. It helps in choosing the most viable source of finance
5. It helps in designing a good dividend policy

CALCULATION OF COST OF CAPITAL (ke)

The different sources of finance (equity, debt, preference shares) have their different cost while the average is
used to screen new investments with similar risk.

COST OF EQUITY
This is the minimum return that ordinary shareholders expect to receive from their investment. It can be
measured in two ways:
1. Dividend valuation model (dvm)
2. Capital asset pricing model (capm)
DIVIDEND VALUATION MODEL (DVM)
DVM states that the current ex market price of a share is a reflection of the expected future dividends on that
share. discounted to infinity. Its assumptions include
1. Dividend is the major determinant of share price
2. dividend is constant
3. dividend growth is constant
4. no transaction cost

NO GROWTH
Ke=d/po
WITH GROWTH
Ke=do{1+g} + g or di/po +g
Po
Do= current dividend
G= growth rate
Po= ex market price
D1= annual year end div after growth or year 1 div
Ke= cost of equity
Where floatation / issue is involved
Ke = Do (Hg) + g or Add the floatation cost to initial in the outlay in the
Po (I-Fc) cost of debt.
Where g values is unknown
Where the value of g is not given, it can be determined in two ways
1. Dividend growth model (DEM)

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2. Gordons model.

DGM
This model states that the difference between the earliest dividend and the most recent dividend is the constant
growth refer and can be related as shown
Earliest dividend (I+g)n – number of growth = Latest dividend Or
n-I LD – 1
ED

Gordon’s model
This model states that the growth rate is determined by relating the return on equity to the retention ratio

g = r (return of equity) and b (retention ratio)

Profit / EPS and Profit /EPS – Dividend / DPS
Equity profit / EPS
It should be noted that whenever the examiner says retained profit is reinvested, this is an indication of growth
assumption.
CAPM
As a result of the weakness of DVM in that it assumes growth ratio of dividend is constant, it does not consider
risk and also it assumes only dividend affects market price, CAPM was introduced.
CAPM has a wider application on the guide price of the share and uses market determined variable which are
common to all companies except Beta factor which is statistically measured and constant over time.
Ke = Rf + (Rm – Rf) β
Cost of Risk = Risk free + (Average market returns – Risk free rate) Beta factor
Rf = Risk Free is certain β = Covariance between market and security = CORms x σs
Variance of market σm
Rm – Rf = market premium that is the difference between average market return and the risk free rate that is
compensation for investing in the market.
β (Rm – Rf) = Risk premium is the compensation for the systematic risk faced for investing in the security.
β = is the response or reaction of a security to changes in the market
When β is greater than 1 indicates an aggressive security which moves faster or slower than the market, β = 1 a
neutral share and β greater than 1 a security that is conservative, hardly affected by market movements.
Weakness of CAPM
1. It assumes that the capital market is perfect
2. It is a single period model
3. It ignores unsystematic risk which may be important in practice.
4. It ignores other factors that may affect returns such as bankruptcy cost, firm size etc.

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5. The components are derived from historical figures.

COST OF DEBT (kd)

In relation to cost of capital, there are 3 major types of debt
i. Irredeemable debt that could not be redeemed till infinity
Kd = 1 or 1 (I – t)
Po po
ii. Redeemable debt – a debt that will be redeemed at a specific time in the future. Use internal rate of
return of associated cash flows.
Tax
0 - market value (xx) 0 – market value (xx)
I-n – interest xx I-n interest net tax xx
n – redemption value xx n -redemption value xx

iii. Convertible debt is one which gives the holder the right to either redeem or transform the debt to
ordinary shares at a specific date in the future. We use the IRR of associated cash flows, that is
comparing outflows, and inflows but confirm if debt should be redeemed or converted.
O (market value) (xx)
I-n Interest xx
n conversion value xx

Cost of preference shares

Kp = Pd – preference dividend
Po –

Value of sources of finance

Ve = Value of equity = ex market price per share x No. of shares
Vp = Value of preference share = ex price per share x No. of shares
Vd = value of debt = ex int market per share x Balance sheet value of debt

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

This is the composite or overall cost of capital. It is the average of the cost of equity, preference share and
various forms of debt, weighted to allow for the market value of each of those capital items.
Ko = Ke Ve + Kd Vd + Kp Vp
Ve + Vd + Vp Ve +Vd+Vp Ve + Vp + Vd

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OR

Item market values cost hash total

Equity xx xx xx
Profit share xx xx xx xx
Loan stock xx xx xx
xx xx xx

Ko ==> hash total x 100

market value

CONDITIONS FOR WACC

1. New sources of fund need to be sought to finance the project.
2. The cost would reflect additional cost of capital
3. It should reflect the firm’s future capital mix and cost

ASSUMPTIONS OF WACC
1. The business risk is not significantly different from existing
2. the size of the project is small compared to the company
3. financial risk of the company’s capital structure remains unchanged
4. the individual cost of capital is expected to be constant for some time
5. the cash flow pattern of the company is expected to be stable for some time

MARGINAL COST OF CAPITAL

This is the additional cost required TO RAISE ADDITIONAL CAPITAL. It may be equal to wacc when the
assumptions of wacc hold firmly. Mcc is calculated by relating increased cost to increased investment.

MCC = INCREASED SERVICES OR DIVIDEND + INTEREST

INCREASED CAPITAL INCREASED CAPITAL
OPTIMUM CAPITAL STRUCTURE is a capital structure which the company intends to retain as it gives
best productivity.

ILLUSTRATION ON COST OF CAPITAL

ILLUSTRATION 1
The capital structure of 2017 Double star plc is as follows
₦
₦1 ordinary shares 500,000,000
Revenue reserves 185,000,000
Share premium 375,000,000
Retained earnings 250,000,000

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12% ₦1 preference shares 100,000,000

6% convertible debenture stock 150,000,000
8% unsecured loan stock 300,000,000
9% irredeemable debt 100,000,000
The ordinary shares have a current market price of ₦3.50 each on the 28th of December 2017. The dividend for
2017 of 70 kobo per share was proposed on the 25th of November 2017 but paid on the 30th of December 2017.
Dividends per share in the preceding years were as follows:
2012 – 45 kobo 2013 – 50 kobo 2014 – 55 kobo 2015 – 60 kobo
Dividends are paid once a year and are expected to grow in the future at the same annual rate as they have
since 2012.
The preference shares have a market price of ₦0.80 each. The 2017 preference dividend of 12 kobo per share
has just been paid. Dividends on the preference shares are paid once a year.
The convertible debenture stock has a market price of ₦120 per nominal. The stock is convertible into ordinary
shares in five years’ time at a rate of ₦100 nominal stock for 50 ordinary shares. The market price of the
shares at the time of conversion is expected to be ₦4.00 each. If not converted the stock will be redeemed in
four years’ time at a price of ₦125 percent.
The unsecured loan stock has a market price of ₦80 percent and is redeemable at par in six years’ time. The
market price on the irredeemable bond is at par. The company has just paid the interest for 2017 on all bonds
except the irredeemable bond. The company pays corporate tax at a rate of 25%.
The shareholders complained bitterly on the 2016 Dividend of 64 kobo as it was lower than what other similar
companies paid as dividend.
The Finance Director is not satisfied with the cost of capital figure calculated. He believes the Capital Asset
Pricing Model (CAPM) model is preferable to the Dividend Valuation Model (DVM) Approach. He is also of
the view that Gordon’s model of growth be adopted in determining the growth rate associated with Dividend
The average market return over the period is 23%, return from treasury bills is 8% while the systematic risk of
the company has been estimated to be 120% of that of the market. The company usually reinvests its retained
earnings. They have a payout ratio of 24% and the average return on investment is 25%.
a. Estimate the weighted average cost of capital of Double star plc without the Finance Director’s
recommendation
b. Calculate the cost of equity using CAPM as advised by the financial director
c. Calculate the cost of equity based on Gordon’s model
d. Analyze the Finance Directors statement. (Risk profile and shareholder’s complaint should be
included).

SOLUTION TO ILLUSTRATION 1 ON COST OF CAPITAL

This is a question on WACC with different types of finance
VE represents value of equity, KE represents cost of equity, KP represents cost of preference shee Vp
represents value of preference shares, KD represents cost of debt and VD represents value of
EQUITY
Note that all reserves are considered in determining the market value per share and so it would be relevant in
WACC calculation.

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Note also that the market price is cum-div (market price before dividend is paid) and so needs t:
converted to ex-div= 3.50 — 0.70 = N2.80

ORDINARY SHARES;
Growth rate = n-1ftD/ED -1 = 6-1'/70/45- 1 -8%
KE - Do(l + g)/Po + g = + 0.08 = 32%
VE = X number of shares = 2.80 x 500 m = NI,400m
PREFERENCE SHARES
PD/PO 12/80= 15%
Vp POX number of shares = 0.80 x 100m = N80m
CONVERTIBLE DEBT; always compare conversion value with redemption value for the final yeadecision.
The higher value should be taken. Where the examiner is silent, redemption value is at pe Note also that the
years differ for both debts and so the one with the highest value determines tie number of years interest will be
received.
Conversion value = price of shares at conversion time x number of shares per debt = 4 x 50 = N200
Redemption value = N125
The conversion value is higher and would be chosen.
Cost of debt is calculated based on IRR of cash flows
Year Description Cash flow PV o Market value (120) 1.000 (120) 1.000 (120 1-5 Interest
net tax ; 6(1-0.25) 4.5 4.329 19.48 3.352 15.OE
5 Conversion value 200 0.784 156.8 0.497 99.4'
56.28 (5.52
IR + (NPV IR)/ (NPN/ HR -NPV LR) X (HR + 5.52) X (15-5) = 14.1%
= PO X number of debt = 120/100 x 150 m = N180 m
REDEEMABLE DEBT; the cost should be calculated using IRR of cash flows year Description Cash
flow dcf@5% dcf@15%
0 Market value (80) 1.000 (80) 1.000 (80)
1-6 Interest net tax; 8(1-0.25) 6 5.076 30.46 3.784 22.70
6 Redemption value 100 0.746 74.60 0.432
25.06 (14.10,
= + (NPV LR)/ (NPV HR - NPV IR) X (HR- IR) = 5+ + 14.10) X (15-5) =
11.4%
VD = PO X number of debt = 80/100 x 300 m = N240 m
IRREDEEMABLE DEBT

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Ex Int= 100-9 =91

Cost of Debt = 9(1-0.25) / 91 = 7.4%
Value of Debt = 91 x 100m = N91 m
WACC calculation
FINANCE SOURCE MARKET VALUE (N M) COST AVERAGE TOTAL
(Nm)
EQUITY 1,400 32% 480.00
Preference shares 80 15% 12.00
Convertible debt 180 14.1% 25.38
Redeemable debt 240 11.4% 27.36
Irredeemable debt 91 7.4% 6.73
1,991 551.47

WACC = average total/ market value in % — 551.47/1,991 = 27.7%

FINANCE DIRECTOR'S COMMENT
b. The major issue under CAPM is RE + ß(R,.,- = 8+1.20( 23 - 8) = 26%
c. Growth = ROI X RETENTION RATIO = (0.25) X (1-0.24) = 19%.
Calculate the cost of equity using a growth rate of 19%
D. The Finance Director's comment on the issue of CAPM being preferred to DVM is realistic as CAPM
considers risk, the wholé market and values a security based on other factors aside dividend. The growth model
to be used depends on the organization's preference between DGM and Gordon's model.
The shareholders complain reveal that they prefer dividend and so it will be of great risk to Double Star if the
dividend policy is not competitive

ILLUSTRATION 3 ON COST OF CAPITAL

ABC Ltd has a capital structure which it considers optimal as follows:

N
Share capital 500,000.00
Share premium 400,000.00
Profit and loss account 100,000.00
Deferred taxation
Equity 15% 72,000 10,800
debt 10% 100,000 10,000
172,000 20,800

200,000.00
7% Debentures (redeemable in 4 years’ time) 400,000.00
10% Debenture (redeemable in 10 years’ time) 400,000.00

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Capital employed 2,000,000.00

Consideration is being given to two mutually exclusive projects. The summarized net after tax cash inflows as
follows: Project A: N110,000 per years 1-10 Project B: N130,000 per year 1-4 and N90,000 per years 5-
10
Each project will cost N500,000 and as only N100,000 is available out of internally generated funds. The funds
will have to be obtained from an issue of new equity and loan stock in optimal proportions. The current selling
price of equity is N10 per share and it is estimated that an issue of ordinary shares will result in net proceeds
per share of N9.50. Loan stock can be sold at par to yield 11.5%. The estimated cost of equity is 14% and it
can be assumed that the company has an effective tax rate of 50%. Other than the calculation of cost of capital
that should be rounded to the nearest whole number, tax should be ignored.
Required
a. What is the appropriate cost of capital to use?
b. Which of the two projects should be selected?

SOLUTION TO ILLUSTRATION 3
This is a question on optimal capital structure. An optimal capital structure is one which the organization
intends to retain for a long time as it maximizes their market value.
The first step would be to determine the proportion of debt to equity and all new funds would be raised in that
proportion. The allocation is done in the table below;
FINANCE TYPE AMOUNT EQUITY N DEBT
N
Share capital 500,000 500,000
Share premium 400,000 400,000
Profit & loss 100,000 100,000
account
Deferred taxation 200,000 200,000
7% debentures 400,000 400,000
10% debentures 400,000 400,000
Total employed 800,000 % capital
In allocation, any short term item such as current
assets and current liabilities should be eliminated. Overdraft should only be included when the examiner states
that it is part of the long term financing/capital structure.
Deferred taxation is treated as equity as the funds is available as a reserve to shareholders until it is paid. This
view is not really supported by IFRS which would see this more of a debt. For the purpose of financial
management this should be treated as equity. All new funds will be raised in the proportion of 60% equity and
40% debt. Recall that retained earnings is part of equity. Amount required is N500,OOO; 60% equity is
N300,OOO and 40% debt N200,OOO Ke= d/po= therefore dividend = ke x PO = 14% x 10 = NI.40 Ke - d/pc=

KD = RATE) = 11.5(1-0.50)- 5.75%

WACC COMPUTATION

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FINANCE SOURCE MARKET VALUECOST AVERAGE TOTAL

(N) (N)
Retained earnings 100,000 14% 14,000
New equity 200,000 14.7% 29,400
Debt 200,000 5.75% 11,500
500,000 54,900
WACC = average total/ market value in % = 54,900 /500,OOO = 10.98% = 11%
PROJECT EVALUATION; Mutually exclusive projects refers to two or more projects that cannot be executed
together. The project with the higher NPV should be selected.
PROJECT A EVALUATION
YEAR DESCRIPTION CASH FLOWS
Initial outlay (500,000) 1.000 (500,000)
1-10 In flows 110,000 5.889 647,790
NPV 147,790
PROJECT B EVALUATION
YEAR DESCRIPTION CASH FLOWS PV N
Initial outlay (500,000) 1.000 (500,000)
In flows 130,000 3.102 403,260
5-10 In flows 90,000 2.787 250,830
N PV 154,090

ILLUSTRATION 4
Better Deal Plc is a Nigerian supermarket chain which has a financial year end of 28 February. An extract from
its statement of financial position at 28 February 2015 is shown below:
Nm
Ordinary shares (50k each) 82.5
Retained earnings 391.5
474.0
8% debentures (at nominal value, redeemable at par in 2019 340.0
814.0
ADDITIONAL INFORMATION N
Current market value per ordinary share ex-div 2.65
Current market value per 8% debenture ex-int 98
Dividends paid on 28 February 2015 29.5m
Dividends paid on 28 February 2011 25.2m
Equity beta 1.1
Market return 11.4% pa
Risk free rate 5.2% pa

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▪ There have been no changes in the number of issued shares over the period 2011 to 2015
▪ Its annual dividend payments have risen steadily since 2011
▪ The company’s management is considering diversifying its product range and opening petrol outlets at
a number of its stores. The finance for its capital investment would be raised in such a way as not to
alter the current gearing ratio of the company (measured by market values). The debt element of the
finance raised will come from a new issue at par of 9% irredeemable debentures.
▪ The company’s finance team has undertaken research into the company’s competitors in the petroleum
market and has realized that the equity beta for the market is 1.5 and companies in that market have,
on average, long term funds in the ratio of 64:31 for equity: debt by market value.
▪ You should assume that the corporation tax rate is 21% pa and is payable in the same year as profits
are earned.
a. Calculate Better Deal’s current weighted average cost of capital based on
▪ Dividend growth model
▪ CAPM model
b. Calculate the cost of capital that Better Deal should use when appraising the proposed investment in
petrol outlets and explain the reasoning for your approach
c. Compare and contrast multiple factor model with the CAPM model as a means of dealing with risk.
d. Advise Better Deal’s management as to what extent the company’s dividend policy will affect the
market value of its shares.

SOLUTION TO ILLUSTRATION 4 ON WACC

Value of equity = 82.5m/0.50 x 2.65 = N437.25m
Value of debt = 98/100 x 340m = N333.20m

I. WACC UNDER DVM

Dividend per share = total dividend / number of shares = 29.5m / 165m = 17.9k
Dividend growth rate = n-1/ latest dividend/earliest dividend -1 = 4V(29.5/25.2) -1 = 4%
Ke = d0 (1 + g)/p0 + g = 17.9(1.04) / 265 + 0.04 = 11%

COST OF DEBT; REDEEMABLE DEBT

year Description Cash flow dcf@5%
PV dcf@10% PV
0 Market value (98) 1.000
(98) 1.000 (98)
1-4 Interest net tax; 8(1-0.21) 6.32 3.546
22.41 3.170 20.03
4 Redemption value 100 0.823
82.30 0.683 68.30
6.71 (9.67)
KD = LR + (NPV LR)/ (NPV HR - NPV LR) X (HR - LR) = 5 + (6.71)/(6.71 + 9.67) X (10 - 5) =
7.05%

WACC
FINANCE MARKET VALUE N COST AVERAGE TOTAL N
EQUITY 437.25 m 11% 48.10 m
REDEEMABLE DEBT 333.20 m 7.05% 23.49m
770.45m 71.59 m
WACC = average total /market value = 71.59/770.45 = 9.29%

II. WACC UNDER CAPM

KE = RF + B(Rm- Rf) = 5.2 + 1.1(11.4 - 5.2) = 12.02%
KD = 7.05% as calculated above WACC FINANCE EQUITY

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FINANCE MARKET VALUE N COST AVERAGE TOTAL N

EQUITY 437.25 m 12.02% 52.56 m
REDEEMABLE DEBT 333.20 m 7.05% 23.49m
770.45m 76.05 m

WACC = average total /market value = 76.05/770.45 = 9.87%

B PART OF THE QUESTION
Industry beta = 1.5
BA = BE X VE / VE + VD (1-T) = 1.5 x 64 / 70 + 31(1 - 0.21) = 1.08
BE = BA + (BA - B) Vd/Ve (1 - T) = 1.08 + (1.08 - 0) x 333.2(1 - 0.21)/437.25 = 1.73
Ke = Rf + BE (Rm - Rf) = 5.2 + 1.73(11.4 - 5.2) = 15.9%
KD = K0(l -1) = 9 (1 - 0.21) = 7.11%; the debt is risk free and so the risk free rate is used Ko = (Ke x
KO = (Ke x VE) + (Kd X V0) = (15.9% X 437.25/770.45) + (7.11% X 333.2/770.45) = 12.1%

C PART OF THE QUESTION

CAPM theory is based on the fact that there is one factor that affects the expected return on a security
(or portfolio) and that is systematic risk. The measure of risk is given by the equity beta of a security
or portfolio Multiple factor model are based on the idea that other factors will also determine the
return as there are other aspects of risk attached to securities, not just the market portfolio. Arbitrage
pricing theory states that there are many factors, but it does not state what these factors are. Multiple
factor models have been designed to get around the problem caused by the simplicity of the CAPM,
but they are complex to understand and the factors are difficult to identify and quantify

D PART OF THE QUESTION

This question entails discussing the various dividend theories and how they affect the market value of
a company.
➢ Traditional theory of dividend policy states that dividend payment determines the clientele
and so should be paid as it affects the value of the firm
➢ Residual theory of dividend policy states that dividend should only be paid after all viable
decisions have been considered
➢ M&M theory states that dividend payments has no impact on the value of an organization.

CHAPTER THREE: BETA FACTOR

This session covers the calculation of adjusted WACC and understanding of beta equity, beta debt and beta
asset.
BETA FACTORS

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BETA has been defined as the systematic risk index which reflects how a security would respond to changes in
the market. It can be calculated as Covariance between security and market divided by the variance of the
market.
A security is said to be aggressive if the beta factor is greater than 1 but conservative if it is less than 1. Where
the beta equals one, it is a normal security and zero means it is risk free.
BETA ASSET βA reflects only business risk and does not consider the method of financing. It should be used
to calculate the cost of equity for an all equity financed firm. It is calculated as
βA = βE X VE / VE + VD (1-T) X βD X VD / VE + VD(1-T)
BETA EQUITY βE reflects both business risk (industry dependent) and financial risk (risk imposed by debt
finance). Beta equity should be used to calculate cost of equity for a geared firm. It is calculated as:
βE = βA + (βA – βD) VD/VE (1 – T)
Company BETA
The beta of the company is the weighted average of the beta factors of all the company’s projects. It is only
suitable for a new project if they belong to the same risk class as the existing projects.
STEPS ON USING BETA FACTOR TO CALCULATE ADJUSTED WACC
▪ Identify the beta factor of the new industry or proxy company
▪ Remove the financial risk of the new industry or company (ungear) if the capital structures are
different by calculating beta asset using the industry’s capital structure
▪ Add your company’s financial risk (regear) by calculating beta equity using your company’s capital
structure.
▪ Use the beta equity calculated above to calculate cost of equity
▪ Calculate cost of debt and WACC

ILLUSTRATIONS ON BETA ISSUE

ILLUSTRATION 1
An all equity financed firm, is about to embark upon a major diversification in the consumer electronics
industry. Its current equity beta is 1.2, whilst the average equity beta for electronics firm is 1.6. Gearing in the
electronics industry averages 30% debt and 70% equity. Assume corporate debt is risk free. Market return is
25%, risk free rate is 10% and corporate tax is 35%.
What would be the suitable discount rate for the investment if it was financed in each of the following
independent ways?
a. Entirely by equity
b. By 30% debt and 70% equity
c. By 40% debt and 60% equity

SOLUTION TO ILLUSTRATION 1 ON BETA ISSUE

1. When a project is financed entirely by equity, there is no financial risk and so only beta asset
which measures business risk is relevant and cost of equity equals WACC
BA = BE X VE / VE + VD (1-T) = 1.6 x 70 / 70 + 30(1 - 0.35) = 1.25 Ke =
Rf + Ba (Rm - Rf) = 10 + 1.25(25 - 10) = 28.75%
2. Where both companies have the same gearing ratio, the beta equity of the industry should be
used as it reflects same business and financial risk.

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KE = RF + BE (RM - RF) = 10 + 1.6(25 - 10) = 34%

KD = Kd(1 -1) = 10 (1 - 0.35) = 6.5% ; the debt is risk free and so the risk free rate is
used K0 = (Ke x VE) + (KD X VD) = (0.70 X 34) + (0.30 X 6.5) = 25.75%
3. Where the gearing ratios are different, then we need to degear (remove financial risk of
industry) and regear (add company's financial risk)
BA = BE X VE / VE + VD (1-T) = 1.6 x 70 / 70 + 30(1 - 0.35) = 1.25
BE = BA + (BA - BD) VD/VE (1 - T) = 1.25 + (1.25 - 0) x 40(1 - 0.35)/60 = 1.79
KE = Rf + Be (Rm - Rf) = 10 + 1.79(25 - 10) = 36.85%
KD = KD(1 -1) = 10 (1 - 0.35) = 6.5%; the debt is risk free and so the risk free rate is
used K0 = (KE x VE) + (Kd X VD) = (0.60 X 36.85) + (0.40 X 6.5) = 24.71%

ILLUSTRATION 2 ON BETA ISSUE

Uche plc produces both cars and bikes. By both turnover and profit, 60% of the company’s business is cars and
40% is bikes. The company’s equity beta is 1.80 and its financial leverage advantage (total asset to equity) is
1.4 times.
Adebayo plc is a competitor company which specializes in car production. Its equity beta is 1.4 and a debt ratio
(debt to total asset) of 25%.
The risk free interest rate is 8% and the market risk premium is 8%. Corporate tax rate is 25%. Corporate debt
is assumed to be risk free.
Uche plc wish to evaluate a bikes project (which will not change the company’s existing capital structure) and
so needs a suitable discount rate to apply to their net present value analysis.
Estimate showing all relevant calculations, the appropriate discount rate to use.

SOLUTION TO ILLUSTRATION 2
When a company needs a suitable discount rate from a proxy company that deals in several
businesses, it must search for the business risk that is specific to the business it is interested in,
taking into consideration that the beta factor of a company is the weighted average beta of all the
different businesses in the company.
I. Determine beta asset of Adebayo pic = BA = BEXVE/VE +VD (1-T) = 1.40 x 75/ 75 + 25(1 -
0.25) = 1.12.
II. Note that the gearing ratio above was calculated thus; VD/ VE + VD = 25/100, Which means
that debt is 25 while equity is 75
III. Determine the beta asset of Uche pic = BA = BE X VE / VE + VD (1-T) = 1.80 x 100 / 100 +
40(1 - 0.25) = 1.38
IV. Note that the gearing ratio above was calculated thus; total asset/equity = Ve + VD / VE =
1.40, which means 140/100 and so if equity is 100, debt is certainly 40.
V. Determine the beta asset of bikes only by deducting Adebayo's beta asset that measures
business risk for cars alone from Uche pic's beta asset that measures both the business risk
for cars and bikes
Ba of Uche pic = (0.60 x BA for cars) + (0.40 x BA for bikes)

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1.38 = (0.60 x 1.12) + (0.40 x BA for bikes) Ba for bikes = 1.77

Regear the beta asset
VI.BE = BA + (BA - BD) VD/VE (1 - T) = 1.77 + (1.77 - 0) X 40(1 - 0.25)/100 = 2.30
VII.KE = RF + BE (RM - RF) = 8 + 2.30(8) = 26.4%
VIII.KD = KD(1 -1) = 8 (1 - 0.25) = 6%; the debt is risk free and so the risk free rate is used
IX. K0 = (KE X VE) + (KD X VD) = (100/140 X 26.4) + (40/140 X 6) = 20.57%

ILLUSTRATION 3
The management of Leventis plc wish to estimate their firm’s equity beta. It has had a stock market quotation
for only two months and the financial manager feels that it would be inappropriate to attempt to estimate beta
from the actual share price behavior over such a short period. Instead it is proposed to ascertain, and where
necessary adjust, the observed equity betas of other companies operating in the same industry, and with the
same operating characteristics as Leventis, as these should be based on similar levels of systematic risk and be
capable of providing an accurate estimate of Leventis beta.
Three companies have been identified as firms having operations in the same industry as Leventis which
utilize identical operating characteristics. However, only one company, UTC operates exclusively in the same
industry as Leventis. The other two companies have some dissimilar activities or opportunities in addition to
operating characteristics which are identical to those of Leventis plc.
Details of the three companies are:
UTC PLC
Observed equity beta 1.12. Capital structure at market value is 60% equity, 40% debt
SHOPRITE
Observed equity beta is 1.11. it is estimated that 30% of the current market value of Shoprite is caused by risky
growth opportunities which have an estimated beta of 1.9. the growth opportunities are reflected in the
observed beta. The current operating activities of Shoprite are identical to those of Leventis. Shoprite is
financed entirely by equity.
NEXT CAFÉ
Observed equity beta is 1.14. It has two divisions – Kubwa and Lugbe. Kubwa’s operating characteristics are
considered to be identical to those of Leventis. The operating characteristics of Lugbe are considered to be
50% more risky than those of Kubwa. In terms of financial evaluation, Kubwa is estimated as being twice as
valuable as Lugbe. Capital structure of Next Café at market values is 75% equity, 25% debt.
Leventis is financed entirely by equity. The tax rate is 40%
Assume all debt is virtually risk-free, determine three statements of the likely equity beta of Leventis plc. The
three estimates should be based, separately, on the information provided for UTC, Shoprite and Next Café.

SOLUTION TO ILLUSTRATION 3
Appropriate beta asset should be calculated
BA=BE x VE/VE + VD(1-T) + BD x VD (1-T)/VE + VD(1-T)
1.7 x 3 / 3 + 2(1-0.25) + 0.2 x 2(1-0.25)/ 3 + 2(1-0.25) = 1.2
This is the overall asset beta of the company made of two divisions.
1.20 = (0.40 x 0.20) + (0.80 x beta asset of electronics ) =

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Bet = 1.4

B part is on calculating beta debt from CAPM. The pre tax cost of debt is the return.
Kd = Rf + Bd (Rm- RF) =
12 = 10 + Bd(15 -10)
BD = 0.40

C PART
The beta asset gotten in A should be regeared
BE =BA + (BA - BD) x VD(1 - T)/VE = 1.40 + (1.40 - 0.40) X 1(1 - 0.32)/4 = 1.57
Cost of equity = RF + B(RM - RF) = 10 + 1.57(15 - 10) = 17.85%
Cost of debt = I (1 - T) = 12(1 - 0.32) = 8.16%
WACC = (KE x VE/V0) + (kd x Vd/V0) = (17.85 x 4/5 ) + (8.16 x 1/5) = 15.91%

CHAPTER 4: CAPITAL BUDGETING

This lesson looks at investing in capital projects considering taxation, inflation, capital rationing,
replacement, leasing and hire purchase as well as uncertainty

A capital budgeting decision may be defined as the firm’s decision to invest its current funds most efficiently in the
long term assets with anticipation of an expected flow of benefits over a series of years.

The investment decision of a firm (expansion, acquisition, modernization and replacement of the long term
assets) is generally known as the capital budgeting decision.

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CHARACTERISTICS / FEATURES OF INVESTMENT DECISIONS

• The decision involves a large initial outlay
• It involves exchange of current funds for future benefits.
• It is a risky decision
• The decision is irreversible
• The funds are invested in long term assets.
• The future benefits will accrue to the firm over a series of years.

WHAT IS A CAPITAL BUDGET AND THE IMPORTANCE OF CAPITAL INVESTMENT DECISIONS?

A capital budget is a programme of capital expenditure for the next few years updated every year setting out
details of capital projects authorized but not yet undertaken and those likely to occur in the next few years but
that have not been authorized.

THE IMPORTANCE OF CAPITAL INVESTMENT DECISION INCLUDE:

• They influence the firm’s growth in the long run
• They affect the risk of a firm as long term funds changes the risk complexity of a firm.
• They involve commitment of large amount of fund which makes it imperative for a careful plan and
advance arrangement for sourcing finance.
• They are irreversible or reversible at a substantial loss as if is difficult to sell capital items once they
have been acquired.
• They involve assessing and predicting the future which makes it a difficult and critical function for
every firm.

STAGES OF THE CAPITAL BUDGETING PROCESS

• Identifying the objective of the organization that is the requirement for the capital expenditure in the
business is forecast.
• Identification of possible projects that meet the above requirements
• Preliminary screening of all identified projects.
• Detailed evaluation of remaining projects considering cash flows, risk, cost- benefit analysis etc.
• Selection of best alternatives
• Authorization and Approval to excrete the project
• Implementation of the project
• Monitoring and review (control) where actual spending and benefits is compared with planned and
monitored over time for deviations which should be taken care of
• Post completion audit which compares the actual performance of a project after sometime with the
forecast made at the time of approval, it aims to encourage a more thorough and realistic appraisal of
future investment projects and facilitates major overhauls of ongoing projects perhaps to alter their
strategic focus. This is carried out at the end of the project unlike control that is done during the
project.

CLASSIFICATION OF CAPITAL INVESTMENT DECISIONS

They can be classified in so many ways such as
• Expansion of existing business
• Expansion of new business
• Replacement and modernization to reduce cost and improve efficiency.
OR
• Capital investment for maintenance of market position
• Capital investment for new products and diversification
• Capital investment for safety and environmental consideration
• Others whose returns are difficult to measure e.g. welfare, R&D, Educational projects.

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OR
1. Mutually exclusive investment are projects which serve the same purpose and compete with one
another so choosing one entails rejecting the other
2. Independent investments are projects which serve different purpose and do not compete with each
other. Taking such projects has no impact on other projects.
3. Contingent / dependent investments are projects performed together and so the undertaking of one
entails undertaking the others.
OR
1. Divisible investments are projects which can be partly performed or executed in fractions.
2. Indivisible investments are projects which must be performed wholly or cannot be executed in part.

FACTORS / INFORMATION REQUIRED FOR EFFECTIVE CAPITAL BUDGETING

• Methods of investment appraisal
• Sources of Finance
• Cash flow forecasting
• Cash budgets
• The risks involved.

CHARACTERISTICS OF A SOUND INVESTMENT EVALUATION CRITERION

▪ It should consider all cash flows
▪ It should provide for an objective and unambiguous way of choosing projects
▪ It should rank projects according to the true profitability
▪ It should help to choose among mutually exclusive projects that which maximizes
shareholder’s wealth.
▪ It should be applicable to any investment project independent of others.

NB
Cash outflows are represented by negative figures while cash inflows are represented by positive
figures. Cash flows are assumed to occur at the end of the year.

Year 0 – represents the initial year or date of making an investment. Start of year 2 is same as year 1
and so on.

INVESTMENT APPRAISAL TECHNIQUES

There are two major classifications of investment appraisal techniques
❖ Traditional or Non-discounted cash flow technique – which refers to a method of appraisal
which does not consider the time value of money, and they include payback period method
and the Accounting rate of return.

❖ Modern or Discounted cash flow technique – which refers to a method which considers the time
value of money such as Net present value, internal rate of return and the profitability index method.

PAYBACK PERIOD METHOD

This is one of the most popular and widely recognized traditional methods of evaluating investment
proposals. It is the period usually expressed in years which takes the cash inflows from a capital
investment project to equal the cash outflows. It is the time that a project will take to pay back the
money spent on it. It is based on expected cash flows from the project and not accounting profits. It
emphasizes on liquidity and net profitability thereby acting as an initial screening device.

Calculating Payback
Constant annual cash flows Initial payment
PBP => Annual cash inflow
Uneven Annual cash flows

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The payback period is calculated by working the cumulative cash flow over the life of the project that is
when the cash flow equals the cash outflow.
DECISION RULE
Accept the project if the payback period is less than the maximum or standard payback period set by
management if not reject for independent projects.
For mutually exclusive projects, accept or rank with preference to project with shortest payback period.

ADVANTAGES OF PAYBACK PERIOD METHOD

1. It is simple to understand and easy to calculate
2. It is cost effective as it cost less and requires less time.
3. It is based on cash flows and not subjective profits
4. It gives insight into the liquidity of the project
5. It can have a favorable short run impact on earnings per share
6. It provides a clear indication of the time required to convert a risky investment to a safe one that is an
initial screening device.
7. It reduces loss through obsolescence because of the short term approach.

DISADVANTAGES OF PAYBACK PERIOD METHOD

1. It does not consider the time value of money
2. It ignores cash flows after the payback period
3. It does not take into account the risks associated with each project and the attitude of the company at
risk
4. It is subjective in determining the company’s target payback period
5. It does not consider the return on capital investment
6. It is not an appropriate method of measuring project’s profitability

PAY BACK PERIOD RECIPROCAL

This is a useful technique to quickly estimate the true rate of return. It is the inverse of the payback period with
constant annual cash flows that is
Cash flows x 100 or 1 x 100
Initial outlay PBP

The payback period reciprocal is a close approximation of the internal rate of return if the following conditions
are satisfied.
The life of the project is large or at least twice the payback period
The project generates equal annual cash inflows.

PAY BACK PERIOD WITH BAIL OUT FACTOR

This is a technique of payback period calculation where the scrap value is treated as cash flow where it is
sufficient enough to recoup the initial outlay. It should be noted that for any year the scrap value is not used, it
is fore gone.

DISCOUNTED PAYBACK PERIOD

This is the number of years taken to recover the initial outlay on the present value basis that is considering the
time value of money. It still does not consider cash flows after payback.

ACCOUNTING RATE OF RETURN (ARR)

This method is based upon accounting profits and not cash flow. It uses financial accounting profits after
charging all financial accounting expenses including depreciation. It is best defined as the ratio of average
profit after tax to the average investment.

ARR = Average PAT

Average investment

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Where Average profit => Total profit / Number of years

Average investment => Initial investment + Scrap value

2
It is also called Return on investment or Return on capital employed.

DECISION RULE FOR ARR

Independent project => Accept if ARR > standard set by management
Mutually exclusive projects => Rank projects with preference to highest ARR

ADVANTAGES OF ARR
1. It is easy to calculate and use
2. It considers all profits for the project’s duration
3. It is easier to understand and apply for divisional performance evaluation
4. It can be readily calculated from available accounting data.
5. It is expressed in percentage terms which are familiar to Managers and Accountants.

DISADVANTAGES OF ARR
1. it does not recognize the time value of money
2. It is based on subjective accounting profit instead of cash flows
3. It does not consider the earnings life of an investment project
4. It is subjective in determining the company’s target accounting rate of return
5. The definition of its variables are unambiguous
6. It ignores the fact that profit for different projects may accrue at an uneven rate.
7. It does not consider risk and managements attitude towards risk.

CASH FLOWS, TIME VALUE OF MONEY IN INVESTMENT ANALYSIS

Sound investment decisions should be based on cash flows and not profit as it is cash that a firm can invest,
pay to creditors to discharge its obligation or distribute to shareholders as dividend. Cash flow is a simple and
objectively defined concept which is the difference between money received / receivable and money paid /
payable.

Cash flow is different from profit for two major purposes

Profit is measured by an accountant using accrual concept where income is recognized when earned and
expenses when incurred while cash flow is only recognized when there is actual movement of cash.
For profit computation expenditure are arbitrarily divided into revenue and capital expenditure (resulting in
some non-cash items such as notional cost, amortization, depreciation) but cash flow considers all expenditures
when they are paid for

The concept of Time Value of Money states that the value of money does not remain the same throughout
time, since the money available today can earn interest (investment preference), uncertainty of the cash flows
and the inflation which may reduce the purchasing power of money. The cash flows to be included in a
discounted cash flow appraisal should be relevant that is cash flows arising as a direct consequence of the
decision to embark on a project.

Characteristics of relevant cash flows include

1. it should be a future cash flow and so all sunk, committed, or historical cost are not relevant
2. It should involve actual movement of cash so depreciation, provisions, notional cost, apportioned cost
are not relevant
3. It should be an incremental or differential cash flow and so fixed cost is not relevant.

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Opportunity Cost is the foregone alternative because of the project and so should be considered as a relevant
cost which may be external (where a single tangible alternative exist) or internal (where two or more tangible
alternative exist). it is always relevant.

Financing Cash flows such as interest on loan, dividend and preference dividend are not relevant for
investment analysis as they have been considered in determining the cost of capital used for discounting.

Working Capital – includes investment in stocks and debtors (current assets) minus trade creditors (current
liabilities). Investment in working capital slow the receipt of cash. An increase in working capital reduces cash
flows and a reduction in working capital improves the cash flow in the year that it happens, by convention in
DCF analysis, if a project will require an investment in working capital, the investment is treated as a cash
outflow at the beginning of the year in which it occurs and eventually released at the end of the project when it
becomes a cash inflow.

Working Capital – An investment in working capital in the context of a capital investment appraisal means an
investment in stock and receivables less payables. Operating cash flows less than profit when there are cash
flows for working capital over the life of the project should always be zero as working capital investment is
reduced to zero at the end of the projects life.

NOTE
Why is working capital treated as cash inflow in the terminal year? This is because actual cash flows will
exceed cash profits in the year by the amount of reduction in working capital.

MATERIALS – When materials needed for a project is available in the company and has alternative uses, the
relevant cost is the replacement cost when materials are available but has no alternative use, the relevant cost is
the net realizable or saleable value but where material is not available, the relevant cost is the current purchase
cost.

LABOUR – When full time workers do the job, salary paid to them is not relevant for decision making but
where casual workers do the job their wages are relevant. Over time will only be relevant when it is paid on the
specific project concerned.
VARIABLE OVERHEAD is always relevant unless stated otherwise.

FIXED OVERHEAD is not relevant unless the examiner gives us the portion that is incremental, attributable,
specific or relevant. An incremental overhead suggest that the figure for the first year will be constant all
through.

NET PRESENT VALUE (NPV)

This is a discounted cash flow technique that explicitly recognizes the time value of money. It correctly
postulates that cash flows arising at different time periods differ in value and are comparable only when their
equivalent or present values of costs and present values of benefits discounted at a targeted rate of return or
cost of capital.

STEPS IN NPV CALCULATION

▪ Estimate or identify the relevant cash flows
▪ Use the appropriate discount rate or cost of capital for discounting

Single year = (1 + rate) -n

Cumulative year = 1 – (1 + rate) -n
r
Infinity = 1/r
▪ Determine the present value of all cash flows

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▪ Compare present value of cash outflows and cash inflows to derive difference which is known as Net
present value.

INTERPRETATION OF NET PRESENT VALUE

A positive NPV is the maximum amount a firm would be ready to pay for purchasing the opportunity of
making an investment or the amount which the firm would be willing to sell the right to invest without being
financially worse off. It can also represent the amount the firm could raise at the required rate of return in
addition to the initial cash outlay to distribute immediately to its shareholders and by the end of the project’s
life to have paid off all the capital raised and return on it. It tells us in absolute terms the addition or loss in the
value of shareholder’s wealth if a project is embarked upon. A positive NPV is also equivalent to an unrealized
capital gain.

DECISION RULE
Independent projects => Accept if NPV is positive, Reject if it is negative and be neutral if it is zero.

Mutually Exclusive projects – Rank projects with preference to the highest NPV in descending order.

ADVANTAGES OF NPV
1. It recognizes the time value of money.
2. NPV gives absolute measure of profitability which immediately reflects in the shareholder’s wealth.
3. Unlike the ARR it uses cash flow instead of accounting profits
4. NPV’s of several projects can be aggregated (value additively principle)
5. It gives a clear accept / reject recommendation
6. Unlike the payback, it uses all cash flows over a project’s life span
7. For every project there is a single NPV unlike IRR that may be multiple
8. Risk can readily be incorporated into the cost of capital to be used to appraisal
9. The cost of capital used for NPV calculation is superior to other rates
10. The NPV intention can be adjusted to accommodate relevant changes in the discount rates during a
period of inflation.
11. It is more preferable to IRR in capital rationing situations for ranking.

DISADVANTAGES OF NPV
1. In practice it is difficult to estimate future cash flows due to uncertainty
2. It is also practically difficult to precisely measure the discount rate
3. It may give ambiguous results when mutually exclusive projects with unequal lives or funds constraint
are evaluated.
4. It does not consider risk or management attitude towards risk.
5. It ignores inflation
6. Its ranking is heavily dependent on discount rate
7. Non accounting managers may not be conversant with the decision rule.

INTERNAL RATE OF RETURN (IRR)

This is a discounted cash flow technique, which takes account of the magnitude and timing of cash flows. It
could also be called the yield on investment, marginal efficiency cost of capital, rate of return on cost, time
adjusted rate of return etc.

The IRR is the rate that equates the investment outlay with the present value of cash inflow received after one
period which implies that if is the rate of return which equals NPV to zero.

Calculation of IRR
Determine NPV using the given and cost of capital
Determine another NPV which must be opposite in sign to that calculation in “1” above (if the initial NPV is
positive use a higher discount rate to get a negative and vice versa).

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Interpolate using the formulae IRR = lower rate + NPV of lower rate
(NPVLOWERRATE – NPVHIGHER)

IRR = LR + NPVLR (HR – LR)

NPVLR - NPVHR

DECISION RULE
Independent projects: Accept all projects whose IRR is greater than the company’s cost of capital.
Mutually exclusive projects: Accept the project with the highest IRR.

ADVANTAGES OF IRR
1. It recognizes the time value of money
2. It considers all cash flows over the project’s life span
3. It is consistent with the objective of shareholder’s wealth maximization
4. It is objective as it makes use of cash flow
5. It provides to us a margin of safety in the calculation of a company’s cost of capital
6. It is more attractive to divisional managers since they are used to the return approach in evaluations.

DISADVANTAGES OF IRR
1. It is difficult to calculate compared to other methods
2. A project may have multiple rates of return
3. Its decision may conflict with NPV where mutually exclusive projects are being considered under
certain situations.
4. It is a trial and error method as it gives a relative profitability
5. The IRR’s of different projects cannot be added
6. It may be difficult to estimate the cash flows
7. It does not consider risk or management’s attitude towards risk.
MODIFICATION OF IRR
The IRR can be modified under the following conditions:
Where the cash flows are unconventional
Where the projects are mutually exclusive

Conventional investment are those whose cash flows take the pattern of an initial cash outlay followed by cash
inflows while a non-conventional investment is one which has cash outflows mingled with cash inflows
throughout the project life.

The above solutions can be taken care of using

Extended yield method
Increment yield method

INCREMENTAL CASH FLOW APPROACH

Where two projects with different initial outlays are to be appraised using the same discount rate. The decision
of the NPV will conflict with IRR and so incremental approach is adapted thus.
▪ Calculate the NPV & IRR of project using the given cost of capital.
▪ Deduct the cash flows of the project having the lower outlay from the cash flows of the project having
the higher outlay (Avoid resultant negative cash flows).
▪ Calculate the IRR of the incremental cash flows in the normal way.
If the IRR is greater than the company’s cost of capital, then the project that was kept constant must be better
than the other project and must be accepted.

UNIQUE IRR

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One of the major demerits of IRR is that it produces multiple rates when dealing with non-conventional
investment which is not good for decision making. The unique IRR should be calculated using the following
steps
▪ Adjust each year’s cash flow by one year except the initial year
▪ Appraise the project in its new state to obtain adapted NPV
▪ Divide the adapted NPV by the outlay expressed in percentage to get unique IRR.
Adapted NPV x 100
Initial outlay

RE – INVESTMENT ASSUMPTION
A major conflict between NPV and IRR is the reinvestment assumption implicit in the NPV and IRR. The
NPV assumes that the project’s cash flows should be re-invested at the cost of capital while the IRR assumes
that the project’s cash flows should be invested at its IRR.

MODIFIED INTERNAL RATE OF RETURN (MIRR)

This is a cosmetic re-statement of an NPV analysis. It addresses the deficiencies of the conventional IRR. It
eliminates multiple IRR, addresses the re-invested rate issue and produces a result which is consistent with the
NPV rule.
MIRR is an IRR that assumes that project cash flows should be under this method at the opportunity cost of
capital and not IRR.

Under this method all cash flows after the initial investment are converted to a single cash flow at the end of
the project.

PROFITABILITY INDEX
This is the ratio of the present value of cash inflows at the required rate of return to the initial cash flows of the
investment.
P1 = PV of cash inflows: - BIR = NPV
Initial outlay Initial outlay

P1 reflects the return per Naira invested

BIR reflects the profit per Naira invested

Decision Rule
Accept if profitability index is greater than 1, reject if less than 1, be indifferent if equal to 1 for independent
project.
Rank in accordance of highest P1 to lowest for mutually exclusive projects.

ADVANTAGES
▪ It recognizes the time value of money
▪ It is consistent with the shareholder’s wealth maximization
▪ It shows a relative measure of profitability
▪ It makes use of cash flows
▪ It is good for ranking divisible projects in capital rationing situation.

DISADVANTAGES
▪ It will fail in a multi period capital rationing situation
▪ It requires estimates of cash flows which may be difficult
▪ it will fail in a situation of project indivisibility
▪ The selection intention is fairly simplistic
▪ It ignores the absolute size of individual projects.

NET TERMINAL VALUE / NET FUTURE VALUE

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POCKET NOTE STRATEGIC FINANCIAL MANAGEMENT ICAN NOV 2019 DIET

This is the sum of money an investor would end up with at the completion of a project over and above the sum
that would have been obtained had the project not been undertaken. Net Terminal value = Net present value (I
+ rate) number of years.

4.2. TAXATION AND INFLATION IN CAPITAL BUDGETING DECISION.

Inflation is the general increase in price leading to a general decline in the real value of money. In analyzing
the effect of inflation on a capital investment appraisal, we will consider two points
1. The effect of inflation on discount rate
2. How to take account of the impact of inflation on future cash flows

As inflation increases so does the minimum return required by investors (cost of capital). It is said that since
inflation affects both cash flows and cost of capital it will cancel out and so should be ignored but this
statement is rendered invalid by the following.
▪ Inflation does not affect cash flows and cost of capital in the same way.
▪ Inflation may not affect all cash flows in the same way
▪ Labour related to cash flows may not move in line with general inflation rate.

TYPES OF INFLATION RECOGNIZED IN CAPITAL BUDGETING

For the purpose of project appraisal, it is necessary to distinguish between two types of inflation
▪ General inflation
▪ Specific inflation

GENERAL INFLATION
This is an increase in the average price of all goods and services in an economy. It could be represented by
changes in consumer or related price index. This is a uniform inflation (equal) on all variables. The existence
of a single inflation rate in a question is a clear indicator of general inflation.

SPECIFIC INFLATION
This a change in the prices of the various elements that make up the project being investigated for example
sales price, labour cost, material cost, transport. Specific inflation affects only the cash flows while general
inflation affects both cash flow and the discount rate. The existence of more than one inflation rate in a
question is an indicator of specific inflation.

TYPES OF CASH FLOWS

MONEY CASH FLOWS: - are the actual amounts of cash flow used in a transaction that is cash flows in
nominal terms. They are inflated cash flows.

REAL CASH FLOWS: - are the purchasing power equivalents of the actual amount of cash flows. These are
cash flows without the effect of inflation. In other words, Real cash flows are money cash flows discounted for
the effect of changing prices.

Real Cash flow (1 + Inflation rate) = Money Cash flow

RCF (1 + F) = MCF

TYPES OF DISCOUNT RATE

MONEY DISCOUNT RATE OR COST OF CAPITAL: - is the company’s real cost of capital plus an
allowance for inflation. It is the discount rate in nominal terms.

REAL DISCOUNT RATE OR COST OF CAPITAL: - is the discount rate in constant price level or current
terms. RCC = Real cost of capital
F = Inflation rate, MCC = Money cost of capital
(1 + RCC) (1 + F) n = (1 + MCC)

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RULES IN SOLVING INFLATION QUESTIONS

▪ Use money cost of capital to discount money cash flows and real cost of capital to discount real cash
flows
▪ Identify the nature of the cash flows that is let the cash flow indicate the cost of capital to be used
▪ Real cash flows are those exposed in year zero prices, constant price level, current terms, now, or in
real terms.
▪ Where the examiner is silent as regards the cash flow or cost of capital, it is assumed to be in money
terms.
▪ Where several items attract different rates of inflation at different times and the cash flow will be
needed at a future date, convert them to money cash flows and discount with money discount rate.
▪ Any item stated in year 1 prices attracts no inflation in year 1 that is inflation becomes applicable from
year 2 (1 + inflation)

TAXATION
Tax is a compulsory levy imposed by the government on its citizenship (individual and corporate) to assist it in
providing the basic infrastructures.

Taxation is considered in capital budgeting because of its important on cash flows. All cash inflows associated
with a project such as income, revenue gives rise to tax payment while cash outflows such as purchase of an
asset, lease rentals by lessee, capital allowance lead to tax savings. There is not tax implication on working
capital.

Depreciation is not allowable for tax purposes due to lack of uniformity and so should be added to profit and
instead be replaced with capital allowance.

Capital allowance is a relief in granted in lieu of depreciation in respect of a qualifying capital expenditure.
These allowances include:

Balancing Allowance – is the relief granted for a loss on disposal of assets.

Balancing Charge – attracts tax payments since it is a gain on disposal.

Unless otherwise stated capital allowance computation commences from year 1 and tax is assumed to be
payable one year after the profit was made.

Note: - For tax purposes we use income and expenditure while for NPV analysis we use cash flows.

STEPS ON SOLVING TAXATION ISSUES IN CAPITAL BUDGETING

▪ Compute the capital allowance
▪ Compute the tax payable or claimable using annual cash flows excluding initial outlay, scrap value or
working capital
▪ Compute the Net present value using the original question incorporating the tax effect as calculated
above.

ILLUSTRATIONS ON CAPITAL BUDGETING BASICS

ILLUSTRATION 1 (MAY 2017 ICAN PAST QUESTION)
K plc, a listed company based in Warri, Delta state, has been involved in producing boats (but excluding the
engines). The company is now considering diversifying into the production of the major component of
outboard engine. For this purpose, the company has recently purchased the patent rights for N15 million to
produce the component.

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K plc has spent N20 million developing prototypes of the component and undertaking market studies. The
research studies came to the conclusion that the component will have a significant commercial potential for a
period of five years, after which, newer components would come into the market and the sales revenue from
the component would virtually fall to zero. The research studies have also found that in the first two years (the
development phase), there will be considerable training and development costs and fewer components will be
produced and sold. However, sales revenue is expected to grow rapidly in the following three years (the
commercial phase).
It is estimated that in the first year, the selling price would be N2,000 per component, the variable costs would
be N800 per component and the total direct fixed cost would be N6,000,000. Thereafter, while the selling price
is expected to increase by 8% per year, the variable and fixed costs are expected to increase by 5% per year for
the next four years. Training and development costs are expected to be 120% of variable costs in the first year,
40% in the second year and 10% in each of the following three years.
The estimated average number of outboard engine components produced and sold per year is given below:
YEAR 1 2 3 4 5
Units produced and sold 15,000 40,000 100,000 120,000 190,000

Machinery costing N480,000,000 will need to be installed prior to commencement of the component
production. K plc has enough space in its factory to manufacture the components and therefore will incur no
additional rental costs. Tax allowable depreciation is available on the machinery at 10% on straight-line basis.
The machinery is expected to be sold for N160,000,000 at the end of year 5. The company makes sufficient
profits from its other activities to take advantage of any loss relief available from this project.
Initially, K plc will require additional working capital for the project of 20% of the first year’s sales revenue.
Thereafter, every N1 increase in sales revenue will require a 10% increase in working capital.
Although this would be a major undertaking for the company, it is confident that it can raise the finance
required for the machinery and the first year’s working capital. The financing will be through a mixture of a
rights issue and a bank loan, in the same proportion as the market values of current equity and debt capital.
Any annual increase in working capital after the first year, will be financed by internally generated funds.
Marine Engineers (ME) plc, is a listed company involved in the manufacture of outboard engine components
for many years.
Additional data
Extracts from Statement of Financial Position
K plc ₦m ME plc
₦m
Non-current assets 1,344 1,668
Working capital 296 628
6% bank loan 624
5% loan notes (2020 – 2022) 368
Share capital ; N0.50 per share 208
; N1.00 per share 500
Reserves 808 1,428

Current market value per share (N) 3.50 3.00

Quoted beta 1.3 1.8
The loan notes of ME plc are quoted at N102 per N100

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OTHER DATA
Tax applicable to K plc and ME plc is 20%. It can be assumed that tax is payable in the same year as the
profits on which it is charged.
Estimated risk free rate of return : 3%
Historic equity market risk premium: 6%
Required
a. Given the information on ME plc, and the project financing mix, including any other relevant
information, calculate the project specific cost of capital. (5 marks)
b. Assess whether K plc should undertake the project of developing and commercializing the major
component of outboard engine, assuming a discount rate of 12% as being applicable for the
assessment, irrespective of your calculations in (a) above. (22 marks)
c. State any three relevant assumptions made for your calculations in (a) and (b) above (3 marks)
(total 30 marks)
SOLUTION TO ILLUSTRATION 1
(a) Ethics impact on many aspects of investment decisions. In theory, companies seek to maximise
shareholders wealth, often subject to constraining secondary objectives. Such secondary objectives
inciude the welfare of the public. Companies are affected by ethical standards relating to:
(i) Health and safety - Employees and the public should be protected from danger, which includes
working conditions, following employment laws and product safety;
(ii) Environmental issues - Environmental issues such as, controlling pollution, protecting wildlife
and the countryside. Fully satisfying these issues might be an expensive element in a capital
investment;
(iii) Bribes and other payments - Investment might proceed more quickly and efficiently if bribes,
'incentive payments1, 'gifts' etc. are paid to officials. This is a difficult area, as gifts are part of the
business culture in some countries. Even the ethics of political contributions is debatable;
(iv) Corporate governance - Many examples exist of companies, e.g. Enron, where the results of
investments and the true financial position have been hidden from shareholders and the public;
(v) Taxation - Companies may try to minimise their tax liability. Tax evasion is illegal, but there is
an ethical question over the use of sophisticated tax avoidance measures, especially in developing
countries;
(vi) Wage levels - Should a company pay low wages to maximise shareholders* wealth, especially in
countries where the standard of living is very low?
(vii) Individual manager's ethics - The ethics of individuals, including pursuing their own goals and
self-interest (such as job security) rather than those of the organisation might influence the outcome
of investment decisions.

There is inevitably some subjectivity as to what constitutes ethical behaviour, but there is little doubt
that ethical issues are of increasing importance to companies. Acting in an ethically responsible way
often has a direct detrimental impact upon expected cash flows and net present value (NPV).
However, stakeholders, including shareholders, are increasingly expecting companies to act ethically.
If they do not, then their share price might suffer as a result of adverse publicity and investors
withdrawing their support.
The concept of ethical shareholders" wealth creation is likely to become increasingly important in
strategic financial management.

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b) Using the Black-Scholes Option Pricing (BSOP) model in company valuation rests upon the idea
that equity is a call option, written by the lenders, on the underlying assets of the business. If the
value of the company declines substantially then the shareholders can simply walk away, losing the
maximum of their investment. On the other hand, the upside potential is unlimited once the interest
on debt has been paid.
The BSOP model can be helpful in circumstances where the conventional methods of valuation do
not reflect the risks fully or where they cannot be used, for example, if we are trying to value an
unlisted company with unpredictable future growth.
There are five variables which are input into the BSOP model to determine the value of the option.
Proxies need to be established for each variable when using the BSOP model to value a company.
The five variables are: the value of the underlying asset; the exercise price; the time to expiry; the
volatility of the underlying asset value; and the risk free rate of return.
For the exercise price, the debt of the company is taken. In its simplest form, the sophisticated tax
avoidance measures, especially in developing countries;
(vi) Wage levels - Should a company pay low wages to maximise shareholders" wealth, especially in
countries where the standard of living is very low?
(vii) Individual manager's ethics - The ethics of individuals, including pursuing their own goals and
self-interest (such as job security) rather than those of the organisation might influence the outcome
of investment decisions.

There is inevitably some subjectivity as to what constitutes ethical behaviour, but there is little doubt
that ethical issues are of increasing importance to companies. Acting in an ethically responsible way
often has a direct detrimental impact upon expected cash flows and net present value (NPV).
However, stakeholders, including shareholders, are increasingly expecting companies to act ethically.
If they do not, then their share price might suffer as a result of adverse publicity and investors
withdrawing their support.

The concept of ethical shareholders" wealth creation is likely to become increasingly important in
strategic financial management.

b) Using the Black-Scholes Option Pricing (BSOP) model in company valuation rests upon the idea
that equity is a call option, written by the lenders, on the underlying assets of the business. If the
value of the company declines substantially then the shareholders can simply walk away, losing the
maximum of their investment. On the other hand, the upside potential is unlimited once the interest
on debt has been paid.

The BSOP model can be helpful in circumstances where the conventional methods of valuation do
not reflect the risks fully or where they cannot be used, for example, if we are trying to value an
unlisted company with unpredictable future growth.

There are five variables which are input into the BSOP model to determine the value of the option.
Proxies need to be established for each variable when using the BSOP model to value a company.
The five variables are: the value of the underlying asset; the exercise price; the time to expiry; the
volatility of the underlying asset value; and the risk free rate of return.

For the exercise price, the debt of the company is taken. In its simplest form, the assumption is that
the borrowing is in the form of zero coupon debt, that is, a discount bond. In practice such debt is not
used as a primary source of company finance and so we calculate the value of an equivalent bond

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with the same yield and term to maturity as the company's existing debt. The exercise price in
valuing the business as a call option is the value of the outstanding debt calculated as the present
value of a zero coupon bond offering the same yield as the current debt.

The proxy for the value of the underlying asset is the fair value of the company's assets less current
liabilities on the basis that if the company is broken up and sold, then that is what the assets would be
worth to the long-term debt holders and the equity holders.
The time to expiry is the period of time before the debt is due for redemption. The owners of the
company have that time before the option needs to be exercised, that is when the debt holders need to
be repaid.
The proxy for the volatility of the underlying asset is the volatility of the business' assets.
The risk-free rate is usually the rate on a riskless investment such as a short-term government bond.

ILLUSTRATION 2 ON CAPITAL BUDGETING (NOVEMBER 2014 PAST QUESTION)

AK PLC is a company listed on the Nigerian Stock Exchange. It is involved in property development and
sales. The company currently imports more than 60% of its cement requirements. At a recent meeting of the
board of directors, a decision was taken to establish a division for the production of cement in Ore, Ondo state.
If the division is set up and cement production goes ahead, output from the division will be sold to AK plc and
external customers at market price. For planning purposes, it has been decided that the financial viability of the
project over the next five years should be determined.
The sum of N2 billion will be required. The sum of N500 million will be spent to acquire an existing factory
considered suitable for the project. The balance of N1.5 billion will be applied for the procurement and
installation of essential plant and equipment. Tax allowance can be claimed on plant and equipment at a
uniform amount over 5 years with nil scrap value.
A total of N20 million has been spent on various surveys (market, technical, financial, etc.) to date out of
which N10 million has been paid. The balance of N10 million is due for payment at the end of year 1.
Production of cement for the next five years is projected as follows:
YEAR BAGS
1 500,000
2 600,000
3 650,000
4 800,000
5 700,000
A bag of cement sells currently for N2,000 in the open market. The price is expected to increase at the rate of
5% per annum. Variable cost is N800 per bag. This will increase at 4% per annum. Fixed overhead cost will be
N50 million at current prices but will rise by 8% per annum. Apportioned head office charges of N25 million
at current prices will rise by 10% per annum. Fifty percent (50%) of the total initial outlay of N2 billion is to
be funded with a loan from a Federal Government bank at a concessionary fixed interest rate of 8%, payable at
the end of each year. Half of the loan will be repaid at the end of year 3 while the balance will be paid at the
end of year 5. The project will require a working capital of 10% of annual revenue to be available at the
beginning of each year.
The company uses a current weighted average cost of capital (WACC) of 11% to appraise all capital projects.
The asset beta of the company is 1.2, equity beta is 1.6, risk free rate is 5% while the market premium is 7%.

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The finance director is of the view that it is not appropriate to use the existing WACC to appraise the new
project. He has found a listed company which currently produces cement and packaged fruit drinks. The
company has the following financial statistics: Equity beta1.82, debt beta 0.42, debt equity ratio 40%.
60% of the market value of the company is attributed to cement production while 40% of the value is attributed
to the fruit drink division. The fruit drink division has an equity beta of 0.8.
The new project is expected to move AK plc to the target Debt/Equity ratio of 30%. Tax rate is 25% for the
two companies and is paid in the year profit is made.
a. Compute the appropriate cost of capital that AK plc should use to appraise the cement project and
state why you consider this rate more appropriate than the existing WACC of 11%. Your final cost of
capital should be rounded up to the nearest whole number stating any assumptions made
(12 marks)
b. Compute the Net Present Value (NPV) and the Modified Internal Rate of Return (MIRR) of the
project assuming a cost of capital of 13% (work to the nearest N million) (16 marks)
c. Recommend whether the project should be accepted or not, using both NPV and MIRR (2 marks)

SOLUTION TO ILLUSTRATION 2
(a) For K Pic. the new project is a diversification from boat making into outboard engine components
making. We must make use of the asset beta of ME Pic. which is currently producing outboard
engine components.

Asset beta - using the leverage of ME Pic. 𝛽A=𝛽E- VEV+E + v(1 – t)+ 𝛽DVD(1 – t)V+E + VD(1 – t)

VE = 500m x h3 = N1,500m
VD = N368m x 1.02 = N 375.36m
𝛽A = 1.8 x 1,5001,500 + 375.36(1 - 0.2)+0 = 1.5
Equity beta - using the leverage of K Pic.
𝛽E = 𝛽A + 𝛽A – 𝛽DVDVE

VE= 2080.5 x N3.50 = N1,456m

VD= 624 (from statement of financial position)
𝛽E = 1.5 + (1.5 - 0) 6241,456 (1 - 0.2) = 2.014
Cost of equity = KE = 3 + 2.014(6) = 15.08%
Weighted Average Cost of Capital (WACC)
WACC = KO = 1,456 X 15.08 1,456 + 624+ 624 X 6 x 0.81,456 + 624 = 1 2% 81

(b) 0 1 2 3 4
Calculation N'000 N'000 N'000 N'000 N'000
of NPV Year
Sales revenue 30,000 86,400 233,300 302,280 516,990
Variable (12,000) (33,600) (88,200) (111,120) (184,680)
costs

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Fixed costs (6,000) (6,300) (6,615) (6,946) (7,293)

Training & (14,400) (13,440) (8,820) (11,112) (18,468)
development
Cash (2,400) 33,060 129,665 173,102 306,549
operating
profit
Tax at 20% 480 (6,612) (25,933) (34,620) (61,310)
Tax savings 9,600 9,600 9,600 9,600 25,600
on depr.
(W2)

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Working (6;000) (5,640) (14,690) (6,898) (21,471) 54,699

capital (W1)
Machinery (480,000) 160,000
NCF (486,000) 2,040 21,358 106,434 126,611 485,538
PVF at 12% 1 0.893 0.797 0.712 0.636 0.567
Present (486,000) 1,822 17,022 75,781 80,525 275,300
value
NPV = (N35,550,000)

RECOMMENDATION
The project is not viable because the NPV is negative. Therefore, it should be rejected.
Working Notes
W1: 1 2 3 4 5
Incremental
WC Year
Incremental - 56,400 146,900 68,980 214,710
revenue
(N"000)
Incremental - 5,640 14,690 6,898 21,471
WC (10%)
(Nw000)
Year due - 1 2 3 4

W2: Tax savings on tax allowable Tax savings @ 20% tt"000

depreciation Depreciation
N ‘000

Year 1 10% of N480,000 48,000 9,600

2 48,000 9,600
3 48,000 9,600
4 48,000 9,600
192,000

Balance = N(480,000 - 192,000 )= 288,000

Year 5: Sales proceeds (160,000)
Balancing allowance 128,000 25,600

ILLUSTRATION 3 ON WORK BACK

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You have been conducting a detailed review of an investment project proposed by one of the divisions of
your business. your review has two aims: first to correct the proposal for any errors of principle and
second, to conduct some sensitivity analysis on the project. The company’s current weighted average cost
of capital is 10% per annum
The initial capital investment is for N150 million followed by N50 million one year later. The post-tax
cash flows for this project, in Nmillion, including the estimated tax benefit from capital allowances for tax
purposes, are as follows:
YEAR 0 1 2 3 4 5 6
Capital investment
(plant &
machinery)
First phase -127.50
Second phase -36.88
Project post tax 104.00 128.00 60.00 35.00 20.00
cash flow Nm
Company tax is charged at 30% and is paid/received in the year in which the liability is incurred. The
company has sufficient profits elsewhere to recover capital allowances on this project, in full, in the year
they are incurred. All the capital investment is eligible for a first year allowance for tax purposes of 50%
followed by a writing down allowance of 25% per annum on a reducing balance basis.
You noticed the following points when conducting your review:
I. An interest charge of 8% per annum on a proposed N50 million loan has been included in the
project’s post tax cash flow before tax has been calculated.
II. Depreciation for the use of the company shared asset of N4 million per annum has been
charged in calculating the project post tax cash.
III. Activity based allocations of company indirect cost of N8 million have been included in the
project’s post tax cash flow. However additional corporate infrastructure cost of N4 million
per annum have been ignored which you discover would only be incurred if the project
proceeds.
IV. You also notice that an estimate of site clearance of N5 million due in year six has been
ignored.
V. The post-tax cash flows ignored the following estimate of total working capital.
YEAR 1 2 3 4 5 6
Total working capital (Nm) 200 250 250 300 200 150
Working capital for each year is made available at the beginning of the year. The working capital is
expected to be released at the end of the sixth year.
1. Show how the following post tax cash flows have been determined; N127.50m and N36.88m outflows
in year 0 and 1 respectively
2. Prepare a corrected version of the project evaluation using NPV technique
3. Provide an assessment of the sensitivity of the project to a N1 million change in the initial capital
expenditure (due in year 0).

SOLUTION TO QUESTION 3

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The appropriate cost of capital should reflect the business risk of the cement industry and the
financial risk of the company.
▪ Determine the equity beta of the cement division of the given proxy company. Note that the
equity beta for the proxy company is a weighted average of the equity beta of the cement
division (unknown;X) and that of the fruits division
(0.8)0.6X + 0.4(0.8) = 1.82 and X = 2.5
▪ Ungear the BE of the cement division to eliminate the financial risk of the proxy company.
▪ BA = BE X VE / VE + VD(l-t) + BD x VD (1-t)/VE + VD (1-t) = 2.5 X 100/ 100 + 40 (1-0.25) +
0.4 X 40(1-0.25)/100 + 40(1 - 0.25) = 2.02
▪ Regear the asset beta using AK pic target ratio
BE = BA + (BA - BD)VD(1-t)/VE = 2 + (2 - 0.4)(30/100) X 0.75 = 2.36
▪ Determine the cost of equity using CAPM
; KE = RF + BE (RM - RF) = 5 + 2.36(7) = 21.52%
▪ Determine the cost of debt net tax
In the absence of additional information, we assume that the appropriate cost of debt, before
tax is the concessionary interest rate of 8%. KD = 8(1 - 0.25) = 6%
▪ Compute the WACC
(100/130 x 21.52) + (30/130 x 6) = 17.93% = 18%.

The WACC is appropriate because it reflects the business risk of the project and the financial risk
associated with the method of financing the project unlike the existing WACC 11% which only
reflects the current risk and so may not be appropriate.

Note that the beta debt was assumed to be universal in this illustration.
PART B IS ON NPV (N'000)
YEAR 0 1 2 3 4 5
Sales revenue W1 0 1,050 1,323 1,505 1,945 1,787
Variable cost W 2 0 -416 -519 -585 -749 -681
Cash fixed cost w3 0 -54 -58 -63 -68 -73
Operating profit 0 580 746 857 1,128 1,033
Tax 0 -145 -187 -214 -282 -258
Tax savings on CA 0 75 75 75 75 75
w6
Initial outlay -2,000
Working capital w4 -105 -27 -19 -45 17 179
NCF -2,105 483 615 673 938 1,029
dcf@13% 1 0.885 0.783 0.693 0.613 0.543
PV -2,105 427 482 466 575 559
NPV N404,000

MIRR =( PVR /PVI)1/n x (1 + r) -1 = (2,509/2,105)1/5 x (1.13) - 1 = 17%

Workings
YEAR 0 1 2 3 4 5
ANNUAL REVENUE
Quantity sold 500,000 600,000 650,000 800,000 700,000
Selling price (N) 2,100 2,205 2,315 2,431 2,553
Sales revenue Nm 1,050 1,323 1,505 1,945 1,787
Annual total variable

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cost

Variable cost per unit (N) 832 865 900 936 973
Total variable cost (Nm) 416 519 585 749 681
Incremental cash fixed
cost
Total Nm Incremental 54 58 63 68 73
working capital
Total (10% of revenue) 105 132 151 196 179
Incremental working-150 -27 -19 -45 +17+179
capital

▪ Loan repayments and interest on loan are irrelevant in NPV calculations

▪ Apportioned overheads are irrelevant because they do not involve cash flow
▪ Cost of surveys are sunk cost and irrelevant
▪ Tax savings on capital allowance = 1,500m / 5 = 300m x 25% = N75m

ILLUSTRATION 4 ON NPV CALCULATIONS AND MIRR

Julie plc is considering an opportunity to produce an innovative component which, when fitted into motor
vehicle engines, will enable them to utilize fuel more efficiently. The component can be manufactured
using either process A or process B. Although this is an entirely new line of business for Julie plc, it
believes developing either process over a period of four years and then selling the production rights at the
end of four years to another company may prove lucrative.
The annual after-tax cash flows for each process are as follows:
YEAR 0 1 2 3 4
PROCESS A AFTER TAX CASH FLOWS (3,800) 1,220 1,153 1,386 3,829
(N’000)
PROCESS B AFTER TAX CASH FLOWS (3,800) 643 546 1,055 5,990
(N’000)
The company has 10 million 50k shares trading at 180k each. Its loans have a current value of N3.6
million and an average after-tax cost of debt of 4.5%. The company’s capital structure is unlikely to
change significantly following the investment in either process.
Uche co manufactures electronic parts for cars including the production of a component similar to the one
being considered by Julie co. Uche co.’s equity beta is 1.40, and it is estimated that the equivalent equity
beta for its other activities, excluding the component production is 1.25. Uche co has 400 million 25k
shares in issue trading at 120k each. Its debt finance consists of variable rate loans redeemable in seven
years. The loans paying interest at base rate plus 120 basis points have a current value of N96 million. It
can be assumed that 80% of Uche co.’s debt finance and 75% of its equity finance can be attributed to
other activities excluding the component production.
Both companies pay annual corporation tax at a rate of 25%. The current base rate is 3.5% and the market
risk premium is estimated at 5.8%.
a. Provide a reasonable estimate of the cost of capital that Julie co should use to calculate the net
present value of the two processes. Include all relevant calculations

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b. Calculate the internal rate of return and the modified internal rate of return for process A. given
that the IRR and MIRR of process B are 26.6% and 23.3% respectively, recommend which
process if any, Julie co should proceed with and explain your recommendation.
c. Estimate the project’s Value at Risk (VAR) at a 99% confidence level for one year and over the
project’s life of five years if Uche co has estimated an annual standard deviation of N800,000 on
one of its other projects, based on a normal distribution of returns. The average annual return on
this project is N2,200,000

SOLUTION TO ILLUSTRATION 4
To get the number of magazines to be sold to break even, we would need to get the number of copies
that need to be sold to make a break even net present value over the four year period.
The first step is to calculate the money cost of capital because this is a case of specific inflation

(1 + R)(l + F) = (1 + M) = (1.077)(1.04) = 1 + M

M = 1.12 -1 = 12%

REVENUE FROM ADVERTISING (note that this is not affected by the number of copies sold
12 times x 18 pages X N2,000,000 N432,000,000
Less tax @ 30% N 129,600,000
Aftertax revenue in current prices N302,400,000
This will inflate at 2% per annum

FIXED RUNNING COST NET OF TAX

N100m (1 - 0.30) = N70m. this will inflate at 6% per annum

UNIT CONTRIBUTION NET OF TAX

Selling price per copy N200
Variable cost N60
Contribution N140
Tax N42
Contribution net tax at current prices N98
This will inflate at 2% per annum

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CAPITAL ALLOWANCE; recall that the examiner says only 50% of the expenditure is qualified
for capital allowance and the scrap value is negligible. Note that capital allowance is always on
nominal basis.
TAX SAVINGS AT 30%
YEAR 0 Qualified expenditure N500m
Capital allowance @ 25% YR 1 N125m 37.50m
NBV N375m
Capital allowance @ 25% YR 2 N93.75m 28.125m
NBV N281.25m
Capital allowance @ 25% YR 3 N70.31m 21.093m
NBV N210.94m
Scrap value NO.00m
Balancing allowance in year 4 N210.94m 63.282m

PRESENT VALUE OF KNOWN CASH FLOWS

YEAR 0 1 2 3 4
Nm Nm Nm Nm Nm
Investment (1,000)
Advert (2% inflation) 308.45 314.62 320.91 327.33
Running cost (6% inflation) (74.20) (78.65) (87.95) (93.23)
Tax savings on capital allowance 37.50 28.13 21.09 63.28
Cash flows (1,000) 271.75 264.10 254.05 297.38
Dcf @ 12% 1.000 0.893 0.797 0.712 0.636
PV (1,000) 242.67 210.49 180.88 189.13

Total PV is equals to N176.83 million

(year 3 figure for running cost has additional 5.5% in addition to the normal inflation 78.65 x 1.06 x
1.055 =N87.95)

PRESENT VALUE OF CONTRIBUTION NET OF TAX PER COPY

YEAR 1 2 3 4
Contribution (2% inflation) 99.96 101.96 104.00 106.08
Dcf @ 2% 0.893 0.797 0.712 0.636
PV 89.26 81.26 74.05 67.47

Total PV = N312.049 per copy

Let q be the breakeven number of copies of magazine needed.

The breakeven quantity would be that quantity that enables the organization attain the NPV of cost
above. Recall that the breakeven point would be that point where total revenue equals total cost.

(PV of contribution per unit x break even quantity) = PV of costs

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312.049xq = 176.83m
Q = 176.83m / 312.049 = 566,690 copies
The company must sell approximately 566,690 copies to break even

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CHAPTER 5; ADJUSTED PRESENT VALUE

ILLUSTRATIONS ON ADJUSTED PRESENT VALUE
ILLUSTRATION 1 (MAY 2016 ICAN PAST QUESTION)
Katam plc has adopted a strategy of diversification into many different industries in order to reduce risk
for the company’s shareholders. This has resulted in frequent changes in the company’s gearing level and
widely fluctuating risks of individual investments. Presently the company has a target debt to asset ratio
i.e. D/ (D + E) of 25%, an equity beta of 2.25 and a pre-tax cost of debt of 5%.
On January 1, 2016 Katam plc with a year end of December 31, is considering the purchase of a new
machine costing N750 million which would enable it to diversify into a new line of business. The new
business will generate sales of N522.5 million in the first year, growing at 4.5% per annum. A constant
contribution margin ratio of 40% can be expected throughout the 15-year life of the project. Incremental
fixed costs will be N84.32 million into the first year growing by 5.4% per annum.
A regional development bank has offered a 10-year loan of 3% interest to finance 40% of the cost of the
machine. The balance of 60% will be financed equally by a 10-year commercial loan (with annual interest
of 5%) and a fresh round of equity.
The issue cost on the commercial loan will be 1% and the new equity will incur issue cost of 3%. All issue
costs are the gross amount raised for the respective capital. Issue costs on debt are allowed for tax
purposes.
A firm that is already in the business of the new project has a gearing ratio of 20% (debt to asset) and cost
of equity of 18.1%. its corporate debt is risk-free.
Tax rate of 30% is payable in the year profit is made. Tax depreciation of 20% on cost is available on the
new machine. Katam plc has weighted average cost of capital of 14% and a cost of equity of 17.5%. the
risk-free rate is 4% and the market risk premium is 7%.
You are required to:
a. Estimate the Adjusted Present Value (APV) and advise whether the project should be accepted (21
marks)
b. Explain the circumstances under which the use of APV is appropriate
c. State the major advantages and limitations of the use of APV method (9 marks)

SOLUTION TO ILLUSTRATION 1
a)

i) Ungeared cost of Equity (KEU)

The base-case NPV is computed using ungeared cost of equity. We need to estimate this from the
information about the proxy company. A number of methods can be used:
*Using MM cost of Equity Formula
KEG = KEU + (KEU- KD) VVDDVVEE- (1 -tt), where
KEG = cost of equity of the proxy company = 18.1 %
KEU = the ungeared cost of equity, i.e. the cost of equity that reflects only the business risk of the new
project = xx

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∙VVDDVVEE ∙ = debt/equity ratio of the proxy company = 20/80 = 0.25

Kd = cost of debt, before tax, of the proxy company = 4%, since we are told it is risk-free.

Substituting figures in the formula, the position will be:

18.1 = xx + {xx- 4) (0.25) (1 - 0.30)
18.1 = xx + (0.25xx - 1) 0.70
18.1 = xx + 0.175xx - 0.70
18.1 + 0.70 =1.175xx
1.175 xx = 18.8
xx = = 16 175.18.18
i.e. 16%

*Using MM WACC Formula

- Current WACC of the proxy company:

VE/ve+V X KE+VEVVEE+VVDD-KKDD- (1-tt) (0.8)(18.1)+(0.2)(4)(l-0.3)

i.e. 14.48 + 0.56 = 15.04%
WACCg = WACCU- 1— VVEEVVEE+VVDD(tt)
Substituting 15.04% for WACCgin the above formula, the position will be:
15.04 = x[1—(0.20)(0.30)]
15.04 = x(1—G.06)
15.04 = 0.94xx
xx = 16%

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ii) Base - Case NPV

Given the life of the project of 15 years and differential growth (inflation) rates, it is faster to
compute the PV of each item separately. Note that the given WACC of 14% and cost of equity of
17.5% of Katam Pic. are irrelevant.

*Contribution, net of tax (Nm)

Contribution at year 0 prices:
(N522.50/1.045) x 0.40 = 200
Less tax at 30% (60)
Net of tax 140
Real cost of capital = (1.16/1.045) - 1 = 0.110048 or say 11%
Annuity factor for 15 years at 11% = 7.191
PV of contribution = N140 x 7.19087 = N1,006.74

*Incremental fixed cost, net of tax

Fixed cost at year 0 prices:
(N84.32/1.054) x (1 - 0.3) = N56m
Applicable real cost of capital:
(1.16/1.054) - 1 = 0.10569 or 10%
Annuity factor for 15 years at 10% = 7.606
PV = N56 x 7.606 = N425.94

ALTERNATIVE METHOD
Growing annuity can be used to calculate the present value of each of the items involving growth
(inflation). As given in the formula sheet, the present value of growing annuity is given by:
grA—1 ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙+ + - nrg111
* Contribution
Contribution, net of tax, in Year 1 is
N(522.50 x 0.4) x (1 - 0.30) = N146.30m
PV = N= N1,006.46 045.016.030.146-∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙- 15 16.1045.11
*Incremental fixed costs
Amount in year 1, net of tax:
N84.32m x (1 - 0.3) = N59.024m
N= N424.53m 054.016.0024.59-∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙-15 16.1054.11
*Tax savings on tax depreciation

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Annua! tax savings = N750 x 0.2 x 0.30 = N45m

These are money cash flows and must be discounted using money cost of capital of 16%
Annuity factor (years 1 - 5) @ 16% = 3.274
PV = N45 x 3.274 = N147.33m Summary

Nm
PV of contribution 1,006.74
PV of fixed costs (425.94)
PV of tax savings on depreciation 147.33
Outlay (750.00)
Base-case NPV (21.87)
Financing side Effects
The project is financed as follows:

Nm
Development Bank Loan 40% of N750m 300
Commercial loan: 60% x 50% x N750m 225
Equity 60% x 50% x N750m 225
Net amount needed 750
Issue costs
Commercial Equity
loan
Nm Nm
Net amount needed 225.00 225.00
Issue costs ∙ 199x225- ∙ 2.27 ∙ 397x225- ∙ ∙ 6.96
Gross amount 227.27 231.96
Tax savings on issue cost, due in year 1 = 2.27 x 0.30 = N0.68m
Tax savings on interest
Nm
Development Bank loan: N300 x 0.03 x 0.30 = 2.70
Commercial loan: N227.27 x 0.05 x 0.30 = 3.41
Total annual tax savings (year 1 -10) 6.11
After tax interest savings on Development Bank's loan
Nm
Gross savings 300 x (0.05 - 0.03) 6.00

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Tax on savings at 30% (1.80)

Net interest savings (years 1-10) 4.20
Present value of the financing side effects

The present values of the financing side effects are calculated at the company's normal cost of
borrowing of 5%, gross of tax.
Items Year NCF PVF PV
Nm @5% Nm
Issue costs - Equity 0 (6.96) 1.000 (6.96) -
Com. loan 0 (2.27) 1.000 (2.27)
Tax savings on issue cost 1 0.68 0.952 0.65
Tax savings on interest 1 - 10 6.11 7.722 47.18
Interest savings on
Development Bank's loan 1 - 10 4.20 7.722 32.43
Total PV of financing side
Effects 71.03

Note: In calculating the present values of the financing cash flows, the discount factor used is 5% to
reflect the normal borrowing/default risk of the company. Alternatively, the risk-free rate of 4%
could be used depending on the assumption made. Credit will be given where these are used to
estimate the discount factor.

Calculation of APV Nm
Base - case NPV (21.88)
Financing side - effect 71.03
APV 49.15

Recommendation
Although the project has a negative NPV if financed purely by equity, it is worthwhile accepting it
because of its proposed financing method. Accepting the project is expected to increase shareholders'
wealth by N49.15 million,

b)
i) The APV method is most appropriate in the following circumstances:
• When it permanently changes the level of gearing of a company.
• When the project involves unusual financing costs such as a subsidised loan.
• It significantly changes the company's debt capacity.
• If a number of project-specific financing options are to be considered.

ii) The main benefits of this method are that

• It should provide a more accurate assessment of the real worth of the project to the company.
• It can deal more transparently with the side effects of financing.

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• The base case NPV stays the same even if assumptions about capital structure change, therefore
fewer recalculations are required.

Limitations of APV
• The equation for asset betas in a taxed world assumes that cash flows are perpetuities. The cash
flows for this investment are not perpetuities.
• APV requires the identification of all financing side effects and their discount at a rate reflecting
their risk. In a complex investment situation, especially an overseas investment, it might be difficult
to identify relevant financing side effects, and their appropriate discount rates.
• Since the regearing process is based on M&M Mode!, it ignores bankruptcy costs, tax exhaustion
and agency costs.

ILLUSTRATION 2 ON ADJUSTED PRESENT VALUE

APV is a well-diversified risk seeking plc. It has a target debt to asset ratio of 25%, an equity beta of 2.25 and
a pre-tax cost of debt of 5%. The company is considering the purchase of a new machine costing N600m,
which would enable it diversify into a new line of business. The machine would have a three-year life after
which it would have no residual value. The machine would generate estimated before tax net cash inflows of
N260m a year. The supplier of the machine is willing to lend APV half of the capital at the rate of 3%. The
remainder will be financed equally by debt and equity. The issue cost on the commercial debt will be 1% and
the equity issue will incur costs of 3%. All issue costs are on the gross amount raised for the respective capital.
A firm that’s already in the trade of the new project has a gearing ratio of 20% (debt to asset) and cost of
equity of 18.1%. its corporate debt is risk free.
A government grant of 10% of the initial cost of the machine is available. It is estimated that the grant will be
received at the beginning of year 2. Tax rate is 30% payable one year in arrears. Straight line depreciation on
the net cost of the machine (after deducting the grant) is tax allowable. The risk free rate is 4% and the market
risk premium is 7%.
You are required to estimate the APV of the proposed project.

SOLUTION TO ILLUSTRATION 2
The gearing ratio of APV is debt 25% and equity 75% while that of the proxy company is 20% debt
and 80% equity.

The base case NPV should be calculated using an ungeared cost of equity
KE = RF + BE(RM- RF) therefore B = 18.1 - 4 / 7 = 2.01
BA = BE x VE/ VE + VD(1 - T) = 80 X 2.014 / 80 + 20(0.7) = 1.71
KEU = 4 + (1.71X7) = 16%
BASE CASE NPV
NET Investment = gross investment less government subsidy = N600m - N60m = N540m
Annual capital allowance = 540m/3 = N180m

Tax savings at 30% = N54m annually year 2 to year 4 because of one year delay.
Item year NCF N.m DCF@16% PV
OUTLAY 0 -600 1.000 -600
SUBSIDY 1 60 0.862 51.72
NET REVENUE 1-3 260 2.246 583.96

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TAX @ 30% 2-4 -78 1.936 -151

TAX SAVINGS 2-4 54 1.936 104.54
NPV -10.78

FINANCING SIDE EFFECTS

Debt finance from supplier N300m at 3%, commercial loan of N150m at 5% and equity finance of
N150m. it should be noted that whenever a company can get a subsidy on the loan, there would be
interest savings.

ISSUE COST;

This is always assumed to occur in year 0 and is on the gross amount (cost % / 100 - cost %)
Commercial loan issue cost = 1/99 x 150 = 1.52 Equity issue cost = 3/97 x 150 = 4.64
Tax savings is assumed to only arise on debt interest = 1.52 x 0.3 = N0.46 m in year 1
The issue cost may be added to the total amount raised in the NPV computation as an outlay.

TAX SAVINGS ON INTEREST PAID

Cheap loan; loan x interest x tax rate =N300m x 0.03 x 0.30 = N2.70m
Commercial loan = (N150m + 1.52m) x 0.05 x 0.30 = N2.27m
Total tax savings = N2.70m + N2.27m = N4.97m in years 2-4.

INTEREST SAVING = cheap loan x difference in interest rate = 300m x (0.05 - 0.03) = N6m (YR 1-
3)
Tax on interest savings = 6m x 0.30 = N1.8m (YR 2-4)
CALCULATION OF PV OF FINANCING EFFECTS

ITEMS YEAR NCF N'm DCF @ 5% PV N'm

ISSUE COST on equity 0 -1.52 1 -1.52

ILLUSTRATION 3 ON ADJUSTED PRESENT VALUE

You have recently commenced working for Airtel co and are reviewing a four-year project which the company
is considering for investment. The project is in a business activity which is very different from Airtell co.’s
current line of business.
The following Net Present Value estimates has been made for the project.
All figures are in N million
YEAR 0 1 2 3 4
Sales revenue 23.03 36.60 49.07 27.14
Direct project cost (13.82) (21.96) (29.44) (16.28)
Interest (1.20) (1.20) (1.20) (1.20)
Profit 8.01 13.44 18.43 9.66
Tax @ 20% (1.60) (2.69) (3.69) (1.93)
Investment/sale (38.00) 4.00
Cash flows (38.00) 6.41 10.75 14.74 11.73

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Discount factors @ 7% 1 0.935 0.873 0.816 0.763

Present values (38.00) 5.99 9.38 12.03 8.95

Net present Value is negative N1.65 million, and therefore the recommendation is that the project should
not be accepted.
In calculating the net present value of the project, the following notes were made:
I. Since the real cost of capital is used to discount cash flows, neither the sales revenue nor the
direct project costs have been inflated. It is estimated that the inflation rate applicable to sales
revenue is 8% per year and to the direct project cost is 4% per year
II. The project will require an initial investment of N38 million. Of this, N16 million relates to
plant and machinery which is expected to be sold for N4 million when the project ceases,
after taking any taxation and inflation impact into account.
III. Tax allowable depreciation is available on the plant and machinery at 50% in the first year
followed by 25% per year thereafter on a reducing balance basis. A balancing adjustment is
available in the year the plant and machinery is sold. Airtell co pays 20% tax on its annual
taxable profits. No tax allowable depreciation is available on the remaining investment assets
and they will have a nil value at the end of the project.
IV. Airtell co uses either a nominal cost of capital of 11% or a real cost of capital of 7% to
discount all projects given that the rate of inflation has been stable at 4% for a number of
years.
V. Interest is based on Airtell co.’s normal borrowing rate of 150 basis points over the 10-year
government yield rate
VI. At the beginning of each year, Airtell co will need to provide working capital of 20% of the
anticipated sales revenue for the year. Any remaining working capital will be released at the
end of the project.
VII. Working capital and depreciation have not been taken into account in the net present value
calculation above, since depreciation is not a cash flow and all the working capital is returned
at the end of the project.
It is anticipated that the project will be financed entirely by debt, 60% of which will be obtained from
a subsidized loan scheme run by the government, which lends money at a rate of 100 basis points
below the 10-year government debt yield rate of 2.5%. Issue costs related to raising the finance are 2%
of the gross finance required. The remaining 40% will be funded from Airtell co.’s normal borrowing
sources. It can be assumed that the debt capacity available to Airtell co is equal to the actual amount
of debt finance raised for the project.
Airtell co has identified a company, Visafone Co, which operates in the same line of business as that
of the project it is considering. Visafone Co is financed by 40 million shares trading at N3.20 each and
N34 million debt trading at N94 per N100. Visafone C0’s equity beta is estimated at 1.5. The current
yield on government treasury bills is 2% and it is estimated that the market risk premium is 8%.
Visafone Co pays tax at an annual rate of 20%.
Both Airtell co and Visafone Co pay tax in the same year as when profits are earned.
I. Calculate the Adjusted Present Value (APV) for the project, correcting any errors made in the net
present value estimate above, and conclude whether the project should be accepted or not. Show
all relevant calculations.
II. Comment on the calculations made to the original net present value estimate and explain the APV
approach taken in part (a) including any assumptions made.

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SOLUTION TO ILLUSTRATION 3
Appropriate cost of capital should be calculated by adjusting the equity beta of the proxy company Note that
for APV; the ungeared cost of equity is used to evaluate the base NPV.
VE = 40m x N3.20 = N128m, VD =N34m X 94/100 = N31.96m
▪ Ungear the equity beta of the proxy company
BA = BE x VE / VE + VD(1 -1) + BD X VD (1 -t)/ VE + VD(1 -t)
BA = 1.5 X 128 / 128 + 31.96(1- 0.2) = 1.25
▪ Ungeared Cost of equity using CAPM = 2 + (1.25 x 8) = 12%

BASE NPV CALCULATION

YEAR 0 Nm 1 Nm 2 Nm 3 Nm 4 Nm
Sales revenue(8%) 24.87 42.69 61.81 36.92
Cost (4%) (14.37) (23.75) (33.12) (19.05)
Tax (0.50) (3.39) (5.44) (3.47)
Working capital (4.97) (3.57) (3.82) 4.98 7.38
Project cost/scrap (38) 4.00
NCF (42.97) 6.43 11.73 28.23 25.78
DCF@12% 1.000 0.893 0.797 0.712 0.636
PV (42.97) 5.74 9.35 20.10 16.40
NPV N8.62m

FINANCING BENEFIT CALCULATION; Note the pre tax cost of debt of 4% is used for evaluation. The risk
free rate can also be used. Always state the rate you use and the justification for the rate.
CF@4% N'm
Issue cost in year 0 = 2/98 XN42.97m =0.88 1.00 (0.88)
Tax shield or Tax savings on interest; year 1-4 = NO.22m 3.63 0.80
Interest savings =0.64m 3.63 2.32
Tax payment on interest savings@ 20% =( 0.13m) 3.63 (0.47)
1.77

APV CALCULATION Nm
BASE CASE NPV 8.62
FINANCING BENEFIT 1.77
APV 10.39

TAX SHIELD WORKINGS

Commercial debt = (N42.97m x 40%) = N17.188m Subsidized debt = (N42.97m x 60%) = N25.782m
Interest on both debt = (17.188m x 0.04) + (25.782m x 0.015) = N0.69m + N0.39m = N1.08m
Tax shield = interest x tax rate = N1.08m x 0.20 = N0.22m

INTEREST SAVINGS ON CHEAPER DEBT

Interest savings = subsidized debt value x (higher interest rate - lower interest rate)

= N25.782m x (0.04-0.015) = N0.64m

TAX payment on the interest saved = N0.64m x 0.20 = NO.13

TAX PAYMENT WORKINGS ALL IN Nm

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YEAR 1 2 3 4
Incremental profit 10.50 18.94 28.69 17.87
Capital allowance (8.00) (2.00) (1.50) (0.50)
Taxable profit 2.50 16.94 27.19 17.37
Tax @ 20% 0.50 3.39 5.44 3.47

WORKING CAPITAL WORKINGS

YEAR 0 1 2 3 4
20% of sales 4.97 8.54 12.36 7.38
Required (4.97) (3.57) (3.82) 4.98 7.38

Note it is on incremental basis and so an increase is an outflow while a decrease is an inflow.

CAPITAL ALLOWANCE WORKINGS

YEAR ITEM Nm Capital Tax savings @ 20% Nm

allowance
0 Cost 16
1 CA@ 50% (8) 8 1.60
TWDV 4
2 CA@ 25% (2) 2 0.4
TWDV 6
3 CA@25% (1.50) 1.50 0.3 4.50
TWDV
4 SCRAP VALUE (4.00)
Balancing allowance 0.50 0.50 0.10

COMMENTS ON THE ORIGINAL NPV CALCULATED

The approach taken to exclude depreciation from the net present calculation is correct, but tax
savings on capital allowances should be brought into the analysis.
Interest is normally taken care of in the discount rate calculations and so should not be part of the
NPV calculations.
Incremental working capital should be part of the analysis as they are subject to different time values
in the present value calculation
The 7% discount rate is inappropriate since it does not consider the financial and business risk of the
new project.
Where different cash flows are subject to different rates of inflation, applying a real rate of return of
7% to non inflated amounts would not give an accurate answer.

SESSION 6: CAPITAL RATIONING AND REPLACEMENT

A capital rationing situation is one in which a company does not have sufficient fund to execute worthwhile
investment projects. Under this situation a company has projects with positive NPV whose combined outlays
all exceed available finance to the company for the same period.

Capital rationing is a situation in which a company has a limited amount of capital to invest in potential
projects such that the different possible investments need to be compared with one another in order to allocate

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the capital available most effectively. It is a technique for selecting projects during a period in descending
order of profitability and accepting them in that order until available funds have been exhausted.

CAUSES / REASONS FOR CAPITAL RATIONING

There are two major reasons that may lead to capital rationing
Soft capital rationing arises as a result of internal factors and is within the control of management.
Hard capital rationing arises as a result of external factors and is beyond the control of management.

ARTIFICIAL /INTERNAL / SOFT CAPITAL RATIONING

This s a rationing situation that is self-imposed within the firm i.e. it is within management’s control. It may
rise for the following reasons.
▪ Management may be reluctant to issue additional share capital because of concern that this may lead
to outsiders gaining control of the business.
▪ Management may be unwilling to issue additional share capital if it will lead to a dilution of earnings
per share.
▪ Management may not want to raise additional debt capital because they do not wish to be committed
to large fixed interest payment (financial risk)
▪ Management may wish to limit the investment to a level that can be financed from internal earnings
only.
▪ Capital expenditure budgets may restrict spending to control expansion

REAL / EXTERNAL / HARD CAPITAL RATIONING

This is a rationing situation that arises due to factors outside the control of the management of the organization
which may be due to
▪ Raising the money through the stock market may not be possible if share prices are depressed.
▪ There may be restrictions on bank Len-ding due to government control
▪ Lending institutions may consider an organization too risky to be granted further loan.
▪ The costs associated with making small issues of capital may be too great.

TYPES OF CAPITAL RATIONING

SINGLE PERIOD CAPITAL RATIONING is a restriction for only one period but will be available in
subsequent period. In this case projects are ranked in terms of profitability index. The following assumptions
hold
▪ If a company does not undertake a project the opportunity is lost i.e. the project cannot be postponed.
▪ There is complete certainty about the outcome of each project so that choice is not affected by risk
consideration.
▪ Projects are divisible, so that it is possible to undertake fractional projects.
Ranking in terms of absolute NPVs will give incorrect results as it leads to selection of large projects each
of which has high individual NPV but which has in total, a lower NPV than a large number of smaller
projects with lower individual NPVs and so Ranking is in terms of what is called the profitability index.

Profitability index is the ratio of the present value of the project’s future cash flows divided by the present
value of the total capital investment.

PI = Gross present value or Benefit loss ratio = Net present value

Initial outlay Excess present value initial outlay
indexes

STEPS IN SOLVING SINGLE PERIOD CAPITAL RATIONING SITUATION

1. Identify the year of restriction
2. Calculate the NPV of project (if not given)
3. Rank all projects using the profitability index

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4. Allocate available finance or funds to all projects in descending order of PI.

5. If a project does not require initial outlay in the year of restriction. It must be ranked first and selected
if it is positive NPV

6. If the project does not require initial outlay in the year of restriction but has negative NPV the cost
benefit ratio of such a project should be compared to the BCR of other viable projects.

TEST: When will a project with negative NPV be considered?

SOLUTION: In a capital rationing situation where there are other projects in the year of restriction with
positive NPV.
NOTE: For indivisible project the ranking is based on trial and error using the NPV and not PI

MULTI PERIOD CAPITAL RATIONING

This is a situation where funds are expected to be limited over several periods. In this case, it becomes difficult
to choose projects or group to projects which yield maximum returns within the limited funds. The solution
under a multi period capital rationing situation is to use mathematical programming; if projects are divisible
use linear programming and if they are indivisible use integer programming. Integer programming is a special
type of linear programming that requires variable to be integers not fractions.

STEPS IN SOLVING MULTI PERIOD PROBLEMS USING LINEAR PROGRAMMING

▪ Identify the variable in the problem
▪ Identify the objective function which is maximization of NPV from all projects
▪ Specify the constraints
▪ Form a linear programming model.

REPLACEMENT DECISION
Replacement decision is the process by which various cost consequences involved are studied so that an
organization can take an optimum replacement decision. Replacement decision enables a financial manager
decide if an asset should be replaced and when or how frequently it should be replaced.

The following elements should be considered in a replacement decision.

i. Capital cost of the asset.
ii. Running costs
iii. Salvage value of the asset
iv. Investment incentives and taxation
v. Opportunity cost
vi. Inflation

EVALUATION OF REPLACEMENT DECISIONS

There are two types of replacement decision
1. IDENTICAL REPLACEMENT DECISION: - which involves deciding how frequently an asset
should be replaced that is the optimum replacement cycle The assets are alike in technicality and
technology. for example, an asset with three-year life span could be replaced every year, every two years
or every three years as its replacement cycle
2. NON INDENTICAL REPLACEMENT DECISION: - which involves deciding when the asset
should be replaced that is the optimum replacement period. This arises when an asset is technically and
technologically different from the existing asset.

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METHOD OF EVAULATING INDENTICAL REPLACEMENT

1. Equivalent Annual cash flow method
2. Lowest common multiple method
3. Finite Horizon method.

EVIQUALENT CASH FLOW METHOD (EAC)

This is the greatest method of deciding the optimum replacement cycle and is applicable only where there is no
specific price inflation affecting cost and residual values. The following steps should be taken
i. Determine the replacement option
ii. For each replacement option estimate the cash flow over the replacement cycle
iii. Calculate the present value after each replacement cycle
iv. Calculate the equivalent annual cost = PV of cost over 1 replacement cycle
Cumulative PV for number of years in cycle
v. The optimal replacement cycle is the cycle with the least annual equivalent cost or the highest annual
equivalent revenue.

LOWEST COMMON MULTIPLE (LCM)

The method examines the cash flow of all possible cycles of the machine over an equal number of years. This
period is usually the least common multiple (LCM) of all cycle. The following steps should be followed:
i. Determine the replacement options
ii. Determine the LCM of all replacement cycles under consideration
iii. For each replacement option estimate the cash flows over the LCM of the period
iv. Discount these cash flows using the after tax cost of capital over the LCM of the period.
v. The option with the lowest PV is the optimum replacement cycle.
It is a very appropriate method in the time of inflation.

FINITE HORIZON METHOD

This method examines cash flows of all cycles over a foreseeable period. Under this method we calculate the
present value of costs over a significant period because the PV of cash flows beyond this period is unlikely to
affect the relative costs of the replacement options. This foreseeable period is normally the length of time
within which the company’s financial management team can generate reliable estimates.

NON INDENTICAL REPLACEMENT OPTION

This involves determining when an existing asset should be replaced and how frequently the new asset would
be replaced. The best option will be the one that gives the lowest present value of cost in perpetuity for both
the existing asset and the asset that eventually replaces it. The following steps should be taken on the
assumption that the new machine should be replaced indefinitely.
i. Determine the optimum replacement of the new asset using any of the methods discussed above.
ii. Using the optimum replacement cycle, calculate the present value of cost to perpetuity of the new asset.
PV of cost to perpetuity => EAC
After tax cost of capital
iii. Determine the replacement option for the existing machine

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iv. Estimate the cash flows for each replacement option including the present value of cost in perpetuity of
the new machine
v. Calculate the present value of each replacement option using firm’s after tax cost of capital
vi. The option with the lowest total present value of cost in perpetuity will be the optimum replacement
policy.

ILLUSTRATIONS ON CAPITAL RATIONING AND REPLACEMENT

ILLUSTRATION 1
The Board of OAP Co has decided to limit investment funds to N10 million for
the next year and is preparing its capital budget. The company is considering five
projects, as follows:
Initial investment Net present value
Project A N2,500,000 N1,000,000
Project B N2,200,000 N1,550,000
Project C N2,600,000 N1,350,000
Project D N1,900,000 N1,500,000
Project E N5,000,000 To be calculated
All five projects have a project life of four years. Projects A, B, C and D are
divisible, and Projects B and D are mutually exclusive. All net present values are
in nominal, after-tax terms.
Project E
This is a strategically important project which the Board of OAP Co have decided
must be undertaken in order for the company to remain competitive, regardless of
its financial acceptability. Information relating to the future cash flows of this
project is as follows:
Year 1 2 3 4
Sales volume (units) 12,000 13,000 10,000 10,000
Selling price (N/unit) 450 475 500 570
Variable cost (N/unit) 260 280 295 320
Fixed costs (N000) 750 750 750 750
These forecasts are before taking account of selling price inflation of 5·0% per
year, variable cost inflation of 6·0% per year and fixed cost inflation of 3·5% per
year. The fixed costs are incremental fixed costs which are associated with Project
E. At the end of four years, machinery from the project will be sold for scrap with
a value of N400,000.
Tax allowable depreciation on the initial investment cost of Project E is available
on a 25% reducing balance basis and OAP Co pays corporation tax of 28% per
year, one year in arrears. A balancing charge or allowance is available at the end of
the fourth year of operation.
OAP Co has a nominal after-tax cost of capital of 13% per year.

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Required:
(a) Calculate the nominal after-tax net present value of Project E and comment on
the financial acceptability of this project. (14 marks)
(b) Calculate the maximum net present value which can be obtained from investing
the fund of $10 million, assuming here that the nominal after-tax NPV of Project E
is zero. (5 marks)
(c) Discuss the reasons why the Board of OAP Co may have decided to limit
investment funds for the next year. (6 marks)
(25 marks)

SOLUTION TO ILLUSTRATION 1
(a) Calculation of NPV

Although the NPV of the project is negative and so financially it is not acceptable, the Board of OAP
Co have decided that it must be undertaken as it strategically important.
Workings

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As Project A is divisible and only N500,000 (20%) of its N2,500,000 initial cost is available after
cumulative investment in Projects E, D and C, the NPV from the project is N200,000 (20% of
Nl,000,000).

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(c) When a company restricts or limits investment funds, it is undertaking 'soft' or internal capital
rationing. Capital rationing means that a company is unable to invest in all projects with a positive
net present value and hence it is not acting to maximise shareholder wealth.
There are several reasons why the Board of OAP Co may have decided to limit investment funds for
the next year. It may not wish to issue new equity finance in order to avoid diluting earning per share.
Issuing new equity finance may also increase the risk of a company's shares being bought by a
potential acquirer, leading to a future takeover bid.
The Board of OAP Co may not wish to issue new debt finance if it wishes to avoid increasing its
commitment to fixed interest payments. This could be because economic prospects are seen as poor
or challenging, or because existing debt obligations are high and so the Board does not wish to
increase them.
The Board of OAP Co may wish to follow a strategy of organic growth, financing capital investment
projects from retained earnings rather than seeking additional external finance. The Board of OAP
Co may wish to create an internal market for capital investment funds, so that capital investment
proposals must compete for the limited funds made available in the budget set by the Board. This
competition would mean that only robust capital investment projects would be funded, while
marginal capital investment projects would be rejected.

ILLUSTRATION 2 ON CAPITAL RATIONING

Slow Fashions Co is considering the following series of investments for the current financial year 20X9:
Project bid proposals (₦'000) for immediate investment with the first cash return assumed to follow in 12
months and at annual intervals thereafter.
Project Now 20Y0 20Y1 20Y2 20Y3 20Y4 20Y5 , NPV IRR
PO8O1 –620 280 400 120 55 16%
PO8O2 –640 80 120 200 210 420 –30 69 13%
PO8O3 –240 120 120 60 10 20 15%
PO8O4 –1000 300 500 250 290 72 13%
PO8O5 –120 25 55 75 21 19 17%
PO8O6 –400 245 250 29 15%
There is no real option to delay any of these projects. All except project P0801, can be scaled down but not
scaled up. P0801 is a potential fixed three-year contract to supply a supermarket chain and cannot be varied.
The company has a limited capital budget of $1.2 million and is concerned about the best way to allocate its
capital to the projects listed. The company has a current cost of finance of 10% but it would take a year to
establish further funding at that rate. Further funding for a short period could be arranged at a higher rate.
Required
(a) Draft a capital investment plan with full supporting calculations justifying those projects which should be
adopted giving:
(i) The priorities for investment
(ii) The net present value and internal rate of return of the plan
(iii) The net present value per dollar invested on the plan (14 marks)
(b) Estimate and advise upon the maximum interest rate which the company should be prepared to pay to
finance investment in all of the remaining projects available to it. (8 marks)
Assume that there is a real option to delay projects PO802 and PO804 for a further year, when capital will not
be restricted. Explain, without further calculations, how this would change the answer to part “a”.
SOLUTION TO ILLUSTRATION 2
(a) Capital investment plan Restrictions:
(i) Project P0801 cannot be scaled down - this project cannot be varied.

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(ii) No project can be scaled up.

(iii) Capital budget is N1.2 million.
In capital rationing situations, projects should be ranked according to the profitability index (PI)
which is the NPV per N of invested capital at year zero. Before we can rank the projects, we must
calculate the PI for each.

Project Initial investment NPV IRR PI Ranking

N'000 N'000
P0801 (620) 55 16% 0.0887 3
P0802 (640) 69 13% 0.1078 2
P0803 (240) 20 15% 0.0833 4
P0804 (1,000) 72 13% 0.072 6
P0805 (120) 19 17% 0.1583 1
P0806 (400) 29 15% 0.0725 5

Now that we have established the order in which investments should be made, we have to determine
how many of the projects we can afford, subject to the restrictions above.

Project Initial investment NPV IRR PI Cumulative investment

N'000 N'000 N'000
P0805 (120) 19 17% 0.1583 (120)
P0802 (640) 69 13% 0.1078 (760)
P0801 (620) 55 16% 0.0887 (1,380)
P0803 (240) 20 ' 15% 0.0833 (1,620)
P0806 (400) 29 15% 0.0725 (2,020)
P0804 (1,000) 72 13% 0.072 (3,020)

The marginal project is P0801. Our problem is that this project cannot be scaled down - it is the
supermarket project that cannot be varied. We now have two choices. We can move P0801 above
P0802 (which can be scaled down) in the ranking - this would allow us to undertake the supermarket
project in its entirety. Alternatively, we could remove P0801 from the problem completely and
ignore it. This would move the other projects up the rankings. The choice with the higher overall
NPV should be undertaken. Choice 1 - move P0801 above P0802

Project Initial NPV Cum Proportion of NPV from

investment investment project investment
N'000 N000 N'000 N'000
P0805 (120) 19 (120) 1 19.00
P0801 (620) 55 (740) 1 55.00
P0802 (640) 69 (1,380) 0.71875 49.59

Total NPV 123.59

Note: the proportion of P0802 that is undertaken is calculated as follows: Proportion = (Capital
budget - cumulative investment to date) / investment required = (Nl,200 - N740) / N640 = 0.71875

Choice 2-ignore P0801

Project Initial NPV Cum Proportion of NPV from

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investment investment project investment

N'000 N'000 N'000 N'000
P0805 (120) 19 (120) 1 19.00
P0802 (640) 69 (760) 1 69.00
P0803 (240) 20 (1,000) 1 20.00
P0806 (400) 29 (1,400) 0.5 14.50

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in the second year when capital is not restricted, although the net present value would be lower than
N72,000, as all associated cash flows would be delayed by one year.
P0802 can now be delayed until the second year, which would allow the whole of project P0803 to
be undertaken as well as (220/400 = 55%) of Project P0806. Again the NPV from project P0802 will
be lower than N69,000 as all cash flows are delayed, but Slow Fashions Co is highly likely to
generate additional overall shareholder wealth from undertaking the two extra projects. Detailed
calculations would need to be performed to support this analysis.

ILLUSTRATION 3 ON REPLACEMENT
No time plc uses regularly a machine which costs N50,000 when new. The machine’s resale value is
N30,000 after 1 year, N17,000 after 2 years, N5,500 after three years and nil after 4 years which is the
maximum physical life. The machine’s annual revenues and costs, which arise on the last day of each year
and vary according to the machine’s age, are as follows:
NET REVENUE N RUNNING COSTS
N
During the ist year of machine’s life 40,000 4,000
During the 2nd year of machine’s life 37,500 5,000
During the 3rd year of machine’s life 35,000 7,000
During the 4th year of machine’s life 31,250 10,000
A deciding factor influencing the company is the possibility of a breakdown, since such an occurrence in
repairs and lost work will cost N10,000 a time. Records show the probability of a break down during the
machine’s first year is 0.05, second year is 0.25, third year is 0.45 and 4th year is 0.75. A break down in
any year, incidentally, in no way affects the probability of break-down in a future year, though it reduces
the probability of a break-down later in the same year to a negligible figure. Cost of capital is 15%.
Prepare calculations showing whether Notime plc should continue to replace the machine in the future
and, if so, at what age should the machine be replaced (assume that the replacement will take place at the
end of the year.

SOLUTION TO ILLUSTRATION 3
This is an illustration on both identical and non - identical replacement. To solve this illustration you
need to solve the identical replacement issue (frequency of replacement) and use the result to solve
the non-identical replacement. Determine the net cash flow

YEAR 1 2 3
REVENUE 1,800 1,600 1,400
COST (800) (700) (700)
NCF 1,000 900 700

OPTION 1; REPLACE EVERY 1 YEARS

ITEM YEAR NCF N DCF@10% PV N
OUTLAY 0 (2,000) 1.00 (2,000)
NCF 1 1,000 0.91 910
SCRAP VALUE 1 1,300 0.91 1,183
NPV 93

AEV = NPV/CDF FOR 1 YEAR = 93/0.91 = N102

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OPTION 2; REPLACE EVERY 2 YEARS

ITEM YEAR NCF N DCF@10% PV N
OUTLAY 0 (2,000) 1.00 (2,000)
NCF 1 1,000 0.91 910
NCF 2 900 0.83 747
SCRAP VALUE 2 800 0.83 664
NPV 321

AEV = NPV/CDF FOR 2 YEARS = 321/1.74 = N184

OPTION 3; REPLACE EVERY 3 YEARS
ITEM YEAR NCF N DCF @ 10% PV N
OUTLAY 0 (2,000) 1.00 (2,000)
NCF 1 1,000 0.91 910
NCF 2 900 0.83 747
NCF 3 700 0.75 525
SCRAP VALUE 3 300 0.75 225
NPV 407
AEV = NPV/CDF FOR 2 YEARS = 407/2.49 = N163

The optimal replacement policy would be to replace every 2 years to give the highest AEV N184

NON- IDENTICAL REPLACEMENT

You can replace now, replace after one year or after 2 more years. Discounting should be done over
the remaining two years. The relevant cash flows are the AEV, the NCF, repair cost and salvage
value. Note that the repair cost nor cash flow will not be relevant if we are replacing now. The net
cash flow is the difference between revenue and cost.

REPLACE NOW
ITEM YEAR NCF N DCF@10% PV N
SCRAP VALUE 0 500 1.00 500
AEV 1-2 184 1.74 320
NPV 820

REPLACE AFTER ONE YEAR

ITEM YEAR NCF N DCF@10% PV N
REPAIR COST 0 (200) 1.00 (200)
NCF 1 600 0.91 546
SCRAP VALUE 1 400 0.91 362
AEV 2 184 0.83 153
NPV 861

REPLACE AFTER TWO YEARS

ITEM YEAR NCF N DCF@10% PV N
REPAIR COST 0 (200) 1.00 (200)
REPAIR COST 1 (500) 0.91 (455)
NCF 1 600 0.91 546
NCF 2 520 0.83 432

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SCRAP VALUE 2 100 0.83 83

NPV 406

The optimal replacement policy would be to replace after one year.

ILLUSTRATION 4 ON CAPITAL RATIONING AND REPLACEMENT

ABC Limited is a large civil engineering company and it has a financial year end of 31 May.
Much of ABC work involves long term contracts for the railway industry. You work for ABC
and have been asked for advice by the board on the following problems:
PROBLEM 1
ABC is considering a major investment involving five possible projects in the south-west which
have been put out to tender. The board of directors have prepared the following estimated cash
flows (and resultant net present values at 31 May 2017) for the five projects.
PROJECT LOCATION Investment on Year to Year to Year to NPV
31/5/2017 31/5/2018 31/5/2019 31/5/2020
N’000 N’000 N’000 N’000 N’000
B Lagos (4,150) (1,290) 530 7,270 577
C Ibadan (3,870) (1,310) 3,130 1,550 (1,309)
G Abeokuta (6,400) 1,770 2,160 3,160 (632)
S Ilorin (5,000) (2,610) 6,450 6,520 2,856
T Akure (4,600) 1,290 2,870 3,620 1,664
You can assume that the net present values shown in the table above are accurate.
Due to financial constraints, the company, if successful with its tenders, would be unable to take
on all five projects. The board is prepared to release N8 million for initial investment (on 31 May
2017) into one or more of the projects, but might increase this figure to N9 million if there are
grounds for doing so. An alternative scenario which has been considered would be to make
available sufficient funds to start all five projects in May 2017, but this would limit the capital
available in the year to 31 May 2018 to a maximum of only N500,000.
PROBLEM 2
ABC runs a fleet of vans to support its operations. Currently it replaces those vans every three
years but the board is not sure whether this is in the company’s best interests. Vans cost, on
average, N12,400 each. ABC transport manager has prepared the following schedule of cost and
resales value for the vans:
Maintenance and running costs N Resale value N
In first year of van’s life 4,300 After one year 9,800
In second year of van’s life 4,800 After two years 7,000
In third year of van’s life 5,100 After three years 5,000

PROBLEM 3

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About a year ago (March 2016), ABC completed construction of a factory for Bakomi Ltd. This
cost ABC N720,000 to construct and Bakomi is paying N190,000 a year for 8 years. ABC will
therefore ultimately make a profit of N800,000, which gives a return on the investment of over
100%. When Bakomi sent its first annual instalment last week, it indicated that rather than make
annual payments it would prefer to settle the outstanding balance by making a one off payment
of N925,000 in a year’s time (March 2018). One of ABC’s directors is keen on this proposal
stating “I know that this is less than we would receive over the full eight years, but my
calculations show that the internal rate of return would be much better.
GENERAL INFORMATION
a. ABC uses a cost of capital of 10% when appraising possible investments
b. You should assume that all cash flows take place at the end of year in question
c. All projects are independent
Requirements
1. For Problem 1, assuming that all of the projects are divisible and
a. Assuming that ABC has no capital rationing, advise its directors as to which projects
should be accepted (2 marks)
b. Assuming that the directors are prepared to spend a maximum of N8 million on 31 May
2017, advise them as to which projects should be adopted (3 marks)
c. Assuming that the directors are prepared to make available sufficient funds to start all
five projects on 31 May 2017, but only N500,000 on 31 May 2018, advise them as to
which projects should be accepted (5 marks)
2. For problem 1, assuming that none of the projects are divisible and that the directors are
prepared to spend a maximum of N9 million on 31 May 2017, advise them as to which
projects should be accepted (4
marks)
3. For problem 2, advise the directors as to the optimal replacement period for ABC vans
and comment on the limitation of the approach used (6
marks)
4. For problem 3, advise the directors as to whether they should accept Bakomi’s proposal
(5 marks).
Ignore taxation.

SOLUTION TO QUESTION 4
To assess the worthiness of the machine, and its optimal replacement age, it is necessary to calculate
the NPV of each possible life cycle. The NPVs are then converted to AEV. Provided that at least one
of these is positive, purchase of the machine is worthwhile. The optimal life cycle is the one with the
highest AEV - when dealing with the revenue generating asset.
The expected breakdown cost annually should be calculated;
Year Cost N Probability - Expected value N
1 10,000 0.05 500
2 10,000 0.25 2,500

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3 10,000 0.45 4,500

4 10,000 0.75 7,500
ANNUAL NET CASH INFLOWS
CYCLE NET Revenue N Running cost N Breakdown cost Net inflow N
N
1 40,000 4,000 500 35,500
2 37,500 5,000 2,500 30,000
3 35,000 7,000 4,500 23,500
4 31,250 10,000 7,500 13,750
Compute the NPV and AEV of each option
OPTION 1; REPLACE EVERY YEAR
YEAR ITEM NCF N DCF@15% PV
0 OUTLAY (50,000) 1.00 (50,000)
1 NCF 35,500 0.87 30,885
1 Scrap value 30,000 0.87 26,100
NPV 6,985
AEV = NPV/CDF 6,985/0.87 N8,029
OPTION 2: REPLACE EVERY 2
YEARS
YEAR ITEM NCF N DCF@15% PV N
0 OUTLAY (50,000) 1.00 (50,000)
1 NCF 35,500 0.87 30,885
2 NCF 30,000 0.76 22,800
2 Scrap value 17,000 0.76 12,920
NPV 16,605
AEV = NPV/CDF 16,605/1.63 N10,187
OPTION 3; REPLACE EVERY 3
YEARS
YEAR ITEM NCF N DCF@15% PV N
0 OUTLAY (50,000) 1.00 (50,000)
1 NCF 35,500 0.87 30,885
2 NCF 30,000 0.76 22,800
3 NCF 23,500 0.66 15,510
3 SCRAP VALUE 5,500 0.66 3,630
NPV 22,825
AEV = NPV/CDF 22,825/2.28 N10.011
OPTION 4; REPLACE EVERY 4
YEARS
YEAR ITEM NCF N DCF@15% PV N
0- OUTLAY (50,000) 1.00 (50,000)
1 NCF 35,500 0.87 30,885
2 NCF 30,000 0.76 22,800
3 NCF 23,500 0.66 15,510

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4 NCF 13,750 0.57 7,838

4 SCRAP VALUE 0 0.57 0
NPV 27,033
AEV = NPV/CDF 27,033/2.86 N9,452
CONCLUSION; purchase of the machine is worthwhile while replacement every two years is
most worthwhile.

ILLUSTRATION 5 ON MULTI-PERIOD CAPITAL RATIONING

A company has N9 million to invest in year 0 and N6 million to invest in year 1. There are three
projects available for investment, all similar in terms of risk. The amount of investment required
and the NPV of each project are as follows:
PROJECT Capital required at Year 0 Capital required at Year 1 NPV
N’m N’m N’m
X 6 3 +4.0
Y 2 1 +2.0
Z 5 2 +2.0
There is capital rationing in both year 0 and year 1 because in each year the capital available for
investment is less than the total needed to invest in all three projects.
a. Construct the above problem in a Linear programming problem
b. Prepare the above information in a simplex model (initial tableau)
FINAL TABLE
SOLUTION X Y Z S0 S1 UX UY UZ Total
TABLEAU
Z 0 2 5 1 0 -6 0 0 0.2
S1 0 1 2 0 1 -3 0 0 1.6
X 1 0 0 0 0 1 0 0 1.0
Y 0 1 0 0 0 0 1 0 1.0
UZ 0 0 1 0 0 0 0 1 0.8
Objective 0 0 0 0.6 0 1.6 0.8 0 6.4
Function
c. Explain the final solution from the simplex final table above
d. What would be the expected return if N1,000,000 is added to the available capital in year
0 and year 1.

SOLUTION TO QUESTION 5
PROJECT 1

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YEAR DESCRIPTION VALUE N DCF@12% PV N

0 INITIAL OUTLAY (300,000) 1.000 (300,000)
1 CASH FLOW 85,000 0.893 75,905
2 CASH FLOW 90,000 0.797 71,730
3 CASH FLOW 95,000 0.712 67,640
4 CASH FLOW 100,000 0.636 63,600
5 CASH FLOW 95,000 0.567 53,865 NPV
32,740 Profitability index = NPV/ initial outlay = 32,740 /
300,000 = 0.11

PROJECT 2
YEAR DESCRIPTION VALUE N DCF@ 12% PV N
0 Initial outlay (450,000) 1.000 (450,000)
1-5 Cashflow 140,800 3.605 507,584
NPV 57,584
Profitability index = NPV/ initial outlay = 57,584 / 450,000 = 0.13

PROJECTS 3
The cash-flows are stated in real terms and so real cost of capital should be used to discount it.
Convert the money cost of capital to real cost of capital and calculate NPV.
RCC = (1 + MCC) / (1 + INF) - 1 = (1.12/1.036) - 1 = 8.1%

YEAR DESCRIPTION VALUE N DCF@ 8.1% PV N

0 Initial outlay (400,000) 1.000 (400,000)
1-5 Cashflow 120,000 3.981 477,720
NPV 77,720
Profitability index = NPV/ initial outlay f 77,720 / 400,000 = 0.19

▪ WHEN PROJECT ARE DIVISIBLE: ALLOCATION of available funds is based on

profitability index ranking in descending order. The most profitable projects are project 3,
project 2 before project 1. Note that you get an NPV equivalent to the proportion invested.

RANKING Amount invested Available N NPV

N
1STPROJECT 3 400,000 N 800,000 77,720
2ND PROJECT 2 400,000 (balance) 400,000 400/450 x 57,584 =51,186
Total NPV 128,906

▪ When projects are indivisible; a trial method is applied to get the project combination that
has the highest NPV.
PROJECTCOMBINATION TOTAL OUTLAY N TOTALNPV N
1 and 2 750,000 90,325
2 and 3 850,000 Beyond available capital
1 and 3 700,000 110,531
Choose project 1 and 3.

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SESSION 7: LEASING
Lease is a contract between the lesser, the owner of the asset, and a lessee the use of the asset where the owner
gives the right to the asset to the user over an agreed period of time for a consideration called the lease rental.

Lease agreement is defined by SAS II as a contractual agreement between an owner (the lessor) and another
party (the lessee) which conveys to the lessee the right to use the leased asset for an agreed period of time in
return for a consideration usually periodic payments called rents.

The lessor has ownership of the asset while the lessee has possession and use of the asset on payment of
specified rentals over a period. It could be an up fronted lease where more rentals are charged in the initial
years and has in the later years or back ended lease where vice versa.

Sometimes the lease agreement is divided into primary lease which provides for recovery of the cost of the
asset and profit through lease rental and a secondary lease which provides for nominal+ lease rentals (pepper
corn rent) to infinity.

LEASE AGREEMENT PROVISIONS

It is essential that rules setting out rights and responsibilities of the parties to the contract should be made and
given to the parties. According to SAS II the following are the things to be expressly agreed upon a lease
agreement
▪ Duration of the lease
▪ Rental payments (periodic cash outlays)
▪ Restrictions which may be prohibition of further debt
▪ Imposition of obligations
▪ A default clause which specifies what constitutes a default, the rights of the lessor and the penalties
imposed under such condition
▪ Termination provisions (conditions and penalties or prohibition of cancellation)
▪ Options available to the lessee where the lease terms run its full course.

TYPES OF LEASE AGREEMENTS

There are two main types of lease agreement they are
Finance lease
Operating lease

FINANCE LEASE / CAPITAL LEASE

This is a lease agreement in which ownership, risks and rewards are transferred to the lessee who is obligated
to pay such cost as insurance, maintenance and similar charges on the property. Usually the agreement is non-
cancellable and the lessee has the option to buy the property for a nominal amount upon the expiration of the
lease.

CONDITIONS FOR FINANCE LEASE

▪ The lease transfers ownership of the asset to the lessee by the end of the lease term
▪ The lessee has the option to buy the asset at a price expected to be lower than fair value of that time
▪ At the beginning of the lease the present value of the minimum lease payment is approximately equal
to the fair value of the asset
▪ The leased assets are of a specialized nature major modification
▪ If the lease gives the lessee the right to cancel the lease, the lessor’s losses associated with the
cancellation are borne by the lessee
▪ Gain or loss from fluctuation in fair value are borne by the lessee
▪ The lessee has the ability to continue the lease for a secondary period at a rent below the marked rent
(pepper corn rent).

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▪ The present value of the minimum lease payments must amount to more than 90% of the fair value of
the leased asset.

OPERATING LEASE
This is a lease in which the lessor retains most of the risk and reward of ownership. He supplies the equipment
to the lessee, services, repairs and maintaining the leased equipment for a period which is shorter than the
economic life of the asset. At the end of the lease the asset can be sold second hand or rent to someone else.

FINANCE LEASE OPERATING LEASE

iLong term source of finance - Short term source of finance
ii 10 years most or all the useful life of asset - Shorter than useful life of asset
iii. Can be divided into primary and secondary -Has only primary period
iv. Lessee bears the risk and reward of -Lessor bears the risk and reward of ownership.
Ownership
v. Lessee repairs, services and maintains asset -Lessor repairs, maintains and service asset
vi. Lessor may not be dealing in such asset -Lessor should be dealing in such asset vii.
Lease payments are usually made at the end -Lease payments are usually made of the
of the year start of the year
viii. The substance of the transaction is a loan from-The substance of the transaction is a
the lessor to lessee for an asset rental by lessee from lessor.
ix. Cannot be cancelled -Can be cancelled at short notice
x. Lessee can claim tax savings on capital -Lessor claims tax savings on capital
allowance allowance
xi. Asset cost and rentals are capitalized on the -They are treated as financing off balance sheet.
balance sheet

OTHER LEASE TERMINOLOGIES OR VARIANTS

LEVERAGED LEASE – This is a three party lease involving the lessor, lessee and the financier. The lessor
(leasing company) provides equity equal to about 25% of the assets cost while the remaining amount is
provided by the financier (a bank or financial institution) mainly as loan. Leverage lease is a popular method of
financing expensive assets. (mortgage on asset, exclusive financed by lease rentals)

➢ SALES AND LEASE BACK is a lease agreement where the lessor first sells the asset owned by him
to the lessee and then leases it back from the lessee on terms specified in the agreement. This provides
liquidity as well as possible tax gains to the lessee which still keeps possession of the asset.

CROSS BORDER LEASE is a lease where the lessor and lessee are situated in two different countries. It
involves relationship and tax implications more complex than the domestic lease. When it is between
manufacturers, lessor and lessee in three different countries it is called foreign to foreign lease.

DIRECT LEASE –is a mix of operating and finance lease on a full payout basis and provides for the purchase
to the lessee.

DIRECT FINANCE LEASE – is a lease which transfers substantially all ownership risk and benefits of the
asset to the lessee with the fair value of the asset being equal to the carrying amount to the lessor at the
inception of the lease.

SALES TYPE LEASE – This is the one where the lessor transfers substantially all ownership risks and
benefits to the lessee with the fair value of the property being greater or less than its carrying amount in the
lessors’ books at the inception of the lease resulting in a profit or loss to the lessor.

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CLOSED LEASE – is one in which the assets get transferred to the lessor at the end and the risk of
obsolescence, residual value remain with the lessor as the legal owner of the asset while in open ended lease
the lessee has the option of purchasing the asset at the end of the lease.

MASTER LEASE – provides for a period longer than the asset’s life and holds the lessor responsible for
providing equipment in good operating condition during the lease.

PERCENTAGE LEASE – provides for a fixed rent plus some percent of the previous year’s gross revenue to
be paid to the lessor as protection against inflation.

WET AND DRY LEASE – in the Air craft industry when the lease involves financing as well as servicing
and fuel, it is called wet lease and if it provides only for financing it is a dry lease.

UPDATE LEASE – is intended to protect the lessee against the risk of obsolescence. The lessor agrees to
replace obsolete asset with new one of specified rent.

TRIPLE NET LEASE – lessee takes care of maintenance, taxes and insurance of equipment
BALLON LEASE – is a variation of finance lease where the lessor pre-determines the sales value of the asset
at the end of the lease as the final ballon payment which is due on a fixed determinable future date (terminal
date of lease) whether or not the asset is actually sold at the that date.

ADVANTAGES OF LEASING – TO LESSEE

1. It is alternative source of making use of an asset for which a company is unable to raise funds to
purchase.
2. It may be easier to arrange than a bank loan especially for small companies
3. It may be cheaper than bank loan.
4. Operating lease ensures that the leased equipment is not shown in the balance sheet (off balance sheet
financing) and so no effect on gearing ratio
5. Operating lease is flexible and so the lessee can cancel the contract where the asset becomes obsolete.
6. The lessee enjoys tax savings from lease rentals paid
7. Under operating lease the lessor repairs the asset for the lessee’s use
8. Leasing could be a hedge against inflation.

TO THE LESSOR
1. He enjoys tax savings on capital allowance of the assets
2. He gets consistent income from lease rentals paid
3. Under a finance lease the lessee repairs the asset
4. He gains where interest rates fall and lease rentals are fixed
5. He is guaranteed payment whether profits are made or not

DISADVANTAGES OF LEASING TO LESSEE

1. The rentals are payable whether profits are made or not
2. The lessee loses where interest rate falls and rentals remain fixed
3. He bears the risks in a finance lease
4. The lessee is tied to the asset even if it is obsolete under finance lease
5. In an operating lease the agreement can be cancelled at short notice

TO THE LESSOR
1. He loses where interest rates rise and rentals remain fixed
2. The asset is not shown in his book under finance lease
3. He does not enjoy the capital allowance on the asset
4. The decision may be irreversible under a finance lease.

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LEASE OR BUY DECISIONS

This involves two steps
Acquisition decision – is the asset worth having? Discounting cash flows at a suitable cost of capital
Financing decision – if the asset should be acquired, compare the cash flows of purchasing and leasing or hire
purchase arrangements discounted at an after tax cost of borrowing.

HIRE PURCHASE / VENDOR CREDIT

This is the acquisition of assets on credit with settlement to be made through installmental payments.
Manufacturers sells asset to the hiree who sells it to the hiree in exchange for the payment to be made over a
specified period of time.

CONDITIONS OF HIRE PURCHASE AGREEMENT

Owner of asset (hiree or manufacturer) gives possession of the asset to the hirer with understanding of agreed
installments over a specified time period
The ownership of the assert will transfer the hirer on the payment of all installments.
The hirer will have the option of terminating the agreement any time before the transfer of ownership of asset.

DIFFERENCE BETWEEN LEASING AND HIRE PURCHASE FINANCING

HIRE PURCHASE FINANCING LEASING
Entitled to claim capital allowance Not entitled to claim capital allowance
Hp payments include interest and repayment Lessee can charge the entire lessee payments for of
principal. Hirer gets tax benefits on the tax on lease payments
interest.
Once all installments are paid hirer Lessee does not become owner of the asset and becomes
owner of asset and can claim has no claim over salvage value
salvage value

Hire purchase agreement differs from installmental sale in the sense that ownership passes with possession
under installmental sales even before any payment is made while the full payment must be made under Hp for
title to pass.

ADVANTAGES OF HIRE PURCHASE

1. It is an alternative source of financing
2. The hirer is entitled to capital allowance on the asset
3. He enjoys tax relief on the interest paid

TO HIREE
1. Guaranteed source of income over a period of time

DISADVANTAGE OF HIRE PURCHASE

1. The interest rate may be higher than other sources of finance
2. The instalment payment is made whether or not profit is made
3. An initial deposit must be made

TO HIREE
1. Not entitled to capital allowance on the assets.

CONCEALED GEARING / OFF BALANCE SHEET FINANCING

This is a method of financing an organization by the use of debt which is not disclosed in the balance sheet due
to the nature of the transaction such as operating lease, factoring, use of quasi subsidiary etc. In such situations
the gearing ratio of the company is not affected.

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ILLUSTRATIONS ON LEASING
ILLUSTRATION 1 ON LEASING
A large retailing organization in Nigeria with revenue exceeding N5 billion in the last financial year has
opened several new stores in a number of Asian countries. It is planning to allow all of its stores to accept
the world’s major currencies as cash payment for its goods and this will require a major upgrade of its
point of sales (POS) system to handle multiple currencies and increased volumes of transactions.
The company has already carried out a replacement investment appraisal exercise and has evaluated
appropriate systems. It is now in the process of placing an order with a large information technology entity
for the supply, installation and maintenance of a new POS system. The acquisition of the system will
include provision of hardware and software. Routine servicing and software upgrading will be arranged
separately and does not affect the investment appraisal decision.
The company is considering the following methods of acquiring and financing the new POS system
ALTERNATIVE 1
Pay the whole capital cost N50 million on 1 January 2015, funded by bank borrowings which includes the
initial installation cost of the POS system. The system has no resale value outside the company.
ALTERNATIVE 2
Enter into a finance lease with the system supplier. The company will pay a fixed amount of N14 million
each year in advance commencing 1 January 2015, for 4 years. At the end of 4 years, ownership of the
system will pass to the company without further payment.
OTHER INFORMATION
a. The company can borrow for a period of 4 years at a pre-tax fixed interest rate of 7% a year. The
entity’s cost of equity is currently 12%.
b. The company is liable to corporate tax at a marginal rate of 30% which is settled at the end of the year
in which it arises
c. Tax depreciation allowances on the full capital cost are available in equal instalments over the first
four years of operation
▪ Calculate which payment method is expected to be cheaper for the company and recommend
which should be chosen solely on the present value of the two alternatives as at 1 January 2015
explaining the reasons for your choice of discount factor in the present value calculations.

SOLUTION TO ILLUSTRATION 1
The appropriate discount rate to use for a financing decision is the cost of borrowing net tax 7(0.70)
= 4.9%.

ALTERNATIVE 1; Borrow and Buy

YEAR ITEM NCF N'm DCF@4.9% PV N'm

0 Purchase cost -50 1 -50
1-4 Tax savings on allowance 50m/4 x 30% 3.75 3.554 13.33
NPV NPV -36.67

ALTERNATIVE 2; FINANCE LEASE

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Interest = payments due less cost = (14m x 4) - 50 = N6m

Annuity factor = amount left / annual payment = 50m - 14m / 14m = 2.5714 after 3 years is 8%.
Internal rate of return can be used to calculate the interest rate.

year BaS b/f Interest @ Rental Nm Principal N'm Bal c/d Tax saving
N'm 8% N'm
0 50 0 14 14 36
1 36 2.88 14 11.12 24.88 N0.86m
2 24.88 1.99 14 12.01 12.87 N0.60m
3 12.87 1.13 14 12.87 0 N0.34m
6.00 56

NPV CALCULATIONS
YEAR 0 N'm 1 N'm 2 N'm 3 N'm
Lease rentals -14 -14 -14 -14
Tax savings on interest 0 0.86 0.60 0.34
Net cash flow -14 -13.14 -13.40 -13.66
Dcf @ 4.9% 1.000 0.953 0.909 0.866
Present value -14 -12.52 -12.18 -11.83
Total value -50.53
TAX savings on capital allowance 13.33
NPV -37.20

The purchase option offers a lower PV of N530,000.

ILLUSTRATION 2 ON OPERATING LEASE

Today is 1 September 2015, Bratim a company based in Nigeria has adopted International Financial Reporting
Standards.
It is currently preparing a bid for a government contract to operate a train service on a new high speed rail link
between Abuja and Lagos. The investment appraisal of the project has been completed and shows that the
project is financially beneficial. The focus of attention has now shifted to considering how best to finance the
initial investment required in the new rolling stock (locomotives and carriages) that is needed to run on the
line.
The rail link would be operated by Bratim for a period of ten years commencing on 1/1/16. The new rolling
stock required would cost N500 million if bought outright. Assume that there is an active market in second
hand rolling and it is estimated that the rolling stock could be sold at the end of the 10-year period for N220
million.
The following two alternative financing approaches are being considered:
a. Bank borrowing from its primary bank for a ten-year term together with outright purchase of the
rolling stock

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b. A ten year operating lease provided by the supplier of the rolling stock
BANK BORROWING AND OUTRIGHT PURCHASE
▪ Bratim would buy the new rolling stock on 1 January 2016.
▪ It can borrow from its primary bank at a 2.5% credit margin above the bank’s published base rate.
The bank’s base rate is currently set at 3.5% but can be expected to change in line with changes in
market interest rates
▪ Maintenance costs are expected to be of the order of N15 million per year if Bratim purchases the
rolling stock outright.
OPERATING LEASE
▪ An initial up-front payment of N58 million would be payable at the start of the lease on 1 January
2016
▪ The further lease payments of N58 million each would be payable on 31 December in each year
starting on 31 December 2016.
▪ The lessor retails responsibility for maintaining the rolling stock throughout the period of the lease and
has included the cost of maintenance service costs within the lease payments
ADDITIONAL INFORMATION
▪ The company’s financial year runs from 1 January to 31 December
▪ The company pays company income tax at a rate of 33.33% payable annually at the end of the
year following that in which the tax charge or tax saving arises.
▪ 100% tax depreciation allowances are available at the time of acquiring an eligible asset such as
rolling stock
▪ Lease payments made by Bratim would be allowable for tax when they are incurred
Required
▪ Evaluate using a discounted cash flow approach as at 1 January 2016, whether it would be
cheaper for Bratim to buy and borrow or enter into operating lease for the new rolling stock.
▪ Advise on the impact of each of the two alternative financing approaches on Bratim’s
statement of financial position.
▪ Advise Bratim which type of financing approach to choose, taking into account your findings
in (a) and (b) & other relevant factors.
SOLUTION TO ILLUSTRATION 2
The tax effects of the transaction need to be considered carefully. Transactions of 31/12/16 and
1/1/17 for discounting purposes will fall into same year but fall into different years for tax purposes.

After tax cost of debt; (2.5 + 3.5) (1 - 0.333) = 4%

ALTERNATIVE 1; BORROW OR BUY

YEAR item NCF N'm DCF@4% PV N'm

0 Purchase cost (500) 1.000 (500)
2 Tax relief 165 0.925 152.63
1-10 Maintenance cost (15) 8.111 (121.67)
2-11 Tax savings on maintenance 5 7.799 39.00
10 Residual value 220 0.676 148.72

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11 Tax charge on residual (73.33) 0.650 (47.66)

Value
NPV (329)

ALTERNATIVE 2 ; OPERATING LEASE

YEAR ITEM NCF N'm DCF@4% PV N'm
0 Initial lease payment (58) 1.000 (58)
2 Related tax relief 19.33 0.925 17.88
1-10 Lease payments (58) 8.110 (470.44)
2-11 Related tax relief 19.33 7.799 150.75
(360)

Recommendation; it is cheaper to borrow and buy.

B QUESTION IS ON ALTERNATIVE FINANCING
The operating lease does not have that grossing effect on the financial statements like the buying
alternative as neither the asset value nor accrued lease payments are reflected in the statement of
financial position.

Using an operating lease therefore has the beneficial effect on the financial statements of lower
gearing and lower bank borrowings, which potentially could make it easier for the company to raise
finance in the future.
The international accounting standard board is currently looking at bringing operating lease
commitments onto a company's statement of financial position.

C PART OF THE QUESTION ON FINANCING OPTION

The borrowing approach appears to be slightly less expensive than the operating lease approach;
however the buy approach has the disadvantage of grossing up the statement of financial position
with both the total borrowing and the value of the asset. This should be considered as well as;

▪ Risk due to variable rate basis for the bank interest cost
▪ Lease payments have made provisions for maintenance cost but under buy approach
additional liquidity may have to be in place to meet any additional maintenance cost
▪ Real option may have a major impact on the choice option; the company under the buy
approach owns the asset and so can continue trading but under the lease may be more costly
▪ Under the lease, the lessor can simply remove the asset, if lease payments are not made but
this may not be so under buy approach if the asset is not secured against the bank loan
▪ The buy appraisal relies heavily on residual value of the asset and ability of the company to
sell the asset at the year end for the expected value

Overall recommendations;
The operating lease approach has major advantages in terms of certainty of future cash flows and
improved statement of financial position structure. However it is slightly more expensive based on
the estimated figures.

If there is a high probability of follow on, the buying option may be more favourable.

ILLUSTRATION 3 ON FINANCE LEASE

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A company is considering a project requiring a new machine. The machine costs N3 million and it would have
a useful life of 3 years and no residual value at the end of that time. The machine will produce cash operating
surplus of N1.6 million per year. Tax allowable depreciation of 15% is on straight line commencing from the
year of purchase. Tax is 30% on operating cash flows and is payable one year in arrears. The company has an
after tax cost of capital of 20%.
It is considering either borrowing from the bank at the pre-tax interest rate of 14% and buying the asset
outright or leasing at a cost of N1.3 million each year for three years., with the lease payments payable in
arrears at the end of each year (the lease is a finance lease)
Evaluate the project. Should the asset be acquired, and if so what financing method should be used?

SOLUTION TO ILLUSTRATION 3

Stage 1: The acquisition decision (investment decision)

Year 0 1 2 3 4
N000 N000 N000 N000 N000
Machine cost (3,000)
Tax relief on machine 135 135 135 495
Operating cash flows 1,600 1,600 1,600
Tax on operating cashflows (480) (480) (480)
Net cash flows (3,000) 1,735 1,255 1,255 15
Discount factor at 20% 1.000 0.833 0.694 0.579 0.482
PV at 20% (3,000) 1,445 871 727 7
NPV (in N000) 50

Acquisition decision
The NPV is positive; therefore the machine should be acquired.
Workings:
Tax-allowable depreciation = 15% x N 3,000,000 = N 450,000 per annum in years 1-3.
Therefore, total tax allowable depreciation = 3 x N 450,000 = N1,350,000.
Therefore, balancing allowance at end of Year 3 = N1,650,000 (N3,000,000 - N1,350,000).
It is assumed that the first tax allowance for depreciation would be claimed early in Year 1, i.e. in
Year 0, resulting in a tax saving (one year later) at the end of Year 1. The savings in tax payments
will therefore be (one year in arrears):
For Years 1-3: N 450,000 x 30% = N 135,000.
For Year 4: N1,650,000 x 30% = N 495,000.

Stage 2: The finance decision (finance lease)

There are two financing options: to buy the asset with a bank loan or to obtain the asset under a
finance lease arrangement.
The present value of the cash flows associated with the two financing options should be compared.
Tax impact of the capital allowances can be ignored as they would be claimed however the asset is
financed
The PV are calculated using the post-tax cost of borrowing which is: 14% x (1-30%) = 9.8%. PV of
cost of purchasing (3,000,000) PV of leasing cost
Year 1 2 3
N000 N000 N000 NOOO

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Lease payments (1,300) (1,300) (1,300)

Tax relief on payments (W) 130 92 49
Net cash flows (1,300) (1170) (1208) 49
Discount factor at 9.8% 0.911 0.829 0.755 0.688
PV at 9.8% (1,184) (970) (913) 34
PV of leasing cost (3,033)
Financing decision
Leasing is more expensive than borrowing the cash to buy the asset.
Company should borrow money at 14% and buy the asset.

Workings (to find the tax relief on the rentals)

Step 1: Calculate the IRR of the rentals
Year Cashflow Discount factor atlO% PV atlO% Discount factor atl5% PVatl5%

N000 N000 N000 N000 N000

0 (3,000) 1.000 (3,000) 1,000 (3,000)
1to 3 1,300 2.487 3,233 1.283 2,968
NPV 233 (32)

Using
IRR = LR% + (NPVLR/ NPVLR + NPV HR) x (HR - LR)%
IRR = 10% + (233/265) x (15 - 10)%
IRR = 14.36

The cost of the lease is 14.4%

Stage 2: The finance decision (finance lease)

Step 2: Construct an amortisation table

Year Opening liability Interest atl4.36% Rental payment Closing liability
1 3,000 431 (1,300) 2,131
2 2,131 306 (1,300) 1.137
3 1.137 163 (1,300) 0

Step 3: Tax relief on interest element of the rentals

Year Interest Tax on interest

(30%)
1 431 130
2 306 92
3 163 49

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SESSION 8: RISK AND UNCERTAINTY

Risk: A risk is a situation in which we do not know exactly the occurrence of future uncertain events but we
can quantity the possibilities of such future events. This is a situation where the future outcome is unknown but
he likelihood of various possible outcomes may be assessed with some degree of confidence probably based on
knowledge of past or existing event.

Uncertainty: An uncertainty is a situation in which we cannot quantity the probability or possibility of

occurrence of such future events. It is a future outcome that cannot be predicted with any degree of confidence
from past or existing event either as a result of lack of experience or absence of research data.

The above distinctive is purely theoretical and so would have no effect on the methods for adjusting or
incorporating risk.

METHODS FOR ADJUSTING RISK AND UNCERTAINTIES

1) Adjusted payback period-the payback period for risky projects would be shorter than the company’s
normal payback period
2) Adjusted accounting rate of return: risky projects are evaluated using a higher ARR than the normal.
3) Finite horizon method evaluation of a risky project is done within a reduced number of years that the
appraisal is comfortable with. This reduced number of years is usually called the FINITE HORIZON or
the foreseeable future.
4) Risk premium or risk adjusted discount rate method: the cost of capital is adjusted to cater for the
risk. Risky projects will then be evaluated at a cost of capital that will be higher than the company’s
normal cost of capital.
5) Certainty equivalent method: this is method allows for risky by adjusting the future cash flow to the
best estimate or certainty equivalent. The cash flows are adjusted to compensate for risk by converting
the uncertain cash flows to riskless or certainty equivalent for risk by converting the uncertain cash
flows to riskless or certainty equivalent cash flows before discounting at a riskless or risk free discount
rate to generate a risk adjusted NPV.

Its major advantage lies in its simplicity but its weaknesses are that the adjustment to be made is
subjectively decided by the management and the cash flows might be inflated and affected the project’s
viability.

a) Expected value approach/Probability theory: this is also known as the mathematical expectation or
Bayesian decision rule. It is the probability distribution of expected cash flows which can often be
estimated from data provided. The probabilities of the various possibilities are used to multiply the
possibilities and the sum total obtained is the expected value.

Advantage of expected value method

i) It is simple to calculate and understand
ii) It takes account of all possible outcomes
iii) It represents the whole distribution by a simple figure
iv) It leads directly to shareholder’s wealth maximization
v) It arithmetically takes account of the expected variability of all outcomes
vi) It leads directly to a simple optimizing decision rule.

Disadvantages of expected value method

i) The expected value method suffers from fundamental limitations of all averaging in that the actual
income may never equate to expectations
ii) The probability assigned to various outcomes are usually subjective
iii) It ignores the decision maker’s attitude to risk

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iv) The concept of expectation may provide an excuse for poor performance as the actual result is being
attributed to one of the possible outcomes
v) It ignores the other characteristics of the distribution by representing the whole distribution by a single
figure.

The probability could be objective that is the frequency of an event repeated over and over or subjective that is
based on decision maker’s personal experience, guesses, judgments and initiatives.

Risk analysis/coefficient of variation

This method measures the risk in projects through an examination of the standard deviation from the mean. It
is a statistical measure of relative dispersion which measures the spread about the mean value.

Coefficient of variation = Standard deviation

Expected value
The higher the coefficient of variation the higher the risk
Variance is the square of standard deviation V2 = ∑ (x-Y)2 x P
Standard deviation: This shows the spread about the mean value and is a statistical measure of absolute
dispersion.
J = ∑ (x –Y)2 x P
V = standard deviation, X= Possible result, Y= Expected result, P= Probability the higher the standard
deviation the higher the risk.
STANDARD DEVIATION OF THE ENPV OF A PROJECT
Since projects are usually based on NPV it could be better to calculate standard deviation of the expected NPV
for the whole project depending on if the projects are mutually dependent or independent.
SD ENPV = ∑ Standard deviation of expected NCF in each year
(1+ required rate of return)
= ∑ 50
(1 + r) t

If independent
SDENPV = ___∑ variance in each year individual____
(1 + required rate of return) time period x 2
= ∑ Variance
(1 + r) 2t
SENSITIVITY ANALYSIS/ DETERMINISTIC SIMULATION
This method identifies the variables of a project that will be critical to our decision (NPV). It shows the
response or sensitivity of our NPV decisions to variables. It determines to what tolerable estimate, the NPV
will be able to accommodate unfavorable changes/errors of estimation in variables such as outlay, contribution,
sales volume and variable cost, fixed cost, projects life, cost of capital etc.

It is calculated as sensitivity = NPV

Sensitivity to cost of capital = IRR – COC IRR-internal rate of return

Sensitivity to project life = PL – BEL PL-Project life, BEL-breakeven life

ADVANTAGES OF SENSITIVITY ANALYSIS

i) It is a less complicated theory to understand
ii) It identifies areas that are critical to the success of the project
iii) It provides management with information in a manner that facilitates a discretionary decision on the
likelihood of various outcomes considered.
iv) It indicates where further investigation may be worthwhile.

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LIMITATIONS OF SENSITIVITY ANALYSIS

i) It only considers the effect of the change in a single variable at a time while in practice more than one
variable may change simultaneously
ii) It does not directly measure the level of uncertainty
iii) It is not an optimizing technique
iv) Calculations may vary from decision to decision

PROBABILITIC SIMULATION/MONTE CARLO SIMULATION/ SIMULATED SAMPLING

This is defined as a modeling process of experimentation on a mathematical structure of a real life system in
order to describe and evaluate the system behavior under various assumptions.
Probabilistic simulation deals with random situation of variables based on the idea of taking random sample of
mathematical model that represents real life system. It involves establishing a probability distribution for each of the
probabilistic variables from the distribution of values for each variable, one particular value is selected at random.
Solutions obtained here are only good enough or near optimal.

Advantages
i) It is useful in very complex case where analytical methods fail
ii) It enables various alternatives to be deeply examined
iii) It considers the risk in the project in depth.

Disadvantages
i) It does not produce an optimal solution
ii) It may need the use of computers in a complex situation
iii) Too much managerial and technical terms may be involved
iv) It may be expensive.
DECISION TREE/ PROBABILITY TREE
This is a diagrammatical representation of the various alternatives involved in a problem requiring sequential
decisions so that all possible alternatives could be properly evaluated.
- Decision rode is used when situations under control
- Chance node is used when there is a probability situation

STEPS
Decision tree
This is a pictorial or diagrammatic representation of the various alternatives and sequences involved in
complex problems requiring inter related decision making.

Decision node are used where the decision maker can select a course of action from available
alternatives.

Chance node are used where probabilities can be attached to decision variables.

Procedures
1) Draw the decision tree carefully
2) Assign the probability
3) Assign the pay off
4) Determine the terminal value of each root by adding together the relevant pay off
5) Find the values at each node by working backwards applying the expected value criterion as chance
nodes and selecting the highest terminal value at the decision node
6) The value at the starting decision node will dictate the course of action i.e. the best possible root to adopt.
7) Where time value of money is involved, the present value of the cash flows need to be computed and
this represents terminal value of each root.
11. TRIPLE ASSESSMENT METHOD/ PAY OFF MATRIX

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This includes either the optimistic estimate (maximax approach) most likely estimate (minimax approach) and
the pessimistic estimate (maximum approach) the NPV is calculated under each of the three levels

Pay off matrix/triple assessment method

When a decision maker is under a complete uncertainty, any of the following decision criteria a could be used
i) Maximax decision rule: the decision maker believes that the best out of the best possible outcomes will
always happen to him (optimistic)
ii) Maximin decision rule: the decision maker believes that the best out of the worst possible outcomes will
always occur (pessimistic)
i) Maximum regret Rule: the decision maker believes in minimizing the possible maximum opportunity
cost to be incurred.

VALUE OF PERFECT INFORMATION

Information only has value if it is used to change the course of events. Perfect information is information that
will predict what will happen with 100% certainty. The value of information is the expected value of benefits
that arises to the decision maker if he changes his mind from an initial alternative as a result of the information.
Value of perfect information =
Expected value based on – optimal expected value
Perfect information under risk

ILLUSTRATIONS ON RISK AND UNCERTAINTY

ILLUSTRATION 1
Hraxin Co is appraising an investment project which has an expected life of four years and which will not be
repeated. The initial investment, payable at the start of the first year of operation, is ₦5 million. Scrap value of
₦500,000 is expected to arise at the end of four years.
There is some uncertainty about what price can be charged for the units produced by the investment project, as
this is expected to depend on the future state of the economy. The following forecast of selling prices and their
probabilities has been prepared:
Future economic state Weak Medium Strong
Probability of future economic state 35% 50% 15%
Selling price in current price terms ₦25 per unit ₦30 per unit ₦35 per unit
These selling prices are expected to be subject to annual inflation of 4% per year, regardless of which
economic state prevails in the future.
Forecast sales and production volumes, and total nominal variable costs, have already been forecast, as
follows:
Year 1 2 3 4
Sales and production (units) 150,000 250,000 400,000 300,000
Nominal variable cost (₦000) 2,385 4,200 7,080 5,730
Incremental overheads of ₦400,000 per year in current price terms will arise as a result of undertaking the
investment project. A large proportion of these overheads relate to energy costs which are expected to increase
sharply in the future because of energy supply shortages, so overhead inflation of 10% per year is expected.
The initial investment will attract tax-allowable depreciation on a straight-line basis over the four-year project
life. The rate of corporation tax is 30% and tax liabilities are paid in the year in which they arise. Hraxin Co
has traditionally used a nominal after-tax discount rate of 11% per year for investment appraisal.
Required:
(a) Calculate the expected net present value of the investment project and comment on its financial
acceptability. (9 marks)
(b) Critically discuss if sensitivity analysis will assist Hraxin Co in assessing the risk of the investment project.
(6 marks)

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(15 marks)

SOLUTION TO ILLUSTRATION 1
Calculation of expected net present value

Year 1 2 3 4
$000 4,524$000 7,843 $000 $000
Revenue Variable cost (2,385) (4,200) 13,048 10,179
(7,080) (5,730)
Contribution Overhead 2,139 (440) 3,643 (484) 5,968 (532) 4,449 (586)

Cash flow before tax Tax 1,699 (510) 3,159 5,436 3,863
Depreciation benefits 338 (948) (1,631) 338 (1,159) 338
338
Cash flow after tax Scrap 1,527 2,549 4,143 3,042. 500
vaiue
Project cash flow Discount 1,527 0-901 2,549 0- 4,143 0- 3,542 0-
at 11% 812 731 659
Present values 1,376 2,070 3,029 2,334
PV of future cash flows $000 8,
809
Initial investment (5,000)

Expected net present value (ENPV) 3,809

The investment project has a positive ENPV of $3,809,000. This is a mean or average NPV which
will result from the project being repeated many times. However, as the project is not being repeated,
the NPVs associated with each future economic state must be calculated as it is one of these NPVs
which is expected to occur. The decision by management on the financial acceptability of the project
will be based on these NPVs and the risk associated with each one.

Workings
Mean or average selling price = (25 x 0-35) + (30 x 0-5) + (35 x 0-15) = $29 per unit
Year 1 2 3 4
Inflated selling price ($ per unit) 30-16 31-37 32-62 33-93
Sales volume (units/year) 150,000 250,000 400,000 300,000
Sales revenue ($000/year) 4,524 7,843 13,048 10,179

Year 1 2 3 4
Inflated overhead ($000/year) 440 484 532 586
Total tax-allowable depreciation = 5,000,000 - 500,000 = $4,500,000
Annual tax-allowable depreciation = 4,500,000/4 = $1,125,000 per year
nnual cash flow from tax-allowable depreciation = 1,125,000 x 0-3 = $337,500 per year

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(b) Sensitivity analysis assesses the extent to which the net present value (NPV) of an investment
project responds to changes in project variables. Two methods are commonly used: one method
determines the percentage change in a project variable which results in a negative NPV, while the
other method determines the percentage change in NPV which results from a fixed percentage
change (for example, 5%) in each project variable in turn. Whichever method is used, the key or
critical project variables are identified as those to which the NPV is most sensitive, for example,
those where the smallest percentage change results in a negative NPV. Sensitivity analysis is
therefore concerned with calculating relative changes in project variables.
When discussing risk in the context of investment appraisal, it is important to note that, unlike
uncertainty, risk can be quantified and measured. The probabilities of the occurrence of particular
future outcomes can be assessed, for example, and used to evaluate the volatility of future cash flows,
for example, by calculating their standard deviation. The probabilities of the future economic states
in the assessment of the investment project of Hraxin Co are an example of probability analysis and
these probabilities can lead to an assessment of project risk.
Sensitivity analysis is usually studied in investment appraisal in relation to understanding how risk
can be incorporated in the investment appraisal process. While sensitivity analysis can indicate the
critical variables of an investment project, however, sensitivity analysis does not give any indication
of the probability of a change in any critical variable. Selling price may be a critical variable, for
example, but sensitivity analysis is not able to say whether a change in selling price is likely to occur.
In the appraisal of the investment project of Hraxin Co, the probabilities of different selling prices
arising with related economic states have come from probability analysis, not from sensitivity
analysis.
Sensitivity analysis will not therefore directly assist Hraxin Co in assessing the risk of the investment
project. However, it does provide useful information which helps management to gain a deeper
understanding of the investment project and which focuses management attention on aspects of the
investment project where problems may arise.

ILLUSTRATION 2 ON RISK AND UNCERTAINTY

An investment proposal has the following probability distribution of returns
Year one Year two Year three
Return ₦ Probability Return ₦ Probability Return ₦ Probability
6000 02 8000 0.5 7000 0.3
8000 0.4 12,000 0.5 11,000 0.5
9000 0.4 17000 0.2

The events of each year are independent of other years. The outlay on the project is fixed at ₦22,000 and the
appropriate discount rate figure is 10%. find
a. The expected net present value
b. The variance of return in each of the years
c. The standard deviation of net present value
d. The coefficient of variation
e. The probability that the NPV will be negative on the assumption of normal distribution of the NPV

SOLUTION TO QUESTION 2

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Expected annual cash flow =

Year 1 = (6,000 x 0.2)+ (8,000 x 0.4) + (9,000 x 0.4) = N8,000
Year 2 = (8,000 x 0.5) + (12,000 x 0.5) = N10,000
Year 3 = (7,000 x 0.3) + (11,000 x 0.5) + (17,000 x 0.2) = Nil,000

YEAR CASH FLOW PV N NPV

0 (22,000) (22,000) DCF@10%
1 8,000 7,280 1.00
2 10,000 8,300 0.91
3 11,000 8,250 0.83
1,830 0.75
VARIANCE OF ANNUAL RETURN = P (RETURN - EXPECTED VALUE)2
YEAR 1
RETURN PROBABILITY EXPECTED VARIANCE
VALUE
6,000 0.20 1,200 800,000
8,000 0.40 3,200 0
9,000 0.40 3,600 400,000
8,000 1,200,000

YEAR 2
RETURN PROBABILITY EXPECTED VALUE VARIANCE
8,000 0.50 4,000 2,000,000
12,000 0.50 6,000 2,000,000
10,000 4,000,000

YEAR 3
7,000 0.30 2,100 4,800,000
11,000 0.50 5,500 0
17,000 0.20 3,400 7,200,000
12,000,000

STANDARD DEVIATION OF THE PROJECT WITH INDEPENDENT CASHFLOWS

SD = √ CF/(1 + R)2N + CF/(1 + R)2N = √1 ,200,000/ 1.12 + 4,000,000/1.14 + 12,000,000/1.16
=3,239.98

COEFFICIENT OF VARIATION = SD/EV = 3,239.98/1,830 =1.77

PROB OF NEGATIVE NPV = X - MEAN / STANDARD DEVIATION = 1,830/3239.98 = -0.56

FROM THE normal distribution table this is 0.2123.
(since it is negative you deduct from 0.5) 0.5 - 0.2123 = 0.2877 = 28.77%.

ILLUSTRATION 3 ON EXPECTED VALUE

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A company designs and manufacturers toys A typical toy has a commercial life of 3 years. Heavy initial
advertising generally leads to relatively high sales during the first two years of a toy’s commercial life but
there is often a substantial decline on demand during the final year. The level of demand for a toy over its life
depends on product acceptance. The company’s marketing department has just completed an analysis of the
demand for the most recent 200 types of toy marketed by the company. The analysis reveals that of the 200
types of toy 50 enjoys an above average demand, 120 an average demand and 30 a below average demand
throughout their commercial lives.

The company has recently developed a new toy “VOLTRON” development cost amounted to N10000 and
have just been paid. The marketing department has made the following estimates of sales for the toy.
SALES REVENUE
Year 1 ₦ Year 2 ₦ Year 3 ₦
If demand is above average 240,000 500,000 160,000
If demand is average 140,000 340,000 80,000
If demand is below average 50,000 180,000 50,000

Variables costs will amount to 30% of sales revenue. Sales revenue will be received, and variable costs will be
paid on the last day of the year in which they arise.

If Voltron is produced, a special machine will have to be purchased at the start of year 1 at a cost of N190,000,
payable at the time of purchase. The machine will have a scrap value at the end of the product’s life of
N10,000, receivable one year after the last year in which production takes place.

The machine would be installed in the unused part of one of the company’s factories if it is purchased. The
company has been trying to let this unused factory space at a rent of N16,000 per annum. Although there now
seems no chance of letting the space during year 1 there is a 60% chance of letting it for 2 (two) years at the
beginning of year 2 and 50% chance of letting it for 1(one) year at the beginning of year 3 if it has not been let
at the beginning of year 2. Any rental receipts will be received annually in advance.

Fixed cost which include depreciation on a straight-line basis are expected to amount to N70,000 per annum.
These costs are all specific to the production of Voltron except for depreciation and will be paid on the last day
of the year in which they arise. Advertising expenses will be paid on the first day of each year and will amount
to N30,000 at the start of year 1 N20,000 at the start of year 2 and N10,000 at the start of year 3. The company
has a cost of capital of 20% per annum. You are required to prepare calculations showing whether the
company should produce Voltron assuming that the decision will be based on expected present values.

SOLUTION TO QUESTION 3
It is necessary to calculate the expected sales of the toy based on the probabilities determined by the
analysis of previous experience. These probabilities are; above average 50/200 = 0.25; average
120/200 = 0.60; below average 30/200 = 0.15.

Expected sales;
Year 1 = (240,000 x 0.25) + (140,000 x 0.60) + (50,000 x 0.15) = N151,500
Year 2 = (500,000 x 0.25) + (340,000 x 0.60) + (180,000 x 0.15) = N356,000
Year 3 = (160,000 x 0.25) + (80,000 x 0.60) + (50,000 x 0.15) = N95,500

Expected value of rent foregone: if the factory space is let at the beginning of year 2, rent of N16,000
each will be received in year 1 and 2 (since rent is payable in advance). This has a probability of 0.6.

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There is a probability of 0.4 that the factory will not be let out in year 2 and a probability of 0.5 that it
could let out the factory at the beginning of year 3. This will produce a cash flow of N16,000 in year
2. This has a joint probability of 0.2 (0.5 x 0.4)

probability Year1 Year 2 Year 3

0.60 N16,000 N16,000
0.4x0.5 = 0.20 N 16,000
0.4X0.5 = 0.20
EXPECTED VALUE N9,600 N12,800

NPV CALCULATION
YEAR 0N 1N 2N 3N 4N
Initial outlay (190,000)
Advert (30,000) (20,000) (10,000)
Cash fixed cost (10,000) (10,000) (10,000)
Scrap value 10,000
Rent foregone (9,600) (12,800)
Contribution;70% 160,050 249,200 66,850
of sales
NCF (220,000) 66,450 206,400 56,850 10,000
DCF @ 20% 1.00 0.83 0.69 0.58 0.48
PV (220,000) 55,154 142,416 32,973 4,800
ENPV N15,343

Other factors held constant, the new product should be produced because the expected net present
value is positive.

ILLUSTRATION 4 ON RISK AND UNCERTAINTY

Copycat electronics operates and specializes in producing pesticides. The company has recently developed a
new form of pesticide and is currently considering whether to produce the pesticide. The Board of directors
will soon meet to make a final decision and has the following information available to help it decide.
i) The cost of developing the pesticide has been N5,000,000 to date; the company is committed to
spending a further N1,500,000 within the next two months.
ii) The company has space production capacity and can produce the pesticide using machinery that will
cost N5,000,000 and which will be purchased immediately. It is expected to be sold at the end of four
years for N1,000,000.
iii) Total fixed cost identified with the production of the pesticide is N2,300,000 per year. This includes a
depreciation charge in respect of the machinery of N1,000,000 per year and a charge allocated to
represent fixed cost of N800,000 per year.
iv) The pesticides are expected to sell for N10,000 each and the marketing department believes that the
business can sell 1000 pesticides per year over the next four years.
v) The variable costs of production are N7,000 per pesticide.
vi) If the business decides not to produce the pesticide, it can sell the patents immediately for N1200000.
The company has a cost of capital of 12%.
Required
i) Calculate the net present value of producing and selling the new pesticide
ii) Carry out sensitivity analysis to show how each of the following factors would have to change
individually for the NPV to be zero.
a. Initial outlay of the machine
b. Unit variable cost

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c. Unit selling price

d. Sales volume
e. Machinery’s residual value
f. Annual net operating cash flows
g. Annual fixed cost
h. Project life
i. Discount rate

SOLUTION TO QUESTION 4

The demand estimates must always be limited to the maximum capacity of the machine.
Small machine (capacity 12,000 units) State A; multiply the sales with the probability to get the
expected value restricting the demand to maximum capacity of 12,000 units
EXPECTED VALUE = (8,000 x 0.2) + (11,000 x 0.6) + (12,000 x 0.2) = 10,600 units
Net cash flow = (10,600 x 25) -100,000 = N165,000
SMALL MACHINE (CAPACITY 12,000) STATE B
EXPECTED VALUE = (12,000 X 0.2) + (12,000 X 0.6) + (12,000 X 0.2) = 12,000 UNITS
NET CASH FLOW = (12,000 X 25) - 100,000 = N200,000
NPV CALCULATION
STATE A STATE B
Annual NCF N165,000 N200,000
DCF @ 15% for 5 years 3.35 3.35
PN OF CASH INFLOW 552,750 670,000
INITIAL OUTLAY (400,000) (400,000)
NPV 152,750 270,000
PROBABILITY 0.50 ' 0.50
PV 76,375 135,000
ENPV N211,375

BIG MACHINE (CAPACITY 20,000 UNITS) STATE A

Expected value = (8,000 x 0.2) + (11,000 x 0.6) + (15,000 x 0.2) = 11,200 units
Net cash flow = (11,200 x 25) - - 100,000 = N 180,000
BIG MACHINE; STATE B
Expected value = (12,000 x 0.2) + (15,000 X 0.6) + (19,000 x 0.2) = 15,200 units
Net cash flow = (15,200 x 25) - -100,000 = N280,000
NPV CALCULATION

STATE A STATE B
ANNUALNCF N 180,000 N280,000
DCF @ 15% FOR YR 1-5 3.35 3.35
PV OF INFLOWS N603,000 N938,000
INITIAL OUTLAY N600,000 N600,000
NCF N3,000 N338,000
PROBABILITY 0.50 0.50 '
NPV Nl,500 N169,500
ENPV N170,500

The small machine should be purchased since it has a larger expected net present value.

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B PART IS ON THE EXPECTED VALUE OF PERFECT INFORMATION

Perfect value of information is the price that would be paid for information that is 100% certain. It
can also be defined as the maximum loss that can be avoided by using such information.
The company would choose the machine with the higher expected value of NPV if the state of
demand is known
MACHINE STATE A NPV STATE B NPV
SMALL N152,750 N270,000
LARGE N3,000 N338,000
DECISION Choose Small Choose Large

Expected NPV = (152,750 x 0.50) + (338,000 x 0.50) = N245,375

Value of perfect information = value under certainty-value under expected value =
N245,375 - N211,375 = N34,000.

ILLUSTRATION 5 ON SIMULATION
The following probability estimates have been prepared for a proposed investment project.
Year Probability N
Initial outlay 0 1 (4000)
Revenue per annum 1-5 0.15 40,000
0.40 50,000
0.30 55,000
0.15 60,000
Running cost 1-5 0.40 25,000
0.25 30,000
0.35 35,000

Cost of capital is 12%

Required

1) Analyze the risk inherent in this situation by simulating the NPV calculation use the random numbers
given at the end of the question to simulate 3 sets of cash flow. On the basis of simulation, what is the
expected Net present value

Random Numbers Set Revenue Running cost

1 30 71
2 20 00
3 79 94

SOLUTION TO QUESTION 5
Note that the development cost of N5m is sunk and not relevant while the committed N1.5m is as a
result of past decision and so not relevant for decision making.
The patent will be treated as opportunity cost that would be lost if the production goes ahead.
Depreciation and allocated fixed overhead would be deducted from the total fixed cost to get relevant
cost.

CALCULATION OF NPV

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YEAR NCF N'000 DCF@12% PV N'000

0 (5,000) 1.00 (5,000)
0 (1,200) 1.00 (1,200)
1-4 2,500 3.04 7,600
4 1,000 0.64 640
NPV 2,040
Fixed cost = 2,300,000 - 1,000,000 - 800,000 = N500,000

discounted payback life) /project life = (4 - project can be shortened to

period 3.09)/4 = 22.75% 3.09 years
Discount IRR - COC /COC 27 - 12 / 12 = 125% The break even rate is 27%
rate

Workings on discounted payback period

Year Cash flow N000 DCF@12% PV N'000 DPP
0 (6,200) 1.00 (6,200) (6,200)
1 2,500 0.89 2,225 3,975
2 2,500 0.80 2,000 1,975
3 2,500 0.71 1,775 200
4 3,500 0.64 2,240 -
DPP = 3 + 200/2240 = 3.09 years

IRR calculation
YEAR CASH FLOW N'000 DCF @ 30% PV N'000
0 (6,200) 1.00 (6,200)
1 -4 2,500 2.17 5,425
4 1,000 0.35 350
NPV (425)

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IRR = LR + (NPVLR / NPVHR + NPVLR) X (HR - LR) = 12 + (2,040/ 2,040 + 425) X (30 - 12)
=27%

ILLUSTRATION 6 ON CAPITAL BUDGETING

FEDEX plc, well established in express parcel delivery business is evaluating a new venture which is the
establishment of a motor cycle courier service offering same day delivery. The venture involves the purchase
of a building for N12,500,000 payables immediately. The building would need extensive alternations costing
N7,500,000 to enable it to become the control and distribution Centre for the venture. The alterations would
take a year, and operations could not commence until the building was ready. Immediately after completion of
the building, AB limited would take delivery of 200 motor cycles at N100,000 each and engage riders.
Running costs of the operation in current prices are expected to be fixed costs of N37,500,000 per annum and a
variable cost of N50 per packet. Fixed cost are expected to increase by 8% per year and variable costs by 5%
per year. N2,500,000 of working capital would need to be injected immediately prior to the completion of the
building.
A market research survey, undertaken at a cost of N2,000,000 payable now, suggests that the price per packet
should be N250 or N400. At these prices the following numbers of packets are forecast.
Expected packets per year in thousands
Probability of demand Price N250 Price N400
0.10 175 160
0.20 275 190
0.40 350 210
0.20 375 230
0.10 400 260
The above prices are at current levels and are expected to increase by 5% at the end of each year.
Over the next five years, FEDEX cost of capital is expected to be 20% per annum constant. The board wishes
to evaluate the venture over the first five years of operations, at the end of which the realizable value of the
venture as a going concern is expected to be N50 million.
Unless otherwise stated, assume all cash flows take place at the end of the year. Ignore tax
▪ Decide with reasons which price for the packets would maximize profit
▪ Calculate the expected net present value of the venture for the first five years of operations
▪ Discuss any limitations of the methods and data used recommending what you would make of the
venture,

SOLUTION TO QUESTION 6 ON SIMULATION

REVENUE PER ANNUM

CASH FLOW PROBABILITY CUM PROB RANDOM ALLOCATION

40,000 0.15 15 00 - 14
50,000 0.40 55 15 - 54 30;;;; 20

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55,000 0.30 85 55 - 84 79
60,000 0.15 100 85 -99
RUNNING COST PER ANNUM
PROBABILITY CUM PROB RANDOM ALLOCATION
25,000 0.40 40 00 -39 00
30,000 0.25 65 40 - 64
35,000 0.35 100 65 - 99 71;;; 94

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CHAPTER NINE: CAPITAL STRUCTURE

Capital structure refers to long term source of financing employed by a company or firm and it is usually made
of ordinary shares (equity) preference shares, Debentures and Retained earnings.
It can also be defined as the split of long term finance of a company between debt and equity i.e. the proportion
of finance available for the existence and survival of a company. The mix of debt and equity in a company’s
structure is referred to as gearing ratio.
When investing in a business, an investor faces two types of risk
Business risk: This is the variability of earnings before interest and tax (EBIT) associated with the firm’s
investment decision. It is usually measured by the level of fixed cost in the total operating cost of the company.
(Operating Leverage)
Financial risk: This is the additional risk introduced by the way a company finances itself. It is a risk
associated with the firm’s financing decision. It is usually measured by the level of debt to equity in the
company or the level of interest payable (Financial gearing / Leverage).

CAPTIAL STRUCTURE DECISIONS

This deals with the question of whether it is possible to trade off the costs (Financial risk) and benefits (lower
cost of capital) of debt by a judicious combination of debt and equity finance to achieve a lower weighted
average cost of capital (WACC) and hence a higher total market value for a given level of operating gearing.

The controversy is: does leverage or gearing ratio i.e. the mix of debt and equity have any effect on the market
value of a company i.e. can the capital structure decisions affect the cost of capital which in turn affects the
firm’s value. This controversy has produced different school of thoughts such as
1. Net income Approach
2. Net operating income Approach
3. Traditional Approach
4. Modigliani and Miller Approach (with and without tax)

UNDERLYING ASSUMPTION OF CAPITAL STRUCTURE THEORIES

1. The firm employs only two sources of capital: debt and equity (Vo=Vd+Ve)
2. The firm operates in a tax free world
3. The firm adopts a 100% dividend pay-out ratio i.e. all earnings after tax and dividend are paid out as
dividend, no retained earnings.
4. Earnings before interest and tax of a company is expected to be constant into the future.
5. Business risk is constant and independent of the capital structure.
6. Shareholders have the same perception of risk about a particular company.
7. There are no transaction or floatation costs.
8. The capital structure of a company can be changed immediately by issuing debt to repurchase shares or
issuing shares to repurchase debt.

NET INCOME APPROACH

This school of thought believes that the capital structure of a company has great impact on the cost of capital
as well as market value of a company. It takes the view that since debt is cheaper than equity

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with increased debt the cost of capital reduces as the value of the firm increases. This approach is based on the
following assumptions
1. Cost of debt is cheaper than cost of equity.
2. Cost of debt and cost of equity remain constant with increased leverage
3. Increased leverage increases earnings thereby reducing WACC and increasing the firm’s value

Cost of As Debt increases WACC

capital decreases while firm’s
Ke value increases and is maximized at
minimum WACC (100% debt)

Ko

Kd

Leverage
ILLUSTRATION
a. A company has an expected Net operating income of =N=200,000.00 with a cost of equity of 16%. It
currently has a debt of =N=500,000.00 at 12% calculate the value of the firm overall cost of capital
under the Net income approach.

b. Differentiate between Net income and Net operating income stating if your answer in “a” above will
change if the value of debt is increased to =N=600,000.00 other things being constant.

TRADITIONAL APPROACH
This is a modification of the Net income approach which assumes that the capital structure of an organization
has significant impact on the cost of capital as well as the market value of the organization if well managed. It
believes that if debt finance is restricted to a certain level, an optimal capital structure will be gotten where cost
of capital is minimum and market value maximized.
STAGE 1: At a certain leverage level the cost of equity will increase slightly while cost of debt
is constant while WACC will fall because the advantage of cheap debt exceeds or
outweighs any increase in shareholders return/cost of equity.

STAGE 11: At a certain leverage level the cost of equity will increase significantly as a result of
added financial risk (adequacy to pay huge interest and still pay dividends,
interference of debt holders with company’s management or liquidation) to offset the

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advantages of cheap debt making the leverage to have a negligible effect on WACC
and within this range the firm will obtain an optimum capital structure.

STAGE 111: Beyond this limit investor perceive a higher degree of financial risk which also
affects the debt holders who will demand higher returns to ensure for the risk of
increased interest payment making the cost of debt to rise. The increase in equity
together with the now increasing cost of debt forces the WACC to rise and market
value falls.

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NET OPERATING INCOME APPROACH

This school of thought believes that capital structure changes has no effect on the cost of capital or the market
value of a firm. It bases its theory on the following assumptions.

1. Cost of debt is cheaper than cost of equity

2. Cost of debt remains constant irrespective of the level of leverage
3. Cost of equity rises in such a way as to offset any advantage from cheap debt finance.
WACC depends on business risk and so is constant.

This approach capitalizes the net operating income using WACC to obtain the market value of the firm
(WACC (K0) = Profit before interest and Tax (PBIT)
Total market value (V0)

Ke
Cost of
Capital
WACC (Ko)

Kd

Leverage

MODIGLIANI AND MILLER (M &M) VIEW (NO TAX)

In 1958 two American economist professors Franco Modigliani and Merton Miller challenged the traditional
view of capital structure. They argued that companies which operated in the same industry face similar
competitive and business conditions or risk and should have the same total value irrespective of their capital
structure. They argued that increased leverage leads to financial risks which forces shareholders to increase
their return offsetting any advantages of cheap debt finance.

Their approach believes that in the absence of tax the cost of capital and the market value of the firm remain
constant throughout all degrees of leverage. M&M are of the view that the only thing that affects the value of
the firm are its earnings and the business risk facing them and so companies having the same profit before
interest and tax as well as business risk should have the same market value unless the forces of demand and
supply will force it to equilibrium.

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Two companies are said to have same business risk where they have the same net operating income, Beta asset
and WACC or fixed cost.
Two companies are said to be in equilibrium when they have the same business risk, earnings, WACC and
market value.
ASSUMPTIONS OF M&M APPROACH
1. Securities are traded in a perfect capital market where investors are free to buy or sell securities,
information is costless and readily available, and investors behave rationally.
2. There are no transaction or floatation costs.
3. The expected value of the operating income for the future periods will be constant.
4. Firms can be categorized into homogeneous / similar risk class i.e. firms whose expected earnings have
identical business risk characteristics
5. All earnings after interest are paid out as dividend
6. The cost of debt remains unchanged as the level of gearing increases
7. The cost of equity rises in such a way to keep the WACC constant
8. Company’s overall return reflects the risky nature of the area of business in which a company is
engaged.
9. Firms and companies can borrow at the same rate.

M&M concluded their approach by stating that market pressure will ensure that the two companies identical in
every aspect apart from capital structure have the same market value in a process called arbitrage.

Cost of Capital Ke

Ko Ko

Kd

Leverage

ARBITRAGE PROCESS
This is the simultaneous buying and selling of shares in different markets with the aim of making a risk free
profit through the exploitation of any price difference between the markets. It is a process where shareholders
in a company with lower WACC sell their shares and purchase shares in a company with higher WACC,
borrowing or lending to maintain financial risk constant all with the intention of making a risk free profit
thereby bringing the companies to equilibrium.
Arbitrage is the process where the market forces of demand and supply forces two companies with identical
business risk and earnings to equilibrium.
HOME MADE GEARING – This can also be called personal leverage and is the process of substituting
corporate debt with personal debt so as to maintain a constant financial risk.

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STEPS IN ARBITRAGE
FROM GEARED TO UNGEARED
1. Determine that the Geared company has been overvalued
2. Determine the present holding and income of the investor.
3. Investor sells his holding in the Geared company at the current market value
4. Investor collects a loan worth an amount that will keep his financial risk constant i.e. his initial
percentage holding
5. Investor invests the whole amount from share proceeds and debt if his intention is to increase income
6. Investor invests only an amount that retains his initial percentage holding if his intention is to maintain
existing income
7. Confirm to check if the investor’s intention has been achieved.

FROM UNGEARED TO GEARED

1. Determine that the ungeared company has been overvalued.
2. Determine the present holding and income of the investor
3. Investor sells his holding in the ungeared company at the current market value.
4. Investor invests the entire amount in the debt and equity of the geared company if his intention is to
increase income.
5. Investor invests only an amount that retains his initial percentage holding if his intention is to maintain
existing income.
6. Confirm to check if investor’s intention has been achieved by comparing existing income to proposed
income.

MODIEGLIANI AND MILLER WITH TAX (M&M WITH TAX)

M&M argued that in a tax situation the cost of debt would be reduced by the tax rate as level of gearing
increases thereby reducing the overall cost of capital (WACC) and increasing market value which is expected
to be maximized at 100% debt finance.

Ke

Cost of capital

Ko

Kd
Gearing
NO TAXATION
Value of geared firm (Vg) = value of ungeared firm (Vu)
WACC of geared firm (Wg) = WACC of ungeared firm (Wu)
Cost of equity firm Keg = cost of equity of ungeared firm + Financial risk premium\

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Keg = Keu + (Keu – Kd) Vd

Ve

WITH TAXATION
Vg = Vu + Vdt (Vd = value of debt, t = tax rate)
WACCg = WACCu (1 – vd t)
ve
Keg=keu + (keu-kd )vd (1-t)
ve

LIMITATION OF M&M APPRAOCH

1. There is no perfect market
2. The rate of borrowing for companies may differ for individuals
3. It is difficult if not impossible to identify firms with homogenous risk.
4. Some earnings may be retained
5. Investors may not be rationale
6. There is no tax free environment
7. There is transaction cost.
8. The risk for investors differ between personal and corporate gearing
9. Only a profitable company can enjoy tax savings
10. High level of debt may lead to liquidation.

FACTORS THAT DETERMINE CAPITAL STRUCTURE

1. BUSINESS RISK: the operational risk facing a business might limit the sources of finance thereby
determining the capital structure
2. ASSET STRUCTURE: providers of finance may prefer a company with tangible assets and so this
might determine the proportion of debt and equity in the organization
3. MANAGEMENT ATTITUDE: the capital structure may depend on if the management is conservative,
aggressive or neutral.
4. TAX SAVINGS: might influence a firm to have more debt than equity
5. SERVICING OF FINANCE: the risk associated with debt finance might discourage the firm i.e.
interest payment
6. GROWTH RATE: for very rapid growth the company might have to opt for debt finance since it is
cheaper
7. LOAN CONVENANTS: might restrict further debt
8. CONTROL: for control purposes debt might be preferred

ILLUSTRATIONS ON CAPITAL STRUCTURE

ILLUSTRATION 1
CAPITAL STRUCTURE OF A plc AS AT 31ST DECEMBER 2015
N
ORDINARY SHARE OF N1 500,000
CAPITAL RESERVES 400,000
REVENUE RESERVES 600,000

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1,500,000
9% PERPETUAL DEBENTURES 400,000
15% PERPETUAL DEBENTURES 600,000
NET ASSETS 2,500,000
The current yield on debentures of this risk class is 12%. The current share price is 550k and earnings per share
are 110k.
The company is considering an expansion plan which will cost N1,000,000 and which will increase earnings
by N200,000 per annum for the foreseeable future. There are two possible ways to raise the funds required:
▪ An issue of 12% debentures which will increase the return required by shareholders to 22% to
compensate for the higher risk due to the increased gearing
▪ An issue of 200,000 new shares at 500k to a consortium of institutions. This will reduce the return
required by shareholders to 19% because of the reduction in gearing
a. Calculate the capital gearing of the company as at 31st December 2015 using the book value approach
b. Calculate the capital gearing of the company as at 31st December 2015 using the market value
approach
c. Explain why the market value approach is superior
d. Calculate the capital gearing of the company after the issue of 12% debenture using market value
approach
e. Calculate the capital gearing of the company after the issue of 200,000 ordinary shares using the
market value approach
f. Explain how preference shares should be treated in the calculation of capital gearing
g. Explain how bank overdrafts should be treated in the calculation of capital gearing

SOLUTION TO THE ILLUSTRATION 1 ON CAPITAL STRUCTURE

a. Using book value; gearing = debt/debt +equity = lm / lm + 1.5m = 40%

b. Using existing market value = market value of an irredeemable debt is the present value of its
future interest to infinity where the discount rate is the current yield of 12%
▪ For 9% debt = 0.09 x 400,000 /0.12 = N300,000
▪ For 15% debt = 0.15 x 600,000 / 0.12 = N750,000
▪ Value of equity 500,000 x 5.50 = N2,750,000
▪ Gearing ratio = (300,000 + 750,000) / 2,750,000 + (300,000 + 750,000) = 27.63%
c. The market value approach is superior to the book value approach because it takes into
consideration the expected earnings potential of the assets under the control of the company
rather than past results of those assets
d. To get the market value of the project, we need to discount the earnings that will accrue to
equity after the new project
Expected earnings to equity (500,000 x 1.10) N550,000
Gross return from new project N200,000
Interest on additional debt (12% x Nlm) (N120,000)
Balance to equity N80,000
New earnings to equity N630,000
PV to infinity at 22% = 630.000/0.22 N2,863,636
Gearing ratio = D/D+E = 2,050,000/2,050,000 + 2,863,636 41.7%
e. Where it is financed by equity
Expected earnings to equity (500,000 x 1.10) N550,000
Gross return from new project" N200,000

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Interest on additional debt 0

Balance to equity N200,000
New earnings to equity N750,000
PV to infinity at 19% = 750.000/0.19 N3,947,368
Gearing ratio = D/D+E = 1,050,000/1,050,000 + 3,947,368 21.01%
f. Preference shares are a source of financing that can be difficult to classify when trying to
assess a company's financial structure. In Law preference shareholders are treated as
members of the company, in the event of liquidation they receive no payment until the claims
of all creditors have been satisfied in full and preference dividend may be paid out of profits.
It would seem appropriate to classify preference shareholders as part of equity as they carry a
fixed right to dividend and do not share in the residual profits of the company. From the point
of view of equity holders assessing the extent to which external financing has been used, it
should be classified as a form of borrowing
g. The concept of gearing is an assessment of the extent to which the company is funded with
other people's money. If this is taken to include short term as well as long term finance,
overdraft should be included in the gearing ratio.

ILLUSTRATION 2 ON CAPITAL STRUCTURE

A company has an expected Net operating income of =N=200,000.00 with a cost of equity of 16%. It currently
has a debt of =N=500,000.00 at 12%
a. calculate the value of the firm overall cost of capital under the Net income approach.

b. Differentiate between Net income and Net operating income stating if your answer in “a”
above will change if the value of debt is increased to =N=600,000.00 other things being
constant.

SOLUTION TO ILLUSTRATION 2
The first step is to determine the profit before tax recalling that all profit after interest and tax are
paid out as dividend as there are no retained earnings as done below
N
Net operating income 200,000.00
Interest (12% x 500,000) (60,000)
Profit before tax; Dividend 140,000

KE = D/VE ; VE= D/KE = 140,000/0.16 = N875,000 = VALUE OF EQUITY

Value of coy = VE + VD = 875,000 + 500,000 = N1,375,000
WACC = EBIT/VO = 200,000/1,375,000 = 15%

B part looks at impact of debt increase on value of company

N
Net operating income 200,000.00
Interest (12% x 600,000) (72,000)
Profit before tax; Dividend 128,000

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KE = D/VE ; VE= D/KE = 128,000/0.16 = N800,000 = VALUE OF EQUITY

Value of coy = VE + VD = 800,000 + 600,000 = N1,400,000
WACC = EBIT/VO = 200,000/1,400,000 = 14%

Net operating income is earnings before interest and tax while net income is earnings after interest
and tax. It would be noticed from the computation above that WACC reduced with increase in debt
in line with the net income approach.

ILLUSTRATION 3 ON CAPITAL STRUCTURE

a. A company has =N=500,000.00 debt at 10% interest and earns =N=500,000.00 a year before interest is
paid. There are 225,000 issued shares and the company weighted average cost of capital (WACC) is
20%. Calculate the cost of equity and market value per share.
b. If the level of gearing is increased by issuing =N=500,000 additional debt at 10% interest to repurchase
56,200 shares (at same market value) with constant weighted average cost of capital (WACC).
Determine the cost of equity and marked value per share.
c. Comment on your results and the impact on capital structure.

SOLUTION TO ILLUSTRATION 3
N
Net operating income 500,000.00
Interest (10% x 500,000) (50,000)
Profit before tax; Dividend 450,000

K0 = EBIT/Vo ; V0 = EBIT/K0 = 500,000/0.20 = N2,500,000 = VALUE OF COMPANY

Value of coy = VE + VD = Value of equity = 2,500,000 - 500,000 = N2,000,000
KE = D/VE = 450,000/2,000,000 = 23%
Market price per share = value of equity/number of shares = 2,000,000/225,000 = N8.89

B part looks at impact of debt increase on value of company

N
Net operating income 500,000.00
Interest (10% x 1,000,000) (100,000)
Profit before tax; Dividend 400,000

K0 = EBIT/VO ; V0 = EBIT/K0 = 500,000/0.20 = N2,500,000 = VALUE OF COMPANY

Value of coy = VE + VD = Value of equity = 2,500,000 - 1,000,000 = N1,500,000
KE = D/VE = 400,000/1,500,000 = 27%

Market price per share = value of equity/number of shares = 1,500,000/(225,000 - 56,200) = N8.89
Market price is calculated based on number of shares

CAPITAL STRUCTURE: ILLUSTRATION 4

A Plc and B Plc are quoted companies. The following figures are from their current balance sheets

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A plc (N’000) B plc(N’000)

Ordinary share capital
Authorized 2m shares @50k 1,000 1,000
Issued 1m shares @50k 500 500
Reserves 1750 150
Shareholders fund 2250 650
6% irredeemable debentures - 2500
Both companies earn an annual profit before charging debenture interest of N500,000 which is expected to
remain constant for the indefinite future. The profits of both companies before charging debenture interest are
generally regarded as being subject to identical levels of risk. It is the policy of both companies to distribute all
available profits as dividend at the end of each year.
The current market value of A plc’s ordinary share is #3 per share cum div. An annual dividend is due to be
paid in the very near future.
B plc has just made annual dividend and interest payments both on its debentures. The current market value of
the ordinary shares is N1.40 per share and the debentures N50 per cent.
Mr. Uche owns 50000 ordinary shares in B plc. He is wondering whether he could increase his annual income
without incurring any extra risk by selling his shares in B plc and buying some of the ordinary shares of A plc.
Mr. Uche is able to borrow money at an annual compound rate of interest of 12%
You are required to
a) Estimate the cost of ordinary share and the weighted cost of capital of the two companies
b) Explain briefly why both the cost of ordinary share capital and weighted average cost of capital differ
for both companies
c) Prepare calculations to demonstrate how Mr. Uche might improve his position by making a constant
income or increasing income at constant risk.

LG has 150 million ordinary N1 shares in issue which are currently trading at N12.83 per share. The cost of
equity is estimated to be 8%.
LG has the following debt finance:
a. N300 million floating rate bank loan maturing in 8 years time with annual interest set at 12 month
interbank rate plus 2%. The 12 month interbank rate is currently 3% per annum
b. N500 million of bonds currently trading at N105 and a yield of 5%
LG pays corporate income tax at a rate of 33% on taxable profits
Required
▪ Explain the relationship between WACC and entity value
▪ Calculate the current gearing (based on market values and measured as debt/debt + equity)
▪ Calculate the current WACC
▪ Calculate using Modigliani and Miller’s theory with tax, the theoretical reduction in LG’s WACC if
gearing were to be increased to 60%
▪ Evaluate the Finance Director’s stated opinion that LG’s gearing should not be increased in the current
economic climate. Your answer should take into account; the risk profile of LG and practical
considerations affecting the optimum choice of gearing.

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SOLUTION TO ILLUSTRATION 4

A PLC N'000 B PLC N'000

EBIT 500 500
INTEREST 150
PBT/DIVIDEND 500 350
VALUE OF EQUITY 2,500 1,400
VALUE OF DEBT 1,250
VALUE OF COMPANY 2,500 2,650
COST OF EQUITY =D/VE 20% 25%
COST OF DEBT = l/VD 12%
WACC = EBIT/VO 20% 18.87%

B PART
The cost of equity of a geared company would be higher than that of an ungeared company under
normal circumstances due to financial risk associated with debt finance as shown in the table above.

The WACC of a geared company would be lower than the WACC of an ungeared company because
cost of debt is cheaper than cost of equity thereby reducing the average cost.

C PART IS ON ARBITRAGE FROM A GEARED TO AN UNGERED COMPANY

% HOLDING = number of investor's shares/ shares of existing coy = 50,000/1,000,000 = 5%
Present income = % holding x dividend payable = 5% x 350,000 = N17,500
Sell his shares = number of shares x share price = 50,000 x 1.40 = N70,000
Loan = %holding x debt (if not given) = 5% x N1.25m = N62,500
Total amount = N70,000 + N62,500 = N132,500
To increase income ; invest all the money
New dividend income = amount invested/ div payable = 132,500/2,500,000 x 500,000 = N26,500
Interest on loan to be paid = interest rate x loan amount =12% x 62,500 = N7,500
0000Net income = N26,500 - N7,500 = N19,000
To keep income constant; invest an amount that keeps your percentage holding constant
Amount to be invested = % holding x value of equity of new coy = 5% x 2,500,000 = N125,000
New dividend income = 125,000/2,500,000 x 500,000 = N25,000
Less interest = 12% x 62,500 = N7,500
Net income = N25,000 - N7,500 = N17,500

CHAPTER 10: CAPM AND PORTFOLIO THEORY

A portfolio is a bundle or a combination of individual assets or securities. The portfolio theory provides a
normative approach on how investors make decisions to invest their wealth in assets or securities under risk.
The portfolio theory assumes that if investors hold a well-diversified portfolio of assets, then their concern
should be the expected return and risk of the portfolio rather than individual assets and their contribution. It
also assumes that the returns of assets are normally distributed which means that the mean (expected value)
and the variance (standard deviation) analysis is the foundation of the portfolio decisions.

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An extension of the portfolio theory to device a framework for valuing risky assets is known as the capital
asset pricing model (CAPM). An alternative model for the valuation of risky assets is the arbitrage pricing
theory (APT)
Individual securities have risk and return characteristics of their own portfolio which are a combination of
securities may or may not take on the aggregate characteristics of their individual parts. Portfolio theory
considers the determination of future risk and return in holding various blends of individual securities.
The expected return from individual securities carry some degree of risk. Risk is defined as the standard
deviation around the expected return. The simple fact that securities carry different degrees of risk leads
most investors to the notion of holding more than one security at a time in an attempt to spread risks by not
putting all their eggs in one basket.
Henry Markowitz says that investors attitude towards portfolio depends exclusively upon i) the expected return
and risk and ii) the quantification of risk. In practice a rational investor seeks to maximize returns and
minimize risk and so will choose a project with higher return when risks is the same and a project with lower
risk when return is the same.

Efficient frontier Position where investors combine best

expected value of return and standard
D deviation to maximize utility
A & D are efficient portfolios while E are
E inefficient portfolios
A

Investors will prefer investment A to E Risk

since it has lower risk at same return level while investment D will be
preferred to E since it has higher return at same risk level.

When all investors prefer a particular security to another security based on the same criterion, the preferred is
said to have stochastic dominance over the less preferred security.
The risk involved in individual securities can be measured by standard deviation or variance but when two
securities are combined we need to consider their interactive risk or co-variance. When the rates of return
move together we say the covariance is positive and negative when the movements are inverse but when they
are independent we say the covariance is zero.
Portfolio theory states that unlike the traditional approach to risk which consider risk and return only the risk,
return and the relationship between securities (correlation) should be considered. The traditional approach to
portfolio stresses that the more securities one holds the better but Henry Markowitz stresses that it is not the
number of securities but the right kinds of securities (correlation).
Separation theorem states that all investors ranging from the risk averse to the cavalier should have the same
mix of risky securities in their portfolio while the interior decorate school of thought says that only securities
that suit a client’s psychology should be included in his portfolio.
Diversification is a strategy adopted by rational investors to hedge against the risk of losing all their return by
spreading their funds in various investments. It could be by adding new and related securities (concentric

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diversification) or new but unrelated securities meant for existing clients (horizontal diversification) or new
and unrelated investments for both old and new clients (conglomerate diversification)
ADVANTAGES OF DIVERSIFICATION
i) Internal cash flows will become less volatile
ii) Reduction in the level of unsystematic risk
iii) Lower probability of corporate failure

DISADVANTAGES OF DIVERSIFICATION
i) Specialized skills may not successfully manage diversified operations
ii) Lack of experience or familiarity
iii) Conglomerates are vulnerable to takeover bids.

PORTFOLIO RETURN: TWO ASSET PORTFOLIO

The return of a portfolio is equal to the weighted average of the returns of individuals assets (or securities) in
the portfolio with weights being equal to the proportion of investment value in each asset.
The expected rate of return on a portfolio or portfolio return is the weighted average of the expected rates of
return on assets in the portfolio.

Expected return on Weight of security X + Weight of security Y x

E (Rp) = W ERx + (1-W) ‘ERY
portfolio = X expected return on X expected return on Y
W is the proportion of investment in security X and (1- W) is the remaining investment in security Y.
PORTFOLIO RISK: TWO ASSET PORTFOLIO
Portfolio risk depends on the correlation between the securities as the standards deviation of portfolio X and Y
is considerably lower than the weighted standard deviation of these individual securities due to the
diversification effect. This shows that investing wealth in more than one security reduces portfolio risk.
However the extents of the benefits of portfolio diversification depend on the correlation between returns on
securities.
The portfolio variance or standard deviation depends on the co-movement of returns on two assets is measured
by the co-variance of returns.
To calculate co-variance
i) Determine the expected return on assets
ii) Determine the deviation of possible returns from the expected return for each asset.
iii)Determine the sum of product of each deviation of returns of two assets and respective
probability.
Covariance XY = Standard deviation X x Standard Deviation Y x Correlation XY
COV XY = x y CORxy
Correlation is a measure of the linear relationship between two variables.
Correlation X, Y= Covariance XY = COV xy
Standard deviation x standard deviation y x y
The value of correlation is called the correlation co-efficient which would be positive, negative or zero/neutral
and ranges between -1.0 and + 1.0

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x 2 Wx 2 + y 2 WY2 + 2Wx Wy COV XY

P

P
x 2 Wx 2 + y 2 WY2 + 2Wx Wy x y COr XY

x = Standard deviation of the returns from investment x

y = Standard deviation of the returns from investment y
WX = Proportion of investment x in the portfolio
Wy = Proportion of investment y in the portfolio
Corxy = Correlation between x and y
COVxy = Covariance between x and y

MINIMUM VARIANCE PORTFOLIO/OPTIMUM PORTFOLIO

P= ___Y2 – COV xy____
X2 + Y2 – 2 COV xy

This gives the minimum risk or the best combination of two securities that the portfolio variance is minimum
PORTFOLIO RISK: THREE ASSET PORTFOLIO

P =
X2 Wx2 + Y2 Wy2 + Z2 WZ2 + 2Wx Wy Corxy x y + 2Wy Wz Cory2 y z +

2Wx Wz Cor x z x z

ILLUSTRATIONS ON CAPM AND PORTFOLIO THEORY

ILLUSTRATION 1
Mr Investor maintains a portfolio of equity investments in ten listed companies. He is considering an
investment in one of two companies, Bratim plc and Unique plc, each of which would then represent 10%
of the enlarged portfolio. He is unsure which investment provides the better fit with his existing portfolio
of shares and has employed the services of an investment analyst to aid him in his decision. The analyst
has produced the following data and conclusions:
BRATIM UNIQUE MARKET Existing portfolio
Expected return 20% 20% 25% 18%
Standard deviation of returns 25% 30% 20% 15%
Correlation coefficient with market 0.7 0.4
returns
Existing portfolio returns 0.1 0.15
Risk free rate is 10%.
Conclusion: both investments give the same expected return (20%). Bratim plc has the lower risk (as
measured by standard deviation) and therefore is the better investment. Mr Investor has approached you,
since he does not completely trust the analyst’s judgement. His main criticisms are

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▪ I can just about understand expected returns, but what are standard deviation and correlation
coefficient all about and why are they relevant?
▪ This analyst chap has produced lot of figures, but does not seem to have used most of them
Requirements
a. Explain in similar terms for Mr Investor’s benefit, the significance of standard deviation and
correlation coefficient.
b. Using portfolio theory, determine which of the two investments is to be preferred.
c. Using CAPM, which investment should be chosen
d. Explain the basis of the calculations above and comment on your findings
e. Assuming that the market value of the shares in Mr Investor’s existing portfolio are in equilibrum.
Calculate the beta factor of the portfolio and hence the correlation coefficient of portfolio returns and
market returns
f. What does the result of “e” suggest regarding Mr Investor’s assertion that he has a well diversified
portfolio of investments.

SOLUTION TO ILLUSTRATION 1
A. Standard deviation is the variation of the actual returns around the expected return. It
represents the level of total risk. The higher the standard deviation, the higher the risk.
Correlation coefficient is a measure of the way 2 variables move together. It is a major
determinant of risk in a portfolio.
B. Return from bratim and existing portfolio = WaRa + WbRb = (0.9 X18) + (0.1 x 20) = 18.20
Risk = √ (0.9 x 0.15)2 + (0.1 x 0.25)2 + (2 x 0.9 x 0.1 x 15 x 25 x 0.10) = 13.97%
Return from Unique and existing portfolio = WaRa + WbRb = (0.9 X18) + (0.1 x 20) = 18.20
Risk = √(0.9 x 0.15)2 + (0.1 x 0.30)2 + (2 x 0.9 x 0.1 x 15 x 30 x 0.15) = 14.26% Based on
portfolio theory Bratim is better as it offers a lower risk
C. Under CAPM, alpha value is used in evaluating projects. Alpha value is the difference
between expected return and required return. Accept if alpha value is positive
B = correlation btw securities x std deviation of security / std deviation of market = Beta for
bratim is 2.5 x 0.7/20 = 0.875 and cost of equity is 23%

Beta for unique is 0.4 x 30/20 = 0.60 and cost of equity is 19%

securities Expected return Required return Alpha value Advice

Bratim 20 23 -3 Not acceptable
unique 20 19 1 accept

D. CAPM looks at the market while portfolio looks at the existing portfolio. Portfolio theory
would be better if the portfolio is not diversified. Equilibrum beta would be 0.53 and the
correlation 0.71 (beta = 18 - 10/ 25 - 10) while correlation = (std dev of market x beta/ std
dev of security = 20 x 0.53 /0.15)

E. The portfolio is not diversified as the beta is not equal to 1.

SECURITIES Expected return Required Alpha value remark Advice

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as given return as

calculated

A 16.88 16.88 0 Properly Hold priced: on the SML

B 12 12.46 -0.46 Overpriced: Sell below the SML
C 14 14.16 -0.16 Overpriced: Sellbelow the SML
D 21.5 20.62 0.88 Underpriced ; buyabove the line

Use the betas to calculate required return for each security under CAPM , A is 32/25, B is 19/25, C is
24/25 and D is 43/25 = 1.72.

ILLUSTRATION 2 ON CAPM & PORTFOLIO

You have purchased the following data from an investment bank.
COMPANY Forecast total equity return Standard deviation of total Covariance with
equity return market return
A 16.88% 6.3% 32%
B 12% 4.8% 19%
C 14% 4.7% 24%
D 21.5% 6.9% 43%
The market return and market standard deviation are 14.5% and 5% respectively, and the risk free rate is 6%.
Returns and all other data relate to a one year period.

Required

Estimate the alpha value for each of these companies shares and explain what use alpha values might be to
financial managers.

SOLUTION TO ILLUSTRATION 2
(a). Assumptions of Capital Asset Pricing Model (CAPM) include the following:
i. Investors only need to know the expected returns, the variances, and the covariances of returns to
determine which portfolios are optimal for them;
ii. Investors have identical views about risky assets' mean returns, variances of returns, and
correlations;
iii. Investors can buy and sell assets in any quantity without affecting price; all assets are marketable
(can be traded);
iv. Investors can borrow and lend at the risk-free rate without limit, and they can sell short any asset
in any quantity;
v. Investors pay no taxes on return;
vi. Investors pay no transaction costs on trades;
vii. All investors' decisions are based on a single time period.

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(b) Computation of the beta of each security:

(Correlaon with market) (Standard deviaon of the project)
Standard deviaon of the market
Akira (A) = (0.975 X 8)/6 = 1.30
Bombadia (B) = (0.64 X 7.5)/6 = 0.80
Courage (C) = (0.74 X 9)/6 = 1.11
Divine (D) = . (0.68 X 15) / 6 = 1.70

• Computation of the required returns:

Return = Rf + B(Rm - Rf)
A: RA= 5 + 1.30 (10 - 5) = 11.50%
B: RB= 5 + 0.80 (10 - 5) = 9%
C: RC= 5 + 1.11 (10 - 5) = 10.55%
D: RD= 5 + 1.70 (10 - 5) = 13.5%

• Calculation of the alpha of each security and make conclusion

C1 C2 C3 C4
Security Expectedreturn Requiredreturn AlphaC2-C3 Remarks
A 12% 11.5% 0.5% Undervalued
B 9.5% 9% 0.5% Undervalued
C 10.5% 10.55% -0.05% Overvalued
D 13% 13.5% -0.5% Overvalued

• Conclusion

Securities with positive alpha are undervalued and securities with negative alpha are overvalued and
should be sold.

ILLUSTRATION 3 ON PORTFOLIO THEORY AND CAPM

Risk free Associates have three new projects under consideration
a. Library
b. Computer annex
c. Photocopy station
Each project will cost N500,000 and only N1,000,000 has been budgeted for capital investment. As a result, a
choice has to be made as to which are the best two investments to undertake.
Details of the three projects are as follows:
PROJECT Expected return Standard deviation Beta value
Library 20% 10% 1.60
Computer annex 15% 8% 0.80
Photocopy station 18% 9% 0.95

Correlation coefficient

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Library and computer annex +0.60

Library and photocopy station +0.70
Computer annex and photocopy station +0.90
The risk free interest rate is 10% and the market return is 17%
▪ Use portfolio theory to analyze the investment decision facing the Risk free Associates
▪ Use the CAPM to re-analyze the company’s investment decision.

SOLUTION TO ILLUSTRATION 3
The portfolio approach is to select the projects with the highest portfolio return and the lowest
portfolio risk
■ Library and computer annex
Return = (0.50 x 20%) + (0.50 x 15%) = 17.5%
Risk = V(0.502 x 10%2) + (0.502 x 8%2) + (2 x 0.50 x 0.50 x 10% x 8% x 0.60) = 8.06%
■ Library and photocopy
Return = (0.50 x 20%) + (0.50 x 18%) = 19%
Risk = V(0.502 x 10%2) + (0.502 x 9%2) + (2 x 0.50 x 0.50 x 10% x 9% x 0.70) = 8.76%
■ Computer annex and photocopy
Return = (0.50 x 15%) + (0.50 x 18%) = 16.5%
Risk = V(0.502 x 8%2) + (0.502 x 9%2) + (2 x 0.50 x 0.50 x 8% x 9% x 0.90) = 8.28% projects
Expectedreturn Standard deviation Coefficient of variation

Library & 17.5% 8.06% 0.460

Computer
Library & 19% 8.76% 0.461
photocopy
Computer & 16.5% 8.28% 0.502
photocopy
Since none of the combination of projects gives a clear dominant portfolio with highest return and
lowest risk, the coefficient of variation should be used and so Library and computer would be chosen.

B PART OF THE QUESTION IS ON CAPM ANALYSIS

BETA VALUE COMBINATIONS & CAPM return calculations

Projects Beta value CAPM
Library and computer (0.50 x 1.60) + (0.50 x 0.80) =1.20 10+ 1.2(17-10) = 18.4%
Library and photocopy (0.50 x 1.60) + (0.50 x 0.95) 10 + 1.275(17 - 10) = 18.925%
=1.275
Computer and photocopy (0.50 x 0.80) + (0.50 x 0.95) 10 + 0.875(17 - 10) = 16.125%
=0.875
ALPHA VALUE CALCULATIONS

Project combination Expected return - CAPM return ALPHA VALUE

Library and computer 17.5% -18.4% -0.90%
Library and photocopy 19% -18.925% +0.075%
Computer and photocopy 16.5% -16.125% +0.375%

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CAPM analysis gives a clear and correct decision. Computer and Photocopy are the best choice as
they produce the largest alpha value

ILLUSTRATION 4 ON PORTFOLIO AND CAPM

The management of YOU plc is evaluating two projects whose returns depend on the future state of the
economy as shown below:
Probability IRR of project A IRR of project B
30% 27% 35%
40% 18% 15%
30% 5% 20%
a. Explain how a portfolio should be constructed to produce an expected return of 20%
b. Calculate the correlation between project A and Project B and assess the risk of the portfolio in (a)
above
c. Calculate the minimum risk portfolio of the portfolio in (a) above and the expected return and risk of
the resulting portfolio
d. Briefly discuss the key limitations of portfolio theory in the analysis of physical investment decisions
in practice

SOLUTION TO ILLUSTRATION 4
To totally eliminate the risk in a portfolio, there must be perfect negative correlation between the
returns on each of the projects. In addition the portfolio must be correctly balanced or weighted.

Expected return on portfolio = RP = (weight of A x RA) + (1 - WA X RB)

Return of A = (27 x 0.30) + (18 x 0.40) + (5 x 0.30) = 16.80%
Return of B = (35 x 0.30) + (15 x 0.40) + (20 x 0.30) = 22.5%
Substitute into portfolio return information
20% = (16.80 x WA) + 22.5(1 - WA) WA = 44%

Invest 44% in A and 56% in B.

Correlation can only be calculated when the deviations are known
ASSET A
IRR; X PROB; P Expected value Deviation P (x - av)2
27 0.30 8.10 10.20 31.212
18 0.40 7.20 1.20 0.576
5 0.30 1.50 -11.80 , 41.722
16.80 16.80
Standard deviation = √73.56 = 8.58

ASSET B
IRR; X PROB; P Expected value Deviation P (x- av)2
35 0.30 10.50 12.50 46.875
15 0.40 6.00 -7.50 22.50
20 0.30 6.00 -2.50 1.875
22.50 71.25

Standard deviation = √71.25 = 8.44

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CALCULATION OF COVARIANCE
Deviation of Deviation of B PROBABILITY COVARIANCE
A
10.20 12.50 0.30 38.25
1.20 -7.50 0.40 -3.60
11.80 -2.50 0.30 8.85
43.50
Correlation = COVAB / SDA X SDB = 43.50/ (8.58 X 8.44) = 0.60
RISK OF Portfolio = V(0.442 x 8.58%2) + (0.562 x 8.44%2) + (2 x 0.56 x 0.44 x 8.58% x
8.44% x0.60) = 7.62%
Minimum risk portfolio = SDB2 - COVAB / SDA2 + SDB2 - 2COVAB = (8.44)2 - 43.50/ 8.582 + 8.442 -
2(43.50) = 48%

To get the possible result 48% should be placed in A and 52% in B resulting in
√ (0.482 x 8.58%2) + (0.522 x 8.44%2) + (2 x 0.52 x 0.48 x 8.58% x 8.44% x 0.60) = 7.61%
Limitations of portfolio theory
• Projects may not be divisible in accordance with diversification principles
• It assumes that there is constant returns to scale
• It is difficult in practice to know shareholders preference of risk and return
• It may be difficult for managers

CHAPTER ELEVEN: CURRENCY HEDGING METHODS

FOREIGN EXCHANGE
Exchange rate is the rate at which a currency can be traded in exchange for another currency. Spot exchange
rate is the rate at which currencies can be bought or sold for immediate delivery and the forward rate is an
exchange rate set for currencies to be exchanged at a future date.
DIRECT QUOTE refers to the number of units of a local/domestic currency that exchange for one unit of a
foreign currency. It could be stated as N125/$ or N/$ 125
INDIRECT QUOTE refers to the number of units of a foreign currency required for a unit of a local
currency. The indirect quote is the reciprocal of the direct quote.
The major consideration is to ascertain when the bank is selling or buying. The bank will always buy at a
lower price (bid price) and sell at a higher price (ask/offer price) so as to make a gain. The difference between
the offer/ask and the bid price is the spread. Bid price is the rate at which the bank is willing to buy the
currency while the offer or ask price is the rate at which the bank is willing to sell the currency.
When a company is buying a currency, the bank would be selling that same currency and vice versa.
Spot rate is the exchange rate to be used today or now while the forward rate is the rate to be used in the future.

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ILLUSTRATIONS ON CURRENCY HEDGING METHODS

ILLUSTRATION 1
You are required to advise on the following independent transactions if $1.5500 - $1.5595 = £1
a. How much pounds would a UK trading company who has imported goods from US for $10,000 need
to pay the supplier.
b. How much pounds would a UK exporting company receive in exchange for $20,000 collected from a
customer
c. The UK company collects a Foreign loan of $15,000 and intends to convert it to its local currency.
How much pounds would the company receive.
d. Mr Johnbury , a UK investor needs to make a deposit in a US bank. How much pounds would he need
to enable him deposit $25,000 in the US bank.
e. How much dollars would a US company need to have if it has to pay a UK supplier £2,000
f. How much dollars would a US company receive from its UK customer that intends to pay £9,000

FORWARD DISCOUNT OR PREMIUM

Forward exchange rates are often quoted at a discount or premium to the spot exchange rate. There is a
premium when the forward exchange rate is higher or stronger than the spot rate and vice versa. Premiums
should be added to the spot rate of a foreign currency quoted at premium.
It is calculated as ; forward rate – spot rate = premium/(discount). The annualized premium is calculated as
(forward rate – spot rate)/spot rate X (12/number of months forward).
APPRECIATION OR DEPRECIATION OF CURRENCY
A foreign currency is said to have appreciated when the number of local currency required to purchase one unit
of the foreign currency increases in the future and vice versa. A Local currency is said to have appreciated
when less of the local currency is required for a unit of a foreign currency in the future and vice versa.
Amount of appreciation is calculated as FR –SR / SR or SR - FR /FR
CROSS RATE AND TRIANGULAR ARBITRAGE
Cross rate refers to the implicit exchange between two currencies A & B based upon the explicit interest rate
between currencies A & C and B& C. A cross rate is the determination of exchange rate between two
currencies based on the exchange rate relationship with a third party.
Triangular Arbitrage is a risk free profit that arises when cross rates are quoted out of alignment. It is a process
where an investor uses his understanding of cross rate to make an abnormal gain in the currency market

CURRENCY RISK
1, TRANSACTION RISK is the risk of adverse exchange rate movements occurring in the course of normal
international trading transactions. This arises when the prices of imports or exports are fixed in foreign
currency terms and there is movement in the exchange rate between the date when the price is agreed and the
date when the cash is paid or received in settlement. Transaction risk is the risk that, for any future transaction
in a foreign currency, the amount received or paid in domestic currency might be different from the amount
originally expected because of movements in exchange rate between the date of the initial transaction and the
date of settlement.

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2. TRANSLATION RISK is the risk that the organization will make exchange losses when the accounting
results of its foreign branches or subsidiaries are translated into the home currency. Translation losses can
result from restating the book value of a foreign subsidiary’s assets at the exchange rate at the balance sheet
date.
3. ECONOMIC RISK refers to the effect of exchange rate movements on the international competitiveness of
a company and present value of future cash flows. It is the long term movement in exchange rates caused by
changes in the competitiveness of a country. It is the degree to which the present value of a firm’s future cash
flow is affected by adverse exchange rate. This risk can be hedged by matching assets and liabilities,
diversifying the supplier and customer base, diversifying operations worldwide and changing of prices.

HEDGING OF TRANSACTION RISK

This is divided into Internal techniques and External techniques.
Internal Hedging Techniques are those techniques that exploit characteristics of the company’s trading
relationship without recourse to the external currency or money markets.
1. LEADING AND LAGGING: Leading involves accelerating payments to avoid potential additional
costs due to currency rate movements and LAGGING is the practice of delaying payments if currency
rate movements are expected to make the later payment cheaper. Leading is used to avoid over
payment when the company paying expects the currency of payment to appreciate while Lagging is
used to pay less when the paying company expects the currency of payment to depreciate.
2. INVOICING IN HOME CURRENCY: the importer ensures that the invoices are in its local
currency while the exporter invoices all customers in its local currency. This method is dependent on
the bargaining strength or the exporter’s competitive position. An alternative method of achieving the
same result is to negotiate contracts expressed in the foreign currency but at a pre-determined fixed
rate of exchange
3. MATCHING RECEIPTS AND PAYMENTS: a company can reduce its transaction risk exposure
by offsetting its payments against receipts in that currency. This can be achieved by having foreign
accounts with a bank with receipts occurring before payments and time difference not been too long.
4. NETTING is a process in which credit balances are netted off against debit balances so that only the
reduced net amounts remain due to be paid by actual currency flows. It could be bilateral netting
where only two companies are involved or multilateral netting which involves more than two group
companies
STEPS TO SOLVE MULTILATERAL NETTING
a. Construct a table with companies receiving money down the left side and companies making
payments across the top
b. Enter all the amounts the company owes to the others and convert to the agreed settlement
currency.
c. Add across and down the table to determine total receipts and total payments for each company
d. Determine the net receivable or payable for each company
5. DO NOTHING: is a method when the company uses the exchange rates available on the date of
payment or receipt.
EXTERNAL HEDGING TECHNIQUES
1. Forward Exchange Contract is an immediate firm and binding agreement to exchange (purchase or
sell) a specified quantity of a stated foreign currency at a rate of exchange rate fixed at the time the

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contract is made for performance (delivery of the currency and payment for it) at a future time which
is agreed when making the contract.
Forward contract hedge against transaction exposure by allowing the importer or exporter to arrange
for a bank to sell or buy a quantity of a stated foreign currency at an agreed future date, at a rate of
exchange determined when the forward contract is made. The trader will know in advance how much
local currency they will receive or how much the local currency they must pay.

ADVANTAGES OF FORWARD CONTRACT

1. The contract can be tailored to the user’s exact requirements with quantity to be delivered, date
and price all flexible
2. The trader will know in advance how much money will be received or paid
3. Payment is not required until the contract is settled
DISADVANTAGES OF FORWARD CONTRACTS
1. The user may not be able to negotiate good terms as the price is dependent on the size of the deal
and how the user is rated
2. Users have to bear the spread of the contract between the buying and selling price
3. Deals can only be reversed by going back to the original party and offsetting the original trade
4. The credit worthiness of the other party may be a problem

FAILURE TO SATISFY A FORWARD CONTRACT

A customer might be unable to satisfy a forward contract for one of the following reasons
a. The supplier fails to deliver the specified goods and the importer rejects the goods and refuses to
pay
b. Supplier sends fewer goods than expected resulting in less payment
c. Supplier is late with delivery and so payment has to be delayed
CLOSE OUT OF FORWARD CONTRACTS
If a customer cannot satisfy a forward exchange contract, the bank will make the customer fulfil the
contract
a. If the customer has arranged for the bank to buy currency but then cannot deliver the currency: the
bank will sell the currency to the customer at the spot rate or buy the currency back under the
terms of the forward exchange contract.
b. If the customer has contacted the bank to sell them currency, the bank will sell the specified
currency at the forward exchange rate or buy back the unwanted currency at the spot rate.
The bank forces the customer to fulfil its own part of the contract by either selling or buying the
missing currency at the spot rate in an arrangement known as closing out a forward exchange contract.

SYNTHETIC FOREIGN EXCHANGE AGREEMENTS (SAFEs)

In order to reduce the volatility of their exchange rates , some governments have banned foreign
currency trading. In such markets SAFEs are used; SAFEs are just like forward contracts but no
currency is actually delivered, instead the two counter parties settle the profit or loss (calculated as the
difference between the agreed SAFE rate and the prevailing spot rate) on a notional amount of
currency. SAFE can be used to create a foreign currency loan in a currency that is of no interest to the
lender.

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2. MONEY MARKET HEDGING involves creating a foreign asset (deposit) to offset a foreign
payment risk or creating a foreign liability (loan) to offset a foreign receipt risk.
Money Market Hedging involves borrowing in one currency, converting the money borrowed into
another currency and putting the money on deposit until the time at which the transaction is
completed, hoping to take advantage of favorable interest rate movements.
STEPS FOR MONEY MARKET HEDGING RECEIPTS
▪ Borrow the appropriate amount from a foreign bank in the foreign currency today. Appropriate
Amount = Receipt / 1 + borrowing rate of the foreign currency
▪ Convert it immediately to home currency
▪ Place it on deposit in the home currency
▪ In the future, the debtor pays the bank, while the company collects its money from the local bank.
(converted amount (1 + deposit rate)
STEPS FOR MONEY MARKET HEDGING PAYMENTS
▪ Deposit an appropriate amount in a foreign bank in the foreign currency today. Appropriate amount =
Payments / 1 + deposit rate
▪ Determine the amount of home currency required to get the deposit now.
▪ Collect a loan from the local bank in the home currency.
▪ In the future, the bank pays the creditor while the company pays the local bank. (converted amount (1
+ borrowing rate)
ARBITRAGE PROFITS
It is the simultaneous purchase and sale of a security in different markets with the aim of making a risk-
free profit through the exploitation of any price differences between the markets.
3. CURRENCY FUTURES : is a standardized contract to buy or sell a fixed amount of currency at a
fixed rate at a fixed future date. Futures are standardized contracts that are traded on an organized
exchange such as the Chicago mercantile exchange or London International Financial Futures and
Options Exchange (LIFFE). Future contracts are assumed to mature at the end of March, June,
September or December. Buying the Futures Contract means receiving the contract currency and
Selling the futures contract means supplying the contract currency.

Futures are a derivative which derives their value from movement in the spot rate. A currency futures
contract is an agreement between two parties to buy/sell a particular currency at a particular rate on a
particular future date. Currency futures deals are in the form of standardized contracts of a fixed
amount of money and are available only in a limited range of currencies and limited range of forward
periods. The exchange rates are quoted in terms of the foreign currency as measured in US dollars and
premiums are quoted in US cents per euro, pound.

The price of currency futures moves in ticks. A Tick is the smallest movement in the exchange rate and
is normally four decimal places. TICK VALUE = size of futures contract X tick size
Basis risk is a risk that the price of a currency future will vary from the price of the underlying asset
(spot rate) as expiry of the contract approaches. Basis is the difference between the spot rate and the
futures price. There is no basis risk when the contract is held to maturity.
It is assumed that the Basis falls over time but the basis may not fall in that predictable way creating
an imperfect hedge.

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IMPERFECT HEDGE is a hedge where the basis is different from the expected basis over time and
the contracts are not whole number contracts. Hedge Efficiency compares the profit made on the
futures market with the loss made on the cash or commodity market and vice versa.

OPERATIONS OF CURRENCY FUTURES: both parties in a futures contract deposit some cash
(initial margin) with the futures exchange in a margin account as a security against the trader
defaulting on their trading obligations. The Futures exchange monitors the margin account on a daily
basis. If the trader is making losses, the futures exchange may require additional margin payments
known as variation margins. The call for extra payment is called a margin call.
An initial margin is similar to a deposit. The profit or loss is received into or paid from the margin
account on a daily process in a process called marking to the market. The company will be required
to maintain a minimum balance in its margin account known as the maintenance margin. This
practice creates uncertainty as the company will not know in advance the extent of such margin
payments.

A company is an open position whenever it has an undertaking to buy futures (Long position) or sell
futures (short position). A company is in a closing position when the futures contract matures or when
the trader closes it out by selling or buying an equal number of futures for the same settlement date.
In order to manage Basis risk, it is important to choose a currency future with the closest maturity date
to the actual transaction. This reduces the unexpired basis when the transaction is closed out.
PRINCIPLES IN CHOOSING FUTURES CONTRACTS
➢ When making a foreign currency payment in future: buy the foreign currency futures now and sell the
same number of foreign currency futures contracts on the date that you buy the actual currency.
(closing out)
➢ When receiving a foreign currency in future: sell the foreign currency futures now and buy the same
number of foreign currency futures on the date you sell the actual currency.
➢ NON American country wishing to pay dollars in future: since you cannot buy $ futures, you sell your
home currency futures now and buy the same number of home currency futures contracts on the date
you buy the US dollars
➢ NON American country wishing to receive dollars in the future. Since you cannot sell $ futures, you
buy your home currency futures now and sell the same number of home currency futures on the date
you sell the US dollars.
STEPS IN CALCULATING FUTURES HEDGE
▪ Choose the contract date, contract type (buy or sell; if the company owes it will wish to buy
and vice versa) and the number of contracts
▪ Identify the closing futures price which may be given or calculate using the knowledge of
unexpired basis.
▪ Determine the Futures profit or loss considering the buying price and the selling price =
(closing futures price – opening futures price) x contract size X number of contracts or
(closing futures price – opening futures price) x tick value x number of contracts
▪ Determine the net outcome =( receipts + profit) or (receipt – loss) or (payments – profit) or
(payments plus loss). The currency used for this calculation will be opposite to the currency
of the receipt or payment being hedged. The value of the futures profit or loss will also have
to be converted using the closing spot rate.
▪ Effective rate can be calculated as ratio of local currency on hedging to the foreign currency.
It can also be calculated as opening futures price – closing basis = effective futures rate.
ADVANTAGES OF CURRENCY FUTURES

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1. The transaction costs are usually lower than the forward contracts
2. The exact date of receipt or payment of the currency does not have to be known because the futures
contract does not have to be closed out until the actual cash receipt or payment is made
3. Counterparty risk should be reduced and buying & selling contracts easier since it is done on
exchange regulated markets.
4. There is a single specified price determined by the market and not the negotiating strength of the
customer
5. Reversal can easily take place in the market
DISADVANTAGES OF CURRENCY FUTURES
1. The contracts cannot be tailored to the users exact requirements
2. Hedge inefficiencies are caused by having to deal in a whole number of contracts and by basis risk
3. Only a limited number of currencies are the subject of futures contract
4. The procedure of converting between two currencies neither of which is the US dollar is twice as
complex for futures as for a forward contract
5. Using the market will involve various costs including brokers fees
6. Volatile trading conditions on the futures markets mean that the potential loss can be high.
EXAMINATION TIPS: you cannot buy or sell US dollars currency futures because they do not exist
and so you will have to sell or buy your own currency (provided futures are traded in your currency).
Don’t recommend currency futures for a minor currency hedging.
4. CURRENCY OPTIONS is something that gives the holder the right but not the obligation to take a
particular course of action at some time in the future (buy or sell a quantity of a particular item on or
before a specified date in the future, at a fixed price that is fixed in the contract). The option could
either be a
▪ Financial Option is an option on financial items like currencies, interest rates, share prices and
stock index value
▪ Commodity option is an option on commodities such as wheat, metal , gold or copper
▪ Real options are real choices facing a company when it is considering whether to invest in a
new capital project. It could be to make a further investment if the project is successful,
abandon the investment after it has been started if it appears it will not be successful or wait
before investing instead of investing immediately.
Currency Option protects against adverse exchange rate movements while allowing the investor to take
advantage of favorable exchange rate movements. This is very useful in situations where the cash flow is not
certain to occur.
CALL OPTIONS is an option that gives the holder the right to purchase the underlying item in option
agreement while PUT OPTIONS gives the holder the right to sell the underlying item in the option
agreement.
TYPES OF OPTIONS
▪ AMERICAN OPTION is one that can be exercised at any time on or before the expiry date
▪ EUROPEAN OPTION is one that can only be exercised at the expiry date and not before.
▪ BERMUDAN OPTION is one that can be exercised on specific restricted dates only.
Options can be traded on regulated exchanges (exchange traded options) or over the counter (OTC options).
In an OTC option buyers and sellers fixes the rate such as caps, floors, collars and so on while the exchange
fixes the strike price. An OTC option is one tailor made to fit a company’s precise requirements.

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The exercise or strike price is the price at which the holder can buy or sell the underlying item. The seller of
the option is the option writer while the buyer is the option holder. Exercise price is the price with which the
future transaction will take place. It is the price with which the prevailing spot rate should be compared in
order to determine whether the option should be exercised or not. The exercise price for the option may be the
same as the current spot rate, or it may be favorable or less favorable to the option holder than the current spot
rate. A long position is a position to buy while a position to sell is called a short position.
OPTION PREMIUM is the price paid by the holder to the writer for the option whether it is exercised or not.
The level of the option premiums depend on the following factors:
▪ The exercise price
▪ The maturity of the option
▪ The volatility of the exchange and interest rate
▪ Interest rate differentials, affecting how much banks charge
EXERCISING OPTIONS
▪ IN THE MONEY (ITM) occurs when the option strike price is more favorable than the market price
▪ AT THE MONEY (ATM) occurs when the option strike price is equal to the market price.
▪ OUT OF THE MONEY (OTM) occurs when the option strike price is less favorable than the market
price.
VALUE OF OPTION is the difference between the strike price and current market price. A call option will be
exercised if the market price of the underlying item is more favorable than the exercise price of the option
while a put option will only be exercised if the market price is greater than the exercise price of the option.
Option does not have to be exercised if it is not favorable as long as the premium is paid. Options can be used
to hedge the company against an adverse movement in exchange rates while also allowing them to take
advantage of a favorable movement in exchange rates (an advantage it has over future and forward contracts)
Steps in hedging
▪ Determine the contract type (put or call)
▪ Calculate the premium
▪ Determine if the option should be exercised or not.
▪ Calculate the profit if it is to be exercised
▪ Determine the net income

5. CURRENCY SWAPS is an arrangement whereby two organizations contractually agree to exchange

payments on different terms. The parties agree to swap equivalent amounts of currency for a period. It
has benefits such as flexibility, lower costs, easier access to finance, financial restructuring,
conversion of debt type and liquidity improvement. Its challenges include the arrangement fees, risk
of default by the other party, position or market risk or sovereign risk.
FOREX SWAP is a spot currency transaction coupled with an agreement that it will be reversed at a
pre-specified date by an offsetting forward transaction. It is also called a buy/sell swap or sell buy
swap with no payment of interest rate.

ILLUSTRATION ON CONVERSION OF CURRENCY

ILLUSTRATION 1 ON CONVERSION OF CURRENCY
Given the spot rate $/£ 0.7354 --- 0. 7400
I. How much dollars would a US company require to purchase 20,000 pounds
II. How much dollars would a US company get in exchange for 45,000 pounds

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III. The US company is owing a UK company £150,000. What is the cost

IV. The Uk company is expecting $225,000 from its customer in US. What is this worth in £
V. The US company needs to deposit £175,000 in a UK bank, what is the worth of this in $
VI. The US company has just received a Loan of £350,000. How much is this in $
VII. The UK company wants to deposit $300,000 in a uk bank. How much £ is needed.
VIII. A uk company has just received a loan of $500,000. How much is this in £

SOLUTION ILLUSTRATION 1 ON CONVERSION OF CURRENCY

Illustration 1 is on currency conversion. The foundation of answering all foreign exchange questions
is a good understanding of when the bank is buying and when the bank is selling. Recall that the
bank will always buy the foreign currency at a lower rate and sell at the higher rate.

Spot rate $/£ = 0.7354 -— 0.7400 (bank will buy £ at lower rate of 0.7354 and sell at 0.7400)

▪ Bank sells; 0.7400 x £20,000 = $14,800

▪ Bank buys; 0.7354 x £45,000 = $33,093
▪ Bank sells; 0.7400 x £150,000 = $111,000
▪ Bank buys; $225,000 / 0.7400 = £304,054
▪ Bank sells; 0.7400 x £175,000 = $129,500
▪ Bank buys; 0.7354 x £350,000 = $257,390
▪ Bank sells; $300,000/0.7354 = £407,941
▪ Bank buys; $500,000 / 0.7400 = £675,676

ILLUSTRATION 2 ON FORWARD DISCOUNT OR PREMIUM

a. The spot rate between Nigeria and Ghana is cedis/N = 1.7780 and the 3 months forward rate is
Cedis/N = 1.8880. is the Naira trading at a discount or premium.
b. The spot exchange rate is cedis/N = 1.4840 – 50 and the 6-months forward rate is cedis/N=1.4812 –
42. Is the Cedis trading at a discount or premium. Compute the annualized forward premium or
discount of the Naira.
c. A UK company expects to receive $75,000 in 6 months , from a US customer and wishes to hedge the
exposure to currency risk by arranging a forward contract. The spot rate and forward rates are as
follows
Spot rate $/£ 1.7530 – 1.7540
6 months forward $/£ 240 ---- 231 premium
Determine how much the UK company’s receipt would be worth in £ if the dollar is trading at a
premium.

SOLUTION ILLUSTRATION 2 ON FORWARD DISCOUNT OR PREMIUM

A forward currency is trading at a premium if its forward rate is higher than the spot rate m 1.8880 -
1.7780. The naira is trading at a premium

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▪ Cedis/naira spot rate= (1.4840 + 1.4850)/2 = 1.4845 while the 6 months cedi/naira = (1.4812 +
1.4842)/2 = 1.4827. The naira is trading at a discount since the forward rate is lower and so
the cedi is at a premium. (1.4827 - 1.4845)/1.4845 x 12/6 = 24.25% discount
▪ The company is expecting to receive dollars and so the bank would be selling pounds to
receive the dollars at 1.7540. The dollar is trading at a premium and so the premium would
be deducted as fewer dollars would be required for pounds in the future.
75,000/ (1.7540 - 0.0231) =£43,330

ILLUSTRATION 3 ON APPRECIATION AND DEPRECIATION OF CURRENCY

The exchange rate between dollars and naira ($/N) has changed from 0.0100 to 0.0080
a. Has the naira appreciated or depreciated and by what percentage
b. Has the dollar appreciated or depreciated and by what percentage
c. Explain using your answer in (a) and (b) the concept of appreciation or depreciation and any
abnormality.

SOLUTION ILLUSTRATION 3 ON APPRECIATION AND DEPRECIATION

OF CURRENCY
A currency is said to have appreciated if it is trading at a premium. It is calculated as Forward rate -
spot rate / spot rate

▪ $/N = 0.0100 to 0.0080. for the naira = 0.0080 - 0.0100 / 0.0100 = 20% depreciation
▪ For the dollar 0.0100 - 0.0080/ 0.0080 = 25% appreciation
▪ The rate of appreciation and depreciation differ because one currency is the inverse of the
other

ILLUSTRATION 4 ON CROSS RATE

a. If the spot rate between dollar and pounds is $/£ = 0.7775 and between Euros and pounds is €/£ is
1.8325. calculate the $/€ and €/$.
b. Advise based on the information below, whether there is an arbitrage opportunity and how much
profit will be gotten in dollars by an investor with $2,000,000.
GTB spot rate $/£ is 2.1530 and Zenith spot rate is ¥/$ is 130.50. Afri bank has quoted a cross rate of
¥/£ as 200.

SOLUTION ILLUSTRATION 4 ON CROSS RATE

▪ Recall that the indirect quote is the inverse of the direct quote

$/£ = 0.7775 then £/$ = 1/0.7775

€/£ = 1.8325 then £/€ = 1/1.8325
To calculate $/€ = $/£ x £/€ = 0.7775 x 1/1.8325 = 0.4243
€/$ = €/£ x £/$ = 1.8325 x 1/0.7775 = 2.3569

▪ The b part of the question is on arbitrage. Arbitrage would only arise if the actual cross rate is
higher than the quoted cross rate If GTB spot rate is $/£ = 2.1530, then £/$ = 1 / 2.1530 If
zenith spot rate is ¥/$ = 130.50 then $/¥ = 1/130.50 Based on the above information ¥/£ = ¥/$

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x $/£ = 130.50 x 2.1530 = 280.97 Afri bank has quoted ¥/£ as 200 which is lower than the
actual cross rate and so there is an arbitrage opportunity. To enjoy the arbitrage

1. Sell the currency you have to buy the overvalued yen; 2,000,000 x 130.50 = ¥261,000,000
2. Sell the yens to purchase the pounds from afri-bank; 261,000,000/200 = £1,305,000
3. Convert back to the currency you have to see if there is a gain or loss; 1,305,000 x 2.1530 =
2,809,665
Calculate the profit in $; 2,809,665 - 2,000,000 = $809,665

ILLUSTRATION 5 ON FOREX
I. Discuss the difference between transaction risk, translation risk and economic risk
II. Explain how inflation rates and interest rates can be used to forecast exchange rates
III. Discuss the significance to a multi-national company of translation exposure and economic
exposure
IV. Discuss briefly four techniques a company might use to hedge against the foreign exchange
risk involved in foreign trade
V. Experience plc is due to receive 500,000 cedis in 6 months’ time for goods supplied. A
forward market is to be used for hedging. The short term interest rate in Nigeria is 12% per
annum and the equivalent rate in the west African country is 15%. The spot rate of exchange
is 2.50 cedis to the naira.
You are required to calculate how much Experience plc actually gains or loses as a result of the
hedging transaction, if at the end of 6 months, naira in relation to the cedis has
a. Gained 4%
b. Lost 2%
c. Remained stable
You may assume that the forward rate of exchange simply reflects the interest differential in the two
countries (interest rate parity)

SOLUTION TO ILLUSTRATION
Transaction risk refers to the risk on short term transactions that the actual income or cost may be
different from the income or cost expected when the transaction was agreed.
Translation risk arises on consolidation of financial statements prior to reporting financial results and
for this reason is also known as accounting exposure.
Economic risk is defined as the risk of the present value of a company's expected future cashflow
being affected by exchange rate movements over time.
Interest rate parity and purchasing power parity

Techniques for protecting against the risk of adverse foreign exchange movements include

o A company could trade only in its own currency thus transferring risk to suppliers or
customers
o A company could ensure that its assets and liabilities in any one currency are as nearly equal
as possible, thereby losses on assets (liabilities) are matched by gains on liabilities (assets),
o A company could enter into forward contracts
o A company could buy foreign currency options
o A company could buy foreign currency futures

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o A company could enter into a money market hedge

E PART ON CALCULATION
Interest rates for 6 months are naira 12/2 = 6%, Bakassi 15/2 = 7.5%
Implied forward rate; 1 + lF / 1 + lD = S/F = 1.075/1.06 = 0.40/F
F = 0.3944 N/Cedis

o If naira has gained 4%, actual 6 month rate is 2.50(1.04) = 2.60cedis/N or 0.3846N/cedis

N
Hedged receipt 500,000 x 0.3944 197,200
Unhedged receipt 500,000 x 0.3846 192,300
Gain from hedging 4,900

If naira has lost 6%, actual 6 month rate is 2.50(0.98) = 2.45cedis/N or 0.4082 N/cedis
N
Hedged receipt 500,000 x 0.3944 197,200
Unhedged receipt 500,000 x 0.4082 204,100
Gain/ loss from hedging (6,900)

o If naira remained stable

N
Hedged receipt 500,000 x 0.3944 197,200
Unhedged receipt 500,000 x 0.4000 200,000
Gain/ loss from hedging (2,800)

ILLUSTRATION ON MULTILATERAL NETTING

Riskfree Group is made up of 3 companies- one in Germany, Hongkong and one in US. The following inter-
company transactions took place during the first quarter of 2015.
RECEIVING PAYING SUBSIDIARY
SUBSIDIARY
GERMANY HONGKONG US
GERMANY - €10M €6M
HONGKONG HK$5M - HK$20M
US $12M $16M -
The Group has introduced a system of multilateral netting to minimize the number of inter-group payments.
The US dollar will be used as a settlement currency. Exchange rates are as follows: HK$11.2475 = €1, €0.6919
= $1 and HK$7.7821 = $1.
Illustrate the effect of multilateral netting on inter group receipts and payments.

SOLUTION TO ILLUSTRATION ON MULTI- LATERAL NETTING

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All figures are in the common settlement currency which is the dollars.
Paying subsidiaries
Receiving Germany hongkong US Total Total Net receipt
subsidiaries receipts payments

Germany - 14.4530 8.6718 23.1248 (12.6425) 10.4823

Honkong 0.6425 - 2.5700 3.2125 (30.4530) (27.2405)
US 12 16 - 28 (11.2418) 16.7582
12.6425 30.4530 11.2418

Hongkong is to pay $10.4823 to Germany and $16.7582 to US.

ILLUSTRATION 7 ON MONEY MARKET HEDGING
Spot exchange rate is $/£ is 1.7770 – 1.7780. The annual interest rates currently available in the money market
are:
DEPOSIT RATE % BORROWING RATE %
US DOLLAR 4.125 4.250
BRITISH POUND 6.500 6.625
a. A UK company expects to receive $800,000 in 3 months’ time, how would this be hedged using
money market hedge
b. A UK company is expected to pay a supplier $500,000 in 6-months’ time. How would this be hedged
using money market hedge?
SOLUTION TO ILLUSTRATION ON MONEY MARKET HEDGING

a. RECEIPT OF N800,000 in 3 months time

▪ Collect a loan of $800,000/(1 + 0.010625) = $791,589 the rate is 3 months 4.25% x 3/12
▪ Convert to local currency immediately at the spot rate ;791,589/1.7780 = £445,213
▪ Invest it in a bank for 3 months = 445,213 (1 + 0.01625) = £452,448 rate is 3 months 6.5% x
3/12
▪ Effective interest rate = $800,000/£452,448 = $1.7682/£

b. Payment of $500,000 to a supplier

▪ Deposit an amount = 500,000/ (1 + 0.020625) = $489,896 rate is 6 months 4.125% x 6/12
▪ Get the equivalent of the amount you want to deposit now; 489,896/1.7770= £275,687
▪ Pay back the local bank for the 6 months loan 275,687 (1 + 0.01625) = £284,819
▪ Effective exchange rate; 500,000/284,819 = $1.7555/£

ILLUSTRATION 8 ON HEDGING METHODS TOGETHER

Jockey Co is a UK based company which has the following expected transactions.
ONE MONTH Expected receipt of $240,000
ONE MONTH Expected payment of $140,000

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THREE MONTHS Expected receipt of $300,000

The finance manager has collected the following information:
$ per £1
Spot rate 1.7820 ± 0.0002
One month forward rate 1.7829 ± 0.0003
Three months forward rate 1.7846 ± 0.0004

Money market rates are:

BORROWING DEPOSIT
One year sterling interest rate 4.9% 4.6%
One year dollar interest rate 5.4% 5.1%
Assume that it is now April 1.
Recommend whether a forward market or money market hedge should be used to hedge the expected receipts
in 3 months’ time.

SOLUTION TO ILLUSTRATION ON FORWARD AND MONEY MARKETS

The first step is to convert the rates into bid and ask price $/£ by adding and subtracting from the
initial rate given
SPOT RATE 1.7818-1.7822
ONE MONTH FORWARD RATE 1.7826-1.7832
THREE MONTHS FORWARD RATE 1.7842-1.7850

FORWARD MARKET METHOD

Receipts in three months time : amount receivable / three months pounds selling rate = 300,000 /
1.7850 = £168,067
MONEY MARKET HEDGE METHOD
STEP
1 Collect loan = 300,000 / 1.0135 Loan = amount/$ borrowing rate for 3
=$296,004 months
2 Convert to local currency at spot rate = Recall that the bank is buying dollars from
296,004/1.7822 = £166,089 the company now
3 deposit value in 3 months at deposit rate it is assumed that you would deposit it in a
= £166,089(1.0115) = £167,999 local bank for the period concerned
DECISION

Since it is a RECEIPT the company would choose the method with a higher value and so the forward
market would be preferred.

Working
1. Borrowing rate for dollars = 5.4% x 3/12 = 1.35%
2. Deposit rate for sterling = 4.6% x 3/12 = 1.15%
3. Money market hedge only makes use of the spot rate as conversions are done now

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ILLUSTRATION 9
On completion of your ICAN examinations, you have been asked to join the international treasury team in the
European country. The company has just completed a major project in the USA and is due to receive the final
payment of US$20 million in four months. The treasury team is considering alternative methods of hedging the
expected receipt against adverse movements in exchange rate
Exchange rate information
Per € 1
Spot US$ 1.3585 – US$1.3618
4 months forward US$ 1.3588 - US$ 1.3623
Currency futures (contract size €125,000,: $ per €)
2 month expiry 1.3633 ; 5 month expiry 1.3698
Currency options (contract size €125,000, $ per € cents Euro)
CALLS PUTS
Exercise price 2 month expiry 5 month expiry 2 month expiry 5 month expiry
1.36 2.35 2.80 2.47 2.98
1.38 1.88 2.23 4.23 4.64

Advise the company on and recommend the appropriate hedging strategy for the US$ income it is due to
receive in 4 months time including all relevant calculations.

SOLUTION TO ILLUSTRATION 9
From the information available, the company can hedge dollars using forward contract, futures
contract or options contract

Forward contract
The 4 months exchange rate is $1.3588 - 1.3623 : 1€. The company is selling and the bank is buying
at $1.3623.
Net payment = 20,000,000 x 0.7341 = €14,682,000
FUTURES CONTRACT
A 5 month contract would be used as a 2 month contract would be too short. The contract would be
closed out in 4 months time.
Current basis = spot price - futures price = 1.3618 - 1.3698 = -0.0080
Unexpired basis
Number of contracts = amount / contract size= (20,000,000 / 1.3698 ) divided vy 125,000 = 117
contracts

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OPTION CONTRACTS
Exercise price of $1.36 per €
Receipts = 20m/1.36 =€14,705,882
Number of contracts = 14,705,882 /125,000 = 117 contracts
Premium payable now = 117 x 0.0280 x 125,000 = $409,500
Premium in € = 409,500/1.3585 = €301,436
Net receipt = 14,705,882 - 301,436 = €

ILLUSTRATION 10 ON CURRENCY SWAPS

A UK company wishes to invest in Germany. It borrows £20 million from its bank and pays interest
at 5%. To invest in Germany, the £20 million will be converted to euros at a spot rate of €1.5 = £1.
The earnings from the German investment will be in euros, but the company will have to pay interest
on the swap. The UK company arranges to swap the £20 million for €30 million with Goddy a
company in the Eurozone. Interest of 6% is payable on the €30 million. Explain to the UK company
how the currency swap hedge works

SOLUTION TO ILLUSTRATION 10 ON CURRENCY SWAP

The UK company receives from the German investment cash remittance of €1.8 million (30m x 6%)
which it gives to Goddy to settle its tax liability while Goddy gives £lm(20m x 5%) to the UK
company to settle its interest liability.

At the end, the UK company pays back the €30m it received and collects £20m from Goddy which it
uses to pay the bank.

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CHAPTER 12: INTERNATIONAL INVESTMENT

DECISIONS
INTERNATIONAL INVESTMENT DECISIONS
The FOUR WAY EQUIVALENCE refers to four concepts that together provide a consistent
explanation of changes in foreign exchange rates, and a method of predicting future spot exchange
rates. These four concepts are:
▪ Purchasing power parity theory (PPP)
▪ Interest rate parity theory (IRP)
▪ The fisher effect (which together with PPP makes International fishers effect)
▪ Expectations theory
PURCHASING POWER PARITY (PPP) states that the exchange rate between two currencies is the same in
equilibrium when the purchasing power of currencies is the same in each country. It predicts that the exchange
rate of foreign currency depends on the relative purchasing power of each currency in its own country, and that
spot rate will vary over time according to relative price changes.
ST = SO X (1 + HD)/(1 + HF) Where So and St are current spot rate and expected spot rate and HD and HF
mean inflation in domestic currency and foreign currency respectively.
INTEREST RATE PARITY (IRP) predicts foreign exchange rate rates based on the hypothesis that the
difference between two countries interest rates should offset the difference between the spot rates and the
forward exchange rates over the same period. This is to say that the difference between spot rates and forward
rates reflect differences in interest rates.
FO = SO x (1 + ID)/(1 + If) where Fo is the forward rate, So is the spot rate while ID and IF are the interest rates
in the domestic and foreign currency.
INTERNATIONAL FISHER EFFECT states that currencies with high interest rates are expected to
depreciate relative to currencies with low interest rates. It states that interest rate diffrentials between countries
provide an unbiased predictor of future changes in spot exchange rates. This idea suggests that the real rate of
return in different countries will equalize as a result of adjustments to spot exchange rates.
1 + IF / 1 + ID = 1 + HF / 1 + HD where I and H represents interest rate and inflation.
EXPECTATIONS THEORY looks at the relationship between differences in forward and spot rates and the
expected changes in spot rates.
Spot/forward = spot / expected future spot.
CALCULATING NPV FOR INTERNATIONAL PROJECTS
APPROACH 1: Forecast the foreign currency cash flows including inflation, forecast the exchange rate and
therefore the home currency cash flows and discount the home currency cash flows at the domestic cost of
capital.
APPROACH 2: Forecast foreign currency cash flows including inflation. Discount at foreign currency cost
of capital and calculate the foreign currency NPV. Convert into Home currency NPV at the spot exchange rate.
STRATEGIES FOR DEALING WITH EXCHANGE CONTROLS
1. Transfer pricing
2. Royalty payments
3. Loans
4. Management charges

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ILLUSTRATIONS ON INTERNATIONAL INVESTMENT DECISIONS

ILLUSTRATION 1
▪ A US company is expecting to receive Zambian Kwacha in one year’s time. The spot rate is $1 =
ZMK4819. The company could borrow in Kwacha at 7% or in dollars at 9%. Estimate the forward
rate in one year’s time.
▪ The spot exchange rate between UK sterling and the Danish kroner is £1 = 8 kroners. Assuming that
there is now purchasing parity, an amount of a commodity costing £110 in the UK will cost 880
kroners in Denmark. Over the next year, price inflation in Denmark is expected to be 5% while
inflation in the UK is expected to be 8%. What is the expected spot exchange rate at the end of the
year
▪ The nominal interest rate in the US is 5% and inflation is currently 3%. If inflation in the UK is
currently 4.5%. what is its nominal interest rate. Would the dollar be expected to appreciate or
depreciate against sterling?
ILLUSTRATION 2 ON INTERNATIONAL INVESTMENT DECISIONS
Broomstick Inc, a US company , is considering undertaking a new project in the UK. This will require initial
capital expenditure of £1,250 million, with no scrap value envisaged at the end of the five year lifespan of the
project. There will also be an initial working capital requirement of £500 million, which will be recovered at
the end of the project. The initial capital will therefore be £1,750. Pretax net cash inflows of £800 million are
expected to be generated each year from the project.
Company tax will be charged in the UK at a rate of 40% , with depreciation on a straight line basis being an
allowable deduction for tax purposes. The tax is paid at the end of the year following that in which the taxable
profit arise.
There is a double taxation agreement between the US and the UK, which means that no US tax will be payable
on the projected profits.
The current £/$ spot rate is £0.625 = $1. Inflation rates are 3% in the US and 4.5% in the UK. A project of
similar risk recently undertaken by Broomstick in the US had a required post tax rate of return of 10%.
Calculate the present value of the project using each of the two alternative approaches.

SOLUTION TO ILLUSTRATION
METHOD 1: Convert £ to $ and discount at $ cost of capital. Estimate the exchange rate for years 1-
6 using purchasing power parity. Si = S0 X (1 + hD/ 1 + hf)
YEAR SPOT RATE CONVERSION FACTOR DCFIN $
0 0.625 1 0.625
1 0.625 1.045/1.03 0.634
2 0.634 1.045/1.03 0.643
3 0.643 1.045/1.03 0.652
4 0.652 1.045/1.03 0.661
5 0.661 1.045/1.03 0.671
6 0.671 1.045/1.03 0.681

NPV computation IN £million

YEAR 0 1 2 3 4 5 6

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Initial cost (1,250)

Working capital (500) 500
Cash inflow 800 800 800 800 800
Tax payment (320) (320) (320) (320) (320)
Tax savings on CA 100 100 100 100 100

Net cash flow (1,750) 800 580 580 580 1,080 (220)
Convert to dollars 0.625 0.634 0.643 0.652 0.661 0.671 0.681
Cash flow in $ (2,800) 1,262 902 890 877 1,610 (323)
DCF @10% 1.000 0.909 0.826 0.751 0.683 0.621 0.564
PV (2,800) 1,147 745 668 599 1,000 (182)
NPV 1,177

METHOD 2: discount £ cash flows at the adjusted cost of capital (1 + IF/1 + ID) = (1 + HF/1 +
HD)'= (1.045/1.03) = (1 + X)/1.10)
X = 11.6%
YEAR 0 1 2 3 4 5 6
Initial cost (1,250)
Working capital (500) 500
Cash inflow 800 800 800 800 800
Tax payment (320) (320) (320) (320) (320)
Tax savings on CA 100 100 100 100 100

Net cash flow (1,750) 800 580 580 580 1,080 (220)
DCF (5)11.6% 1.000 0.896 0.803 0.719 0.645 0.578 0.518
PV (1,750) 717 466 417 374 624 (114)
NPV IN £ 734

NPV IN $ = 734 / 0.625 = $1174.40m

The difference in the dollar NPV is due to approximation error

ILLUSTRATION ON FOREX

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Topnotch (a Nigerian company) is evaluating an investment in Bakassi, a potentially stable country. The
project involves the establishment of training schools for accountancy and finance. it will cost an initial 10
million bakassian dollars (BK$) and it is expected to earn post tax cash flows as follows
YEAR 1 2 3 4
FLOWS 3,000 4,000 5,000 5,000
(BK$’000)
The following information is available
a. The expected inflation rate in Bakassi is 3% a year
b. Real interest rate in the two countries are the same
c. The current spot rate is NBK$2 per N1
d. The risk free rate of interest in Bakassi is 7% and 9% in Nigeria
e. It requires a naira return from this project of 16%.
▪ Calculate the net present value of the project using
a. Discounting cash flows in Naira
b. Discounting annual cash flows in bakassian dollars
▪ Discuss the problems, other than those related to taxation involved in making investment in foreign
countries
▪ Discuss how investment in foreign countries should be financed
▪ Why do firms expand into other countries
▪ What are the major factors which distinguish multinational financial management from financial
management as practiced by a purely domestic firm

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CHAPTER 13: OPTION VALUATION

INTRODUCTION TO VALUATION OF OPTIONS
It is difficult to determine an appropriate discount rate as prices changes daily in an unpredictable way
(randomly) and so risk changes unpredictably. Black and Scholes have come up with an option equivalent
(investment in a share in which the option is written together with an amount of borrowing). This is known
as a replicating portfolio.
BINOMIAL OPTION PRICING METHOD
This is based on the assumption that an option’s life can be represented by a single interval and that the
value of the share upon which the option is written can only take one of two values at the end of this
interval (binomial). Share values can either rise or fall by a given percentage based on the standard
deviation of the annual returns on the share. Black and Scholes realized that an option could be valued by
setting up an option equivalent. An option equivalent is an investment in a share upon which the option is
written together with an amount of borrowing. This is known as a replicating portfolio which has a value
same as option value.
The option’s life starts at t0 and ends at t1.
STEPS IN BINOMIAL OPTION PRICING MODEL
1. Calculate the two possible share values at the end of the interval (t1 = exercise date) by applying the
percentage increase or decrease to share value at the start of interval.
2. Use these values to calculate the possible payoffs on the options at the end of the interval (possible
share price – exercise price).
3. Identify the spread in option values (highest – lowest) and the spread in share values (highest –
lowest) at this point in time.
4. Construct the option delta. It is the ratio of spread in option values to spread in share values at that
point in time.
5. Construct the replicating portfolio using the option delta at t1 (share price in step 1 x option delta) less
borrowing repayment necessary to make the payoff equal to the possible payoffs in step 2.
6. The option value at t0 is found by valuing the replicating portfolio at this date t0 (share price at start x
option delta) – present value of borrowing/repayment amount.
EXPECTED INCREASE AND DECREASE IN SHARE PRICE
U = 1 + UPSIDE CHANGE = eSD√d SD = standard deviation of share annual returns; d= size of interval
(fraction of year expressed as a %).
D = 1 + Downside change = 1/u.
BLACK SCHOLES MODEL
C = PaN(d1) - PeN(d2)e-rt and p = c – Pa + Pe-rt
D1 is deviation from the price of the underlying item and is calculated as In(Pa/Pe) + (r + 0.5s2)t / s√t
D2 is deviation from the price of the underlying item and is calculated as d2= d1 - s√t
Nd1 and Nd2 is determined from the distribution table. If it is positive add 0.5 to the value obtained from the
normal distribution table but if it is negative, it should be deducted from 0.5.
C is the price of the call option
Pa is the price of the underlying item
Pe is the exercise or strike price for the option
E is the exponential function = 2.71828
R is the risk free rate

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T is the time to expiry of the option in years (fractional)

S is the standard deviation of the value/ returns of the underlying item (annual volatility)
P is the value of the put option
Value of put + current market price of underlying item = value of call + pv of exercise price (pv = e-rt)
REAL OPTIONS
A REAL OPTION is an alternative or choice that exists with an investment project or opportunity. They are
real choices that management will be able to make at some stage during the life of the project. They are called
real because they are associated with choices in relation to real tangible assets.
TYPES OF REAL OPTIONS
SN TYPES OF OPTIONS SUB-TYPES EXPLANATION
1 INVEST/GROW OPTIONS SCALE UP Incremental, start up
SWITCH UP New technology, market power
SCOPE UP Increase activity range
2. DEFER/DELAY/LEARN OPTION SUNDRY Delay until new information or better
START skills are acquired
3 DIVEST/ABANDON/WITHDRAW SCALE DOWN Reduce project size or divest
OPTIONS
SWITCH More effective use of assets
DOWN
SCOPE DOWN Reduce activity range

APPLICATION OF BLACK SCHOLES MODEL FOR VALUATION

This model can be used to value equity and also assess default risk of debt. These applications are based on the
idea that when a company borrows money, the shareholders acquire a call option and a put option written by
the lenders on the underlying assets of the business with an exercise price equal to the face value of debt.
A call option has an option to default on a loan it borrows which reflects in higher interest rates.

CALL OPTION
When a firm borrows money, the lender acquires the firm’s assets while the shareholders acquire an option to
buy them back by paying off the debt. Call option of assets with exercise price equal to face value of debt.
If the value of the assets is worth more than the face value of the debt (the exercise price), the shareholder will
exercise the option by paying the debt at the exercise date (redemption date). The shareholders will allow the
option to lapse (by bankruptcy) if the value of the assets is worth less than the face value of the debt (exercise
price).
PUT OPTION
Shareholders acquire a put option on the assets of the company where the exercise price (face value of debt) is
more than the firm’s asset. This is based on the fact that shareholders will not exercise the call options if the
firm’s asset are worth less than the face value of the debt.
DELTA HEDGING
Delta of an option is defined as the change in the price of an option in proportion to the change in the value of
the underlying item. Delta = change in value of option / change in market value of underlying shares. Option
will go up (call) or down (put) if share price goes up.

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A call option that is deeply ITM has a delta close to +1, while a put option that is deeply ITM has a delta close
to -1. A put option that is deeply OTM has a delta close to +0. A put option that is deeply ATM has a delta
close to +0.5 (call) or -0.5(put). Delta is always positive for calls and negative for put.
CALCULATING DELTA FOR CALL OPTIONS
Amount of underlying to hold as a hedge = amount of underlying item to be hedged x N(d1)
CALCULATING DELTA FOR PUT OPTIONS
Amount of underlying to hold as hedge = amount of underlying items to be hedged x N(-d1).
EXPECTED LOSS AND PROBABILITY OF DEFAULT
Credit risk reflects the expected loss from a loan. The expected loss is a function of the loss given default
(LGD) and the probability of default (POD). The loss given default is the amount that could be lost if a lender
defaults. It is not necessarily the amount of the loan as the lender might hold some form of collateral or the
borrower may be able to pay a percentage of the amount owed.
Probability of default; the value of Nd2 is the probability that a call option will be in the money at the
exercise date i.e. the probability that it will not be in the money 1 – N(d2)
EXPECTED LOSS; cash loan means the shareholders are given a put option on firm’s assets written by
lenders. The expected loss on the debt is the value between the value of an asset and the face value of debt to
shareholders as provided by lender. Expected loss (put option) can be calculated using put call parity.
Value of Put = value of call + PV of exercise price – current market price of underlying item
LOSS GIVEN DEFAULT = expected loss / probability of default
EXPECTED LOSS = loss given default x probability of default
Change in Due to change interpretation
Delta Option price Underlying asset value Probability that the option will expire in the money
Gamma delta Underlying asset value Probability that an option will expire ITM or OTM. It
is low when certain and increases with uncertainty
Vega Option price volatility Probability that an option price increases with
volatility of market
Rho Option price Interest rate With higher interest rates, the price of calls increases
while price of put decrease & vice versa
Theta Option price Time to expiry Sensitivity of option price to the remaining time to
expiry of the option

ILLUSTRATION ON OPTION VALUATION

ILLUSTRATION 1 ON BINOMIAL PRICING
An investor buys a call option on a share price in Ozone Plc. The details are:
Share price at start N50
EXERCISE PRICE N50
OPTION PERIOD 6 MONTHS
ANNUAL INTEREST rate 4%
Standard deviation of share’s annual returns 40%
Expected increase in share value over option period 32.7%
Expected decrease in share value over the option period 24.6%
Calculate the value of the option using the binomial option pricing method.

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SOLUTION TO ILLUSTRATION 1 ON BINOMIAL PRICING

SHARE VALUE AT END N50 N50
LOWER PRICE/UPPER PRICE N37.68 (50X0.754) 66.35 (50X1.327)
PAY OFFS BASED ON CALL
OPTION
SHARE VALUE N37.68 N66.35
EXERCISE PRICE N50.00 N50.00
PAYOFF NIL N16.35
SPREAD ; OPTION VALUE X Option gain = 16.35 -0 = 16.35
SHARE VALUE
Share value = 66.35 - 37.68 =
28.67
Option DELTA= OPTION 16.35/28.67 0.5703
GAIN/share value
Replicating portfolio = share N37.68 N66.35
price
Option delta 0.5703 0.5703
Value 21.48 37.83
Borrowing repayment to make (21.48) (21.48)
payoff equal
PAYOFF 0 16.35
OPTION VALUE= share price x 50x0.5703 N28.52
option delta
PV of replacement 21.48 @ 2% for period 1 (N21.06)
OPTION VALUE N7.46

SESSION IB: OPTION VALUATION

SOLUTION TO ILLUSTRATION 1 ON BINOMIAL PRICING
SHARE VALUE AT END N50 N50
LOWER PRICE/UPPER PRICE N37.68 (50X0.754) 66.35 (50X1.327)
PAY OFFS BASED ON CALL
OPTION
SHARE VALUE N37.68 N66.35
EXERCISE PRICE N50.00 N50.00
PAYOFF NIL N16.35
SPREAD ; OPTION VALUE X Option gain = 16.35 -0 = 16.35
SHARE VALUE
Share value = 66.35 - 37.68 =
28.67
Option DELTA= OPTION 16.35/28.67 0.5703

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GAIN/share value
Replicating portfolio = share N37.68 N66.35
price
Option delta 0.5703 0.5703
Value 21.48 37.83
Borrowing repayment to make (21.48) (21.48)
payoff equal
PAYOFF 0 16.35
OPTION VALUE= share price x 50x0.5703 N28.52
option delta
PV of replacement 21.48 @ 2% for period 1 (N21.06)
OPTION VALUE N7.46

ILLUSTRATION 2 ON BLACK SCHOLES MODEL

a. The current share price of GTB is N170. Calculate the price of an European call option on the
company’s shares at an exercise price of N165, if the expiry date is in 6 months, the standard
deviation of annual returns on a share is 12% and the risk free rate of return is 7%.
b. Determine the price of a put option using the information in (a) above.

SOLUTION TO ILLUSTRATION 2 ON BLACK SCHOLES MODEL

D1 is deviation from the price of the underlying item and is calculated as ln(Pa/Pe) + (r + 0.5s2)t / s√t
D2 is deviation from the price of the underlying item and is calculated as d2= di - sVt
Nd1 and Nd2 is determined from the distribution table. If it is positive add 0.5 to the value obtained
from the normal distribution table but if it is negative, it should be deducted from 0.5.
C is the price of the call option
Pa is the price of the underlying item
Pe is the exercise or strike price for the option
E is the exponential function = 2.71828
R is the risk free rate
T is the time to expiry of the option in years (fractional)
S is the standard deviation of the value/ returns of the underlying item (annual volatility

D1 = In (PA / Pe) + (r + 0.5s2)t /sVt = in (170/165) + (0.07 + 0.5 x 0.122)0.5 / 0.12 x V0.5 = 0.8067 = 0.81
d2= d1 - sVt = 0.81 - 0.12 x √0.5 = 0.7219 = 0.72
Nd1 = 0.2910 + 0.5000 = 0.7910
Nd2 = 0.2642 + 0.5000 = 0.7642
e-rt = 0.9656

a. C = PaN(d1) - PeN(d2)e-rt = (0.7910 x 170) - (0.7642 x 0.9656) = 12.7

b. Put = call - Pa + pee-rt = 12.7 - 170 + (0.9656 x 165) = N2.32

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ILLUSTRATION 3 ON REAL OPTIONS

Julius Berger is considering a major investment to build and operate social housing in the capital city of Abuja.
The project would require an initial investment of N300m and result in positive cash flow with a PV of N310m
giving an NPV of N10m.
In order to encourage investment of this type, the Nigerian Government has agreed that Julius Berger can sell
the project back to the government without recourse for N200m after 4 years. The risk free rate is estimated to
be 5% and standard deviation is 30%. Calculate the value of the abandonment option and hence the total NPV
of the project.

SOLUTION TO ILLUSTRATION 3
This is a put option (option to sell).
Di = In (PA / Pe) + (r + 0.5s2)t /sVt = in (310/200) + (0.05 + 0.5 x 0.302)4 / 0.30 x V4 = 1.368 =
1.37 d2= di - sVt = 1.368 - 0.30 x V4 = 0.768 = 0.77

D1= 1.368 = 1.37

D2= 0.768 = 0.76
Nd1= 0.4147 + 0.5000 = 0.9147
Nd1 = 0.2764 + 0.5000 = 0.7764
C = PaN(d1) - PeN(d2)e-rt = (310 x 0.9147) - (200 x 0.7764 x 0.8187) = 156.44
P = c - Pa + pee-rt = 156.44 - 310 + 200(0.8187) = 10.18
NPV = N10 m + N10.18 m = N20.18 m

ILLUSTRATION 4 ON REAL OPTIONS

China white is considering a major investment to build and operate social housing in the capital city of Accra.
The project would require an initial investment of N300m and result in positive cash flow with a PV of N310m
giving an NPV of N10m.
Currently there is a major offshore oil and gas exploration project in Accra. If China White were to accept the
project under consideration, they would be well placed to secure a further government construction project if
and when the oil and gas production commences.
Initial investment in the future project would be N400m in four years’ time and the PV of cash inflows from
the project are estimated at N240m but there is a great deal of uncertainty associated with this. An analyst has
estimated that volatility on the cash flows could be as high as 30%. Risk free rate is 5%. Calculate the value of
the follow on opportunity.

SOLUTION TO QUESTION 4
This is a call option (an option to buy or invest)
D1 = In (PA / Pe) + (r + 0.5s2)t /s√t = in (240/400) + (0.05 + 0.5 x 0.302)4 / 0.30 x √4 = -0.218 = -

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0.22
D1= d1 - s√t = -0.218 - 0.3√4 = -0.818 =-0.82
Nd1= 0.5-0.0871 = 0.4129
Nd2 = 0.5-0.2939 = 0.2061
C = PaN(d1) - PeN(d2)e-rt = (240 x 0.4129) - (400 x 0.2061 x 0.8187) = 99.1 - 67.5 = 31.6M
NPV = N10 m + N31.6 m = N41.6 m

ILLUSTRATION 5
a. A Nigerian bank is writing currency call options on €200m in exchange for naira. The value of delta
option is 0.5326 measured as N(d1). What quantity of euros should the bank hold in order to be certain
that it will not make a loss.
b. A Nigerian company needs to buy €100m in 3 months time and wants to use currency call options to
create a hedge that would eliminate the exchange rate risk entirely. ATM call options on euros have a
delta value of 0.5326. each option is for €100,000. Calculate the number of euros for which ATM call
options should be purchased.

SOLUTION TO ILLUSTRATION 5
a. Amount of underlying to hold as hedge = amount of underlying item to be hedged x N(D2)
€200mx 0.5326 = €106.52m
b. Using same formula as in 'a ' above, amount of underlying item to be hedged = amount of
underlying to hold as hedge/ N(DX) = 100,000/0.5326 = €187.758m
Number of contracts = 187.758m / 100,000 = 1,878 contracts

ILLUSTRATION 6 ON BSOP MODEL AND DEBT

A firm has assets less current liabilities of N100m. this figure varies with a standard deviation of 0.4. the face
value of the outstanding debt is N80m. The debt is zero coupon and is to be paid in 5 years time. Risk free rate
is 5%. Calculate the value of the debt , interest rate carried by the debt and the credit risk on the debt.

SOLUTION TO ILLUSTRATION
PA = N100m, PE = N80m, t = 5yrs, std deviation = 0.40, riskfree rate = 0.05

D1 = In (PA / Pe) + (r + 0.5s2)t /s√t = in (100/80) + (0.05 + 0.5 x 0.402)5 / 0.40 x √5 = 0.9762=
0.98
P2= d1 - s√t = 0.9762 - 0.4√5= 0.0818 =-0.082_
Nd1= 0.5 + 0.0.3355 = 0.8355_
Nd2 = 0.5 + 0.0326= 0.5326_
C = PaN(d1) - PeN(d2)e-rt = (100 x 0.8355) - (80 x 0.5326 x 0.7788) = 83.55 - 33.183 = 50.37m

CHAPTER 14: INTEREST RATE HEDGING

INTEREST RATE RISKS

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Interest rate movements cause risks for companies. It is the risk to the profitability or value of a company
resulting from changes in interest rates. Risk from interest rates include
Fixed rate versus floating rate debt A company can get caught paying higher interest rates by having
fixed rather than floating rather than fixed rate debt, as market interest
rates change,
Term of loan A company can be exposed by having to repay a loan earlier than it
can afford to resulting in a need to re-borrow, perhaps at a higher rate
of interest
Term loan or overdraft facility A company might prefer to pay for borrowings only when it needs the
money as with an overdraft facility.
Deposit at floating rates If interest rates fall then a company would suffer a loss of interest

REDUCING INTEREST RATE RISK

Methods of reducing interest rate risk include:
▪ Pooling of assets and liabilities
▪ Forward rate agreements (FRA)
▪ Interest rate futures
▪ Interest rate options (interest rate guarantees)
▪ Interest rate swaps
POOLING OF ASSETS AND LIABILITIES : Some of the interest rate risks to which a firm is exposed
may cancel each other out, where there are both assets and liabilities which both have exposure to interest rate
changes. More interest would be pay on loans which would be compensated for by higher interest on money
market deposits, if interest rates rise.
FORWARD RATE AGREEMENTS: allow borrowers or lenders to fix their future rate of interest. The FRA
runs for a given period in the future. ‘3-9’ FRA shows that the FRA starts in 3 months time and last for 6
months. If the actual interest rate proves to be higher than the rate agreed, the bank pays the company the
difference. If the actual interest rate is lower than the rate agreed, the company pays the bank the difference.
INTEREST RATE FUTURES are similar in effect to FRAs, except that the terms, amounts and periods are
standardized as for other contracts. With interest rate futures what we sell is the promise to make interest
payments and what we buy is entitlement to interest receipts. Borrowers hedge an interest rate price by selling
futures now and buying it on the day the interest rate is fixed (closing out) while lenders would hedge an
interest rate fall by buying futures now and selling futres on the day the actual lending starts.
Future use the inverse relationship between interest rate and bond prices to hedge against interest rate risk. A
borrower will enter to sell futures today, so if the interest rates rise in the future, the value of the futures will
fall and the hedger can buy at a lower price thereby making a profit. This involves the actual
lending/borrowing in the money market and the futures market.
Short term interest rate futures contracts (STIRs) normally represent interest receivable or payable on notional
lending or borrowing for a three month period beginning on a standard future date. The contract size depends
on the currency in which the lending or borrowing takes place. Whole number of contracts should be used and
maturity dates are March, June, September and December. Interest rate for borrowing or lending is fixed for a
3 month period starting from an agreed future date.
Profits and losses on futures are measured in ticks (one tick equals 0.0001 or 1% = 100 ticks). Tick = contract
size x 3/12 x 0.0001

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The pricing on an interest rate futures contract is determined by the interest rate (r) and is calculated as 100 – r.
interest futures are usually quoted in the form of index and so a price at 82 means 18% (100-82).
STEPS IN SETTING UP AN INTEREST RATE FUTURES
▪ Determine the target interest amount based on the desired interest rate (principal x interest rate x
duration)
▪ Determine number of contracts required = (face value of exposure /face value of contract) x (maturity
of exposure / maturity of futures contract)
▪ Determine whether to buy or sell futures (borrowers sell while lenders buy futures is a general rule).
The contract to buy is the contract with the next expiry date after the date when the loan is required.
INTEREST RATE OPTIONS
▪ This grants the buyer of the option the right but not the obligations, to deal at an agreed interest rate
(strike price) at a future maturity date. On the expiry date of the option, the buyer must decide whether
or not to exercise the rights. Clearly, a buyer of an option to borrow will not wish to exercise it if the
market interest rate is now below the option price, just as the lender will not exercise if the market rate
of interest is higher than that in the option agreement.
▪ Borrowers can set a maximum on the interest they have to pay by buying put options known as
Borrowers option. The option will be exercised if the LIBOR is higher than the strike rate.
▪ Lenders can set a minimum on the interest they receive by buying call options known as lenders
option. The option will be exercised if the LIBOR is lower than the strike rate.
SWAPTIONS is an option on a Swap which gives the holder the right but not the obligation to enter into a
swap agreement at a future date on terms that are fixed now.
INTEREST RATE CAP is an option which sets an interest rate ceiling. It is a series of borrowers option
setting a maximum interest rate on a variable rate borrowing protecting holders from adverse movements in
interest rates by setting a maximum borrowing cost for any roll over date on a variable rate loan. It is an
agreement where the seller (writer) agrees to compensate the buyer (holder) if interest rates rise above the
exercise rate at each reset date.
INTEREST RATE FLOOR is an option which sets a lower limit to interest rates. It is a series of successive
lender options that can be used to fix minimum interest rate for a series of interest rate periods. The writer
agrees to compensate the buyer if interest rates fall below the strike rate at each reset date.
COLLAR ARRANGEMENT is a situation when the borrower can buy an interest rate cap and at the same
time sell an interest rate floor which reduces the cost for the company. The cost of a collar is lower than for a
cap alone. The aim is to receive compensation from the CAP when interest rate is higher and pay
compensation when interest rate is lower than the strike price. It is a combination of cap and floor.
ZERO COST COLLARS is a collar for which the premium is zero. It is a collar where the premium value to
and from a cap and floor are equal or close
INTEREST RATE SWAPS is an agreement whereby the parties to the agreement exchange interest rate
commitments over an agreed period. A swap between floating rate interest and fixed rate interest is known as a
“plain vanilla” or generic swap”. The variable rate included in a swap is LIBOR (London inter- bank offered
rate). This benchmark of interest is the rate paid between banks.
Annual volatility of share price 35% 10%
FACTORS AFFECTING OPTION PRICES

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1. CURRENT PRICE OF THE UNDERLYING ASSET: As price goes up, the higher the probability
that the call option will be in the money and so the price of the call option increases and vice versa for
put option.
2. STRIKE PRICE OR EXERCISE PRICE OF THE OPTION: the higher the exercise price , the
lower the probability that a call will be exercised. Call prices will decrease as the exercise price
increases and vice versa for the option.
3. VOLATILITY OF THE UNDERLYING: both options will increase in price as the underlying asset
becomes more volatile.
4. TIME TO EXPIRATION: Both benefit as there is time for the price to move. Present value of the
exercise price decreases as time increases,, which increases the value of the call option and decreases
the value of the put option. The price of the underlying asset may also be reduced by cash dividend
there by increasing the value of the put option.
5. RISK FREE INTEREST RATE: the higher the interest rate, the lower the present value of the
exercise price and so the value of the call option will increase.

ILLUSTRATIONS ON INTEREST RATE HEDGING

ILLUSTRATION 1 ON FRA
It is 30 June, LYNNA plc will need £10 million six month fixed rate loan from 1 October. The company wants
to hedge using an FRA. The relevant FRA rate on 30 June is 6%
▪ State what FRA is required
▪ Explain the result of the FRA and the effective loan rate if the six month FRA benchmark rate has
moved to 5% or 9%.

SOLUTION TO ILLUSTRATION 1 ON INTEREST FORWARD RATE

AGREEMENT
▪
▪ The FRA required is a 3 - 9 FRA which means a forward rate agreement due to commence in
3 months' time and would last for 6 months with the FRA as 6%
▪
▪ IF RATE IS 5%
PAYMENT ON LOAN ; 5% X £10m X 6/12 (£250,000)
FRA PAYMENT (6 - 5)% X £10m X 6/12 (£50,000)
Net payment on loan (£300,000)
Effective rate £300,000/£5,000,000 6%
▪ IF RATE IS 9%
PAYMENT ON LOAN ; 9% X £10m X 6/12 (£450,000)
FRA PAYMENT (9 - 6)% X £10m X 6/12 £150,000
Net payment on loan (£300,000)
Effective rate £300,000/£5,000,000 6%

ILLUSTRATION 2 ON INTEREST RATE FUTURES

It is 1 January, and a company has identified that it will need to borrow £10 million on 31st March for six
months. The spot rate on 1 January is 8% and March 3-month interest rate futures with a contract size of

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£500,000 are trading at 91. Demonstrate how futures can be used to hedge against interest rate rises. Assume
that at 31st March, the spot rate of interest is 11% and the March interest rate futures price has fallen to 89.

ILLUSTRATION 3 ON INTEREST RATE OPTIONS

Bagga wishes to borrow £4 million fixed rate in June for 9 months and wishes to protect itself against rates
rising above 6.75%. it is 11 May and the spot rate is currently 6%. The data is as follows:

Interest rate guarantees: short sterling options (LIFFE); £1,000,000 points of 100%
Effective interest rate calls puts
% JUN SEP DEC JUN SEP DEC
6.75 0.03 0.03 0.03 0.14 0.92 1.62
6.50 0.01 0.01 0.01 0.28 1.15 1.85
6.25 0.01 0.01 0.01 0.49 1.39 2.10
Bagga negotiates the loan with the bank on 12 june (when the £4 million loan rate is fixed for the full nine
months) and closes out the hedge. What will be the outcome of the hedge and the effective loan rate if prices
on June 12 have moved to 7.4% or 5.1%.

SOLUTION TO ILLUSTRATION 3
IF INTEREST RATE IS 7.4%
Amount to be borrowed £4,000,000
Type of contract Sell /PUT option
Contract duration June contract
Strike price 93.25 = 100-6.75%
Number of contracts = amount/contract size x loan period 4m / lm x 9/3 = 12 contracts
/contract length
Premium = 12 x (0.14 x 0.01) x 1,000,000 X 3/12 £4,200
Should we exercise? = strike price sell at 6.75
Closing rate at 7.40
Yes because strike price will result in lower payment.
Net outcome; payment in spot market 4m x 6.75% x 9/12 202,500
Premium 4,200
Net payment 206,700
Effective interest = net payment/ amount borrowed
206,700/ 4,000,000 x 12/9 6.89%

INTEREST RATE IS 5.1%

Amount to be borrowed £4,000,000
Type of contract Sell /PUT option
Contract duration June contract
Strike price 93.25 = 100-6.75%
Number of contracts = amount/contract size x 4m / lm x 9/3 = 12 contracts

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loan period /contract length

Premium = 12 x (0.14 x 0.01) x £4,200
1,000,000/(12/3)
Shouid we exercise? = strike price sell at 6.75
Closing rate at 5.10 NO because strike price
will result in lower payment.
Net outcome; payment in spot market 4m x 153,000
5.1% x 9/12
Premium 4,200
Net payment 157,200
Effective interest = net payment/ amount
borrowed
157,200/ 4,000,000 x 12/9 5.24%

ILLUSTRATION 4 on INTEREST RATE FUTURES

Fourwanine Ltd is a consumer electronics wholesaler with a highly seasonal business. The business is highly
cash generative in the first half of the year but needs to borrow to cover its cost in the other half of the year.
The company will move into the borrowing period in three months’ time and expects to borrow £5 million for
the entire low season. The directors are concerned that interest rates are expected to rise over the next few
months.
Interest rates and FRAs are currently quoted as follows:
Spot rate 5.75 - 5.50
3---6 FRA 5.82 - 5.59
3 – 9 FRA 5.94 - 5.64

The three month £500,000 sterling future maturing in three months is quoted at 94.15.
Requirements
I. Explain how a forward rate agreement (FRA) may be useful to the company. Illustrate this on the
basis that interest rates
a. Rise to 6.5%
b. Fall to 4.5% (8 marks)
II. Explain how the 3-month £500,000 sterling future may be useful to the company and illustrate its
usefulness under the same two interest rate scenarios of a rise to 6.5% or a fall to 4.5%.
(9 marks)
III. Explain how interest rate guarantees or short term interest rate caps could be used (3 marks)

SOLUTION TO ILLUSTRATION ON INTEREST RATE FUTURES

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Under Interest rate futures, you enter a sell contract when you are borrowing as you have to pay back
and you enter a buy contract if you are depositing funds.
Amount to be borrowed £10 million
Type of contract Sell contract
Contract duration 3 month contract
Number of contracts = amount/contract size x 10m / 0.5m x 6/3 = 40 contracts
loan period /contract length
Profit /loss = opening sell at 91 Closing buy at
89 Gain 2%
Total profit = gain x contract size x contract 2% x 0.5m x 3/12 x 40 contracts = £100,000
length x number of contracts
Net outcome; payment in spot market £10m x £550,000
11% x 6/12
Gain (£100,000)
Net payment £450,000
Hedge efficiency = gain on futures/ loss on
spot market
100,000/ 150,000 67%

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B PART OF THE INTEREST RATE FUTURES

Amount to be DEPOSITED £2 million
Type of contract Buy contract
Contract duration 3 month contract
Number of contracts = amount/contract size x 2m / 0.5m x 3/3 = 4 contracts
loan period /contract length
Profit /loss = opening buy at 94 Closing sell at
95 Gain 1%
Total profit = gain x contract size x contract 1% x 0.5m x 3/12 x 4 contracts = £5,000
length x number of contracts
Net outcome; receipt in spot market £2m x £25,000
5% x 3/12
Gain £5,000
Net RECEIPT £30,000
Effective interest rate.
30,000/2,000,000 x 12/3 4.5%

Solution to C
Amount to be borrowed $10,000,000
Type of contract Sell contract
Contract duration 6 month contract
Number of contracts = amount/contract size x loan period 10m / lm x 6/3 = 20
/contract length contracts
Profit /loss = opening sell at 91
Closing buy at 88.50
Gain 2.50%
Total profit = gain x contract size x contract length x number of 2.5% xlmx 3/12x20
contracts contracts = $125,000
Net outcome; payment in spot market $10m x 11% x 6/12 $550,000
Gain ($125,000)
Net RECEIPT $425,000
Effective interest = net payment/ amount borrowed
425,000/ 10,000,000 x 12/6 8.5%

ILLUSTRATION 5 (MAY 2017 ICAN PAST QUESTION)

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Large plc(LP) wishes to borrow N200 million for five years to finance the purchase of new non-current assets.
The preference of the company’s directors is that these funds are borrowed at a fixed rate of interest. The
company’s long term debt is currently rated BBB, meaning LP would have to pay 6.5% per annum for fixed
rate borrowing. Alternatively, LP could borrow at a floating rate i.e., the prime lending rate (PLR) + 2.25% at
the present time.
The directors of LP have recently been informed by its bank that TK plc, is also currently looking to borrow
N200 million for five years at a floating rate of interest and its AA rating gives it access to floating rate
borrowing at PLR + 1.50% per annum. TK plc would pay 5.5% per annum for fixed rate borrowing at the
present time.
Required :
a. State five reasons that a company might have for entering into an interest rate swap (5 marks)
b. Show how an interest rate swap could be used to the equal benefit of both companies, assuming that
the terms of the swap agreement are such that LP’s swap payment to TK plc is to be 5.5% fixed per
annum (7 marks)
c. Identify, with a supporting brief explanation, which of the two companies would be disadvantaged, if
PLR were to fall consistently within the five year terms of the interest rate swap (1 mark)
d. Identify two risks that both companies will face, should they decide to enter into the interest rate swap
agreement (2 marks)

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CHAPTER 15: BUSINESS VALUATION

ILLUSTRATIONS ON BUSINESS VALUATION
ILLUSTRATION 1 ON BUSINESS VALUATION
You are employed by Godspower print, a very large printing firm with retail outlets across Nigeria. Its board is
considering making an offer to buy 100% of the shares of Ilabe Startle Limited (ISL), a competitor of
Godspower print in the south east of Nigeria. ISL’s financial year end is 28 February and its most recent year
financial statements are summarized below:
ISL INCOME STATEMENT FOR THE YEAR ENDED 28 FEBRUARY 2014
N MILLION
REVENUE 17.3
PROFIT BEFORE INTEREST AND TAX 5.9
INTEREST (0.3)
PROFIT BEFORE TAXATION 5.6
CORPORATION TAX AT 21% (1.2)
PROFIT AFTER TAXATION 4.4
DIVIDENDS DECLARED 1.1

ISL STATEMENT OF FINANCIAL POSITION AT 28 FEBRUARY 2014

N MILLION N MILLION N MILLION
NON CURRENT ASSETS
FREEHOLD LAND&BUILDING (Original cost N4.1 3.5
m)
MACHINERY (Original cost N8.8 m) 5.3
8.8
CURRENT ASSETS
INVENTORIES 3.0
RECEIVABLES 0.5
CASH AND BANK 2.8
6.3
CURRENT LIABILITIES
TRADE PAYABLES 3.5
DIVIDENDS 1.1
TAXATION 1.2
(5.8) 0.5
9.3
NON CURRENT LIABILITIES
10% DEBENTURES( REDEEMABLE 2024) (3.0)
6.3
EQUITY
ORDINARY SHARES OF N1 EACH 2.1
RETAINED EARNINGS 4.2
6.3

ADDITIONAL INFORMATION

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a. ISL’s management had some of the company’s assets independently revalued in January 2014. Those
values are shown below:
FREEHOLD LAND AND BUILDING 8.3 M NAIRA
MACHINERY 4.1 M NAIRA
INVENTORIES 3.1 M NAIRA
b. The average price/earnings ratio for listed business in the printing industry is 9 and the average
dividend yield is 6% per annum.
c. The cost of equity of business in the printing industry, taking account of the industry average level of
capital gearing is 14% per annum.
d. ISL’s finance department has estimated that the company’s pre-tax net cash inflows (after interest) for
the next four trading years ending 28 February, before taking account of capital allowances will be
N MILLION
YEAR TO 2015 4.6
YEAR TO 2016 4.3
YEAR TO 2017 5.2
YEAR TO 2018 5.7
▪ ISL’s machinery pool for taxation purposes had a written down value of N3.6 million at 28 February
2014. The pool attracts 18% (reducing balance) tax allowances in every year of ownership by the
company, except the final year. In the final year, the difference between the machinery’s written down
value for tax purpose and its disposal proceeds will be either:
▪ Treated by the company as an additional tax relief, if the disposal proceeds are less than the tax
written – down value or
▪ Be treated as a balancing charge to the company, if the disposal proceeds are more than the tax
written- down value.
You should assume that ISL will not be purchasing or disposing of any machinery in the years 2015 – 2018
and that it would dispose off the existing pool of machinery on 28 February 2018 at its tax written – down
value.
▪ Godspower print’s board estimates that in four years time, i.e. 28 February 2018, it could, if necessary
dispose off ISL for an amount equal to four times its after-tax cash flow (ignoring the effects of capital
allowances and the disposal value of the machinery) for the year to 28 February 2018.
Assume that the corporation tax rate is 21% per annum and paid in the same year it arises.
Requirement
Using the information provided, prepare a report for Godspower print Board which
X. Calculates the value of one share in ISL based on each of these methods
a. Net asset basis (historic cost)
b. Net asset basis (revalued)
c. Price/earnings ratio
d. Dividend yield
e. Present value of future cash flows
XI. Explain the advantages and disadvantages of using each of the five methods in part (a) above
XII. Identify and explain the different methods by which ISL shareholders could be remunerated
for their shares.
ILLUSTRATION 2 ON BUSINESS VALUATION (MAY 2015 ADJUSTED)
The directors of Dangote plc, a large conglomerate, are considering the acquisition of the entire share capital of
Ozone Limited, a private limited company which manufactures a range of engineering machinery. Neither

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company has any long term debt capital. The directors of Dangote plc believe that if Ozone is taken over, the
business risk of Dangote will not be affected.
The statement of financial position of OZONE as at 31/07/2013 is expected to be as follows
TOTAL ASSETS N N
NON CURRENT ASSETS (NET OF DEPRECIATION) 1,303,200
CURRENT ASSETS; STOCK AND WIP 1,031,800
RECEIVABLES 1,490,000
BANK 316,200 2,838,000
4,141,200
EQUITY AND LIABILITIES
ISSUED ORDINARY SHARES @ N1 EACH 100,000
DISTRIBUTABLE RESERVES 808,200
SHAREHOLDERS FUND 908,200
PAYABLES 1,507,200
BANK OVERDRAFT 1,725,800 3,233,000
4,141,200

SUMMARISED FINANCIAL RECORD FOR THE FIVE YEARS TO 31/07/2013 IS AS FOLLOWS;

YEAR ENDED 31/07 2009 2010 2011 2012 2013
ESTIMATED
(N)
Profit before extra-ordinary 121,600 276,000 197,600 192,800 212,800
items
Extra ordinary items 11,600 8,800 24,400 39,200 4,000
Profit after extra ordinary items 110,000 267,200 173,200 153,600 208,800
Dividend 33,000 80,160 51,960 46,080 62,640
Retained earnings 77,000 187,040 121,240 107,520 146,160
The following additional information is available
I. There have been no changes in the issued share capital of Ozone Limited during the past five
years.
II. The estimated values of Ozone’s non current assets and work in progress as on 31/07/13 are;
REPLACEMENT COST (N) REALISABLE VALUE (N)
NON CURRENT ASSETS 1,450,000 900,000
STOCK AND WIP 1,100,000 1,140,000
III. It is expected that 4% of Ozone Limited receivables as at 31/07/13 will be uncollectable
IV. The cost of capital of Dangote is 12% but the directors of Ozone estimate that the
shareholders of Ozone require a minimum return of 16% per annum from their investment in
the company.
V. The current PE ratio of Dangote is 18. Quoted companies with business activities and
profitability similar to those of Ozone have PE ratios of approximately 12, although these
companies tend to be larger than Ozone.
Requirements
Estimate the value of the total equity of Ozone Limited as on 31 July 2013 using each of the following
bases:
1. Historical basis of net assets valuation

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2. Replacement cost
3. Realizable value
4. Gordon dividend growth model
5. PE ratio model
State and justify briefly the approximate range within which the purchase price is likely to be agreed.
ILLUSTRATION 3 ON TERMINAL VALUE
a. Bratim PLC has declared a dividend of 20k per share and has a cost of equity of 15%. What is the
estimated value per share in Bratim, if the dividend is constant for 4 years and then 7% per annum to
infinity thereafter?
b. A company earned N6 per share and paid N3.48 per share as dividend in the previous year. Its
earnings and dividends are expected to grow at 15% for 6 years and then at a rate of 8% indefinitely.
Capitalization rate is 18%. What is the share price today

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SESSION 16: FREECASH FLOW MODEL

FREE CASH-FLOW MODEL OF BUSINESS VALUATION
The market value of equity is given by the present value of the associated future cash-flows. Future cash-flows
are represented by future dividends under Dividend Valuation Model (DVM) , but analyst would prefer to use
the Free cash-flow or Free cash-flow to equity when any of the following occurs:
▪ The company does not pay dividend
▪ The investor can take control of the company, change dividends substantially to the company’s
capacity.
▪ The company pays a dividend that differs significantly from the company’s capacity to pay dividends
FREE CASH FLOW (FCFF)
This is the actual amount of cash that a company has left from its operations that could be used to pursue
opportunities that enhance shareholder value. The free cash flow is the cash flow derived from the operations
of a company after subtracting working capital, investment, taxes and represents the funds available for
distribution to the capital contributors that is shareholders and debt holders.
Free cash flow = EBIT – T + NON CASH CHARGES – CAPITAL EXPENDITURES – LESS NET
WORKING CAPITAL INCREASES + NET WORKING CAPITAL DECREASES + SALVAGE VALUE
RECEIVED.
FREE CASH FLOW TO EQUITY (FCFE)
This is the cash-flow available to the company’s equity holders after all operating expenses, interest and
principal payments have been paid and the necessary investments in working capital and fixed capital have
been made. It is the cash-flow from operations minus capital expenditure minus payments to (plus receipts
from) debt holders.
STEPS IN USING FCFF TO DETERMINE VALUE OF EQUITY
▪ Compute the future FCFF using whatever formula
▪ Determine the appropriate WACC, if not given
▪ Calculate the present value of future FCFF which is same as the total market value of the company
▪ The value of equity = total market value of the company less market value of debt
STEPS IN USING FCFE TO DETERMINE VALUE OF EQUITY
▪ Estimate the future FCFE
▪ Determine the appropriate cost of equity
▪ Determine the market value of equity by discounting the FCFE using cost of equity.
EXAM TIPS
Check carefully the differences between FCFF and FCFE in the scenario to determine the formula to use. Care
should also be taken in the treatment of cash & cash equivalent as well as loans included in current liabilities.

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ILLUSTRATIONS ON FREECASH FLOW MODEL

ILLUSTRATION 1 (MAY 2017 PAST QUESTION)
LA Ltd, a food packaging company has operated as a private company for the past 10 years. The company has
been growing rapidly over the last few years. The Directors are now considering listing the company on the
stock market. Preparatory to this, the Directors are interested in determining a fair price per share for the
company. Assume today is November 1, 2016.
The following information has been extracted from the most recent audited financial statements of LA Ltd.
STATEMENT OF PROFIT OR LOSS, OCTOBER 31,2016:
N million
Sales revenue 15,790
Cost of sales (13,514)
EBITDA 2,276
Depreciation (440)
EBIT 1,836
Interest expense (330)
Earnings before tax 1,506
Tax at 30% (452)
Profit after tax 1,054
STATEMENT OF FINANCIAL POSITION AS AT OCTOBER 31:
2016 Nm 2015 Nm
Non current assets 6,224 5,942
Current assets
Cash and bank 476 542
Account receivables 1,072 980
Inventory 2,542 2,078
Total current assets 4,090 3,600
Total assets 10,314 9,542
Equity and liabilities
Non-current liabilities (bonds) 2,400 2,500
Current liabilities
Short term loans 1,936 1,432
Account payables 3,084 2,792
Total current liabilities 5,020 4,224
Equity 2,894 2,818
Total equity and liabilities 10,314 9,542

The following additional facts are available:

▪ The Directors believe that the free cash flow to equity model should provide appropriate valuation for
the company’s shares
▪ An investment banker has provided the following estimates of cost of capital; cost of equity 15%, post
tax cost of debt 4% and WACC 12.5%
▪ The Directors believe that the free cash flow to equity will grow by 18% for the next 5 years and 5%
thereafter.
▪ The company currently has 600 million shares in issue
a. Calculate the free cash flow available to equity for the year ended October 31, 2016 (7 marks)
b. Use free cash flow to equity model to calculate the current value per share (5 marks)
c. What are the key advantages and disadvantages of stock exchange listing (8 marks)

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ILLUSTRATION 2 ON FREE CASH FLOW MODEL

Uche plc was incorporated on 31 December, 2015. Given below are the company’s financial statements for the
two years following incorporation.
UCHE PLC INCOME STATEMENT
2016 N’000 2017 N’000
EBITDA 200.00 220.00
Depreciation 45.00 49.50
EBIT 155.00 170.50
Interest expense 15.68 17.25
Income before taxes 139.32 153.25
Tax at 30% 41.80 45.97
Net income 97.52 107.28

UCHE PLC STATEMENT OF FINANCIAL POSITION

2015 N’000 2016 N’000 2017 N000
Non -current asset at cost 500.00 500.00 550.00
Depreciation (0.00) (45.00) (94.50)
500.00 455.00 455.50
Current Assets
Cash 0.00 108.92 228.74
Receivables 0.00 100.00 110.00
Inventory 60.00 66.00 72.60
60.00 274.92 411.34
Total assets 560.00 729.92 866.84
Current liabilities
Trade payables 0.00 50.00 55.00
Short term loan 0.00 10.00 12.00
0.00 60.00 67.00
Long Term Loan 224.00 236.40 259.04
Share capital 336.00 336.00 336.00
Retained earnings 0.00 97.52 204.80
Total liabilities and equity 560.00 729.92 866.84
Required
a. Calculate the Free Cashfow of the firm for 2016 and 2017
b. Calculate the Free Cashflow for Equity for 2016 and 2017
c. Calculate the value of the firm using the free cash flow for the firm if the cost of equity is 15% and the
weighted average cost of capital is 12%
d. Calculate the value of the firm using the free cash flow to equity, if the cost of equity is 15% and the
weighted average cost of capital is 12%

SOLUTION TO ILLUSTRATION 2

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FREE CASH FLOW TO FIRM AND FREE CASH FLOW TO EQUITY

2016 2017 N N
Net income 97.52 107.28
add back interest net tax 10.98 12.08
add back depreciation 45.00 49.50
less investment in non current asset - (50.00)
less increase in working capital (56.00) (11.60)

FREE CASH FLOW TO FIRM 97.50 107.26

less interest net tax (10.98) (12.08)
add increase in debt 22.40 24.64

FREE CASH FLOW TO FIRM 108.92 119.82

WORKING NOTES
CHANGE IN WORKING CAPITAL YR 2015 YR 2016 YR 2017
Current assets excluding cash current 60.00 166.00 182.60
liability excluding short term loan
working capital 50.00 55.00
CHANGE IN WORKING CAPITAL 60.00 116.00 127.60

CHANGE IN DEBT 56.00 11.60

NON current liabilities 224.00 236.40 259.04
short term loan 10.00 12.00
debt balances 224.00 246.40 271.04
CHANGE IN DEBT 22.40 24.64

NON CURRENT ASSETS 500.00 500.00 550.00

Investment in NCA - 50.00

Note: cash and cash equivalents are ignored in calculating change in working capital while short term
loans should be treated under debt and not working capital as they are seen as financing cash flows
investment in non current assets should be treated based on cost but where cost is not given, the net
book values should be added to depreciation to get the gross cost

NON CURRENT ASSETS 500.00 455.00 455.50

DEPRECIATION - 45.00 94.50
GROSS COST 500.00 500.00 550.00
Investment in NCA - 50.00

For the C and D aspect, to get value of company using FCFF, WACC should be used to discount
while using FCFE, cost of equity should be used as the discount rate.

PROJECTED CASHFLOW 1 2 3

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REVENUE (9%) 272,500 297,025 323,752

COST OF SALES (9%) 163,500 178,215 194,254
GROSS PROFIT 109,000 118,810 129,503
OPERATING COST 100,601 107,935 115,886
EBIT 8,399 10,875 13,617
ADD DEPRECIATION 6,726 7,201 7,771
LESS INTEREST 3,700 3,700 3,700
LESS TAXATION 750 1,410 2,153
INCREMENTAL WORKING CAPITAL 970 1,079 1,176
INVESTMENT IN NON CURRENT ASSETS 3,960 4,752 5,702
FREE CASH FLOW TO EQUITY 5,725 7,135 8,657

Value of business given by present value of FCFE including terminal value

Yr CASH FLOW Dcf @10% Pv
1 5,725 0.909 5,205
2 7,135 0.826 5,897
3 8,657 0.751 6,504
4 ONWARDS Terminal value = 8,657 0.751 95,704
(1.03)/0.10-0.03)
113,310
Workings
1. Non current assets and depreciation
YEAR 1 2 3
START 63,300 67,260 72,012
20% GROWTH 3,960 4,752 5,702
END 67,260 72,012 77,714
DEPRECIATION 6,726 7,201 7,771
2. OPERATING COSTS
YEAR 1 2 3
VARIABLE 40,875 44,554 48,564
COST(9%)
FIXED COST(6%) 53,000 56,180 59,551
DEPRECIATION 6,726 7,201 7,771
TOTAL 100,601 107,935 115,886
3. INCREMENTAL WORKING CAPITAL
YEAR 1 2 3
CUMULATIVE 11,990 13,069 14,245
(9%)
INCREMENTAL 990 1,079 1,176
INITIAL WORKING CAPITAL IS net current assets less cash = 13,500 - 2,500 = 11,000 x 1.09 =
Nil,990.
4. Tax computation
year 0 1 2 3
EBIT 8,399 10,875 13,617
1 3,700 3,700 3,700

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TAX @ 30% 750 1,410 2,153 2,975

YEAR DUE 1 2 3 4

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CHAPTER 17: ECONOMIC VALUE ADDED, MARKET

VALUE ADDED AND SHAREHOLDERS VALUE
ANALYSIS
SHAREHOLDER VALUE ANALYSIS
This is simply defined as the process of analyzing the activities of a business to identify how they will result in
increasing shareholder wealth.
This is a concept that believes that the value of a business is affected or driven by just seven factors known as
value drivers. To increase the value of a business that is to generate additional value, one or more of these
seven will need to alter in a favorable direction. The value drivers and their effect on shareholder value, are
▪ Sales growth rate: if a greater level of sales can be generated in the future than was expected, this
should create more cash flows and therefore value. The greater level of sales could come from a new
product and provided that this did not have an adverse effect one of the other value drivers, greater
value would necessarily be created.
▪ Operating profit margin: is the ratio of net profit before financing charges and tax to sales. The
higher the ratio, the more cash flows there are for each sale. Thus if costs can be controlled more
effectively, more cash will tend to flow from each side and value will be enhanced.
▪ Corporation tax rate: this clearly affects cash flows and value because tax is levied directly on
operating cash flows and management’s ability to affect tax rate and amount of tax paid is marginal.
▪ Investment in non -current assets: normally cash has to be spent on additional non- current assets in
order to enhance shareholder value. Wherever managers can find ways of reducing the outlay on non-
current assets without limiting the effectiveness of the business will tend to enhance shareholder
value.
▪ Investment in working capital: nearly all business activities give rise to a need for working capital;
inventories, receivables, payables and cash. Amounts tied up in working capital can be considerable.
Steps taken to encourage trade receivables to pay more quickly than expected will bring cash flows
forward and tend to generate value, as long as the benefits of quicker payments outweigh the cost of
delivering it.
▪ Cost of capital: the cost of funds used to finance the activities of the business will typically be a
major determinant of shareholder value. So if the business can find alternative, cheaper, sources of
long term finance, value would tend to be enhanced.
▪ Life of projected cash flows: clearly, the longer that the life of any cash generating activity can
continue, the longer its potential to generate value.

ILLUSTRATIONS ON ECONOMIC VALUE ADDED, MARKET VALUE

ADDED AND SHAREHOLDERS VALUE ANALYSIS
ILLUSTRATION 1 (NOVEMBER 2016 ICAN PAST QUESTION)
Jack Limited is a family-owned business which has grown strongly in the last 50 years. The
key objective of the company is to maximize the family’s wealth through their shareholdings.
Recently the directors introduced value-based management, using Economic Value Added
(EVA) as the index for measuring performance.
You are provided with the following financial information

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Statement of Profit or Loss and Other Comprehensive Income for the year ended 31
December, 2015
N million
Operating profit 340.0
Finance charges (115.0)
Profit before tax 225.0
Tax at 25% (56.3)
Profit after tax 168.7
Notes
I. The following items
2015 Nm 2014 Nm
Capital employed from the statement of financial 6,285 6,185
position
Operating cost
Depreciation 295 285
Provision for doubtful debts 10 2.5
Research and development 60 -
Other non cash expenses 35 30
Marketing expenses 50 45
II. Economic depreciation is assessed to be N415 m in 2015. Economic depreciation
includes any appropriate amortisation adjustments. In previous years, it can be
assumed that economic and accounting depreciation were the same.
III. Tax is the cash paid in the current year (N45 million) and an adjustment of N2.5
million for deferred tax provision. There was no deferred tax balance prior to 2015
IV. The provision for doubtful debt was N22.5 million on the 2015 statement of financial
position
V. Research and development cost is not capitalised in the accounts. It relates to a new
project that will be developed over five years and is expected to be of long term
benefit to the company. The first year of this project is 2015
VI. The company has been spending heavily on marketing each year to build its brand
long term
VII. The cost of equity is 16%, pretax cost of debt 5% and the gearing (debt/equity) ratio
is 1.5:1
Required
a. Calculate, showing all relevant workings , the Economic Value Added (EVA) for
year ended 31 December, 2015. Make use of the adjusted opening capital employed.
Comment on your result and make appropriate recommendations
(15 marks)
b. Irrespective of your answer in (a) above , assume the company’s current EVA is
N120 million and that this will decline annually by 2% for the next 10 years and then
increase by 4% per annum in perpetuity. Assume the following for this part only.

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Cost of equity is 14% and WACC is 10%. Calculate the market value added (MVA)
by the company (5 marks)

SOLUTION TO ILLUSTRATION 1
• Calculation of Net Operating Profit After Tax (NOPAT)

Nm Nm
Operating profit 340.00
Add back:
Non-cash items 35.00
Accounting depreciation 295.00
Doubtful debts 10.00
Research and development 60.00
Marketing expenses 50.00 450.00
Less
Economic depreciation 415
Tax cash paid (45 - 2.5) 42.50
Loss tax relief on interest 28.75
(25% of N 115m) (486.25)
NOPAT 303.75
Adjusted opening capital employed (AOCE)
Per 2014 Statement of Financial Position Add back: 6,185.00
Provision for doubtful debt at the end of 2014 (22.50-10) 12.50
Other non-cash expenses (2014) 30
Marketing expenses (2014) 45
Adjusted opening capital employed (AOCE) 87.50
• Weighted Average Cost of Capital (WACC)
WACC = 16X2
5+5x3
5X0.75 = 8.65%
• EVA (Economic Value Added)
EVA = NOPAT - (AOCE x WACC)
= N303.75 - (&6,272.50m x 0.0865) = - N238.82 million

Comments and recommendations

The company is currently destroying value as it is failing to meet the economic cost of its own
capital. This is an unsustainable position in the long term and will lead to shareholders'
dissatisfaction.
To improve EVA, the following are recommended:
• Dispose assets in excess of requirement to minimize capital cost.
• Exercise tighter expenditure control to reduce expenses.
• Adopt a more aggressive sales drive to improve revenue.
• Market Value Added (MVA) is the present value (using WACC) of future EVA.
• First 10 years when g= -2%. It is faster to work with growing annuity in this
case.
PV = EVA(l+g)/k0-g x 1 - (1 + g)/(l + k0)n

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120(1 0.02) 11 0.02

1.10
10 0.10 0.02 = N671.28m
• Years 11 to infinity Using Terminal Value
EVAn = 120 (1 - 0.02)10x 1.04 = 101.97m
PV =
101.97
0.100.04 X (1.10) 10 = ft655.23m
Total MVA = N671.28m + f$655.23m = N1,326.51million

ILLUSTRATION 2 ON SHAREHOLDERS VALUE ANALYSIS

Brave plc is a family run business, which obtained a stock market listing around three
years ago. The board is comprised of 75% members of the founding family. The
company has a current stock market capitalization of N250 million and the board owns
45% of the issued shares. The net book value of assets held by Brave plc is N300 million.
The company enjoys competitive advantage through being a low cost producer and the
board feels that this competitive advantage is likely to continue for the next six years. The
following information relating to the company and the period of competitive advantage is
available.
Current sales revenue N200 million
Estimated sales growth 6%
Operating profit margin after depreciation 15%
Additional working capital investment 7% of sales increase
Additional non - current asset investment 12% of sales increase
Following the end of the competitive period, cash flows are expected to remain constant
for the foreseeable future.
Brave plc currently has no long term debt and holds short term investment worth
N2.5million. The corporation tax rate is expected to be 21% for the foreseeable future.
The company has an equity beta of 0.75, the risk free interest rate is 3% and the return on
the market portfolio is 11%.
The company has a policy of paying out 10% of its post tax earnings as dividends.
▪ Calculate the value of Brave plc using SVA methodology and comment on the results (13
marks)
▪ Discuss the reasons why Brave plc has a market capitalization lower than its book value
of assets (7 marks).

SOLUTION TO ILLUSTRATION ON SHAREHOLDERS VALUE ANALYSIS

All in Nm

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YEAR 1 2 3 4 5 6
Sales 212 224.72 238.20 252.50 267.65 283.70
Profit @ 15% 31.80 33.71 35.73 37.87 40.15 42.56
tax@21% (6.68) (7.08) (7.50) (7.95) (8.43) (8.94)
NWC (0.84) (0.89) (0.94) (1.00) (1.06) (1.12)
NCA (1.44) (1-53) (1.62) (1.72) (1.82) (1.93)
Free cashflow 22.84 24.21 25.67 27.20 28.84 30.57
dcf@9% 0.917 0.842 0.772 0.708 0.650 0.596
PV 20.94 20.38 19.82 19.26 18.75 18.22

PV of cashflows from years 1 - 6 = N117.37 million

Post year 6 cash flows (to infinity)= 30.57/0.09 x 0.596 = N202.44
Total SVA value = N117m + N202.44 = N322.31m
The majority of the value comes from the residual value, which is based on the assumption of zero
growth in cash flows from year 6. This is highly dependent on the growth being as predicted in the
period of competitive advantage.
The SVA value is significantly higher than the market capitalization of N250m. this may be caused
by the market assuming a lower growth rate or a higher discount rate than those used in the SVA
calculation.
Year 0 1 2 3 4 5 6
sales 200 212 224.72 238.20 252.50 267.65 283.70
Sales growth 12 12.72 13.48 14.29 15.15 16.06
NCA 12% 1.44 1.53 1.62 1.72 1.82 1.93
NWC 7% 0.84 0.89 0.94 1.00 1.06 1.12
Discount factor = 3 + 0.75(11 - 3) = 9%
B PART
The current market capitalization is below its net assets value which suggests that the company may
be worth more if it was liquidated. In reality the assumption of matching net book value to market
value of assets may not hold. This may be the explanation of low market capitalization as the market
may not see any future in the company and is already valuing it on a break up basis.
There are other factors which may cause the market to place low valuation on Brave
▪ The dividend policy offers a relatively low payout of 10%. If there are no plans to reinvest
retained earnings then cash balances will be substantial. This may explain the high net assets
valuatio.
▪ The stock market may be suspicious of the level of control exercised by the founding family.
The founding family appears to control the board and also own a substantial number of
shares and as such they may dominate the smaller shareholders. The market may view the
current management as less able than similar companies due to this family dominance and
this affects the valuation.
▪ The company is currently all equity funded, which the market may think is too low and does
not allow the company to exploit the advantage of debt being cheaper than equity due to tax
shield.

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ILLUSTRATION 3 ON ECONOMIC VALUE ADDED (EVA)

The directors of Stardom plc were surprised at a recent newspaper article which suggested that the
company performance in the last two years had been poor. The CEO commented that turnover
had increased by nearly 17% and pre-tax profit by 25% between the last two financial years, and
that the company compared well with others in the same industry.
STATEMENT OF PROFIT OR LOSS
2013 N MILLION 2014 N MILLION
TURNOVER 326 380
PRE TAX ACCOUNTING PROFIT (NOTE 67 84
1)
TAXATION 23 29
PROFIT AFTER TAX 44 55
DIVIDENDS 15 18
RETAINED EARNINGS 29 37

STATEMENT OF FINANCIAL POSITION

2013 N MILLION 2014 N MILLION
NON CURRENT ASSETS 120 156
NET CURRENT ASSETS 130 160
250 316
EQUITY 195 236
NON CURRENT BANK 55 80
LOANS
250 316
NOTE 1: After deduction of economic depreciation of the company’s non-current assets. This is
also the depreciation for tax purposes.
OTHER INFORMATION
a. The company has non capitalized leases valued at N10 million in each year 2012 to 2014
b. Statement of financial position capital employed at the end of 2012 was N223 million
c. The company’s pre tax cost of debt was estimated to be 9% in 2013 and 10% in 2014.
d. The company’s cost of equity was estimated to be 15% and 17% in 2013 and 2014.
e. The target capital structure is 60% equity and 40% debt
f. The effective tax rate is 35% in both 2013 and 2014.
g. Economic depreciation was N30 million
h. Other non cash expenses were N10 million per year both in 2013 and 2014.
i. Interest expense was N4 million in 2013 and N6 million in 2014.
Estimate the economic value added for the both 2013 and 2014 stating the assumptions and
appraising the performance of the company.
1. Calculate the appropriate discount rate
2. MVA uses EVA, explain MVA first then explain how to get EVA (no calculation)
3. Calculate EVA for 2015e, 2016e and 2017e
4. Explain the process to get value of equity using MVA

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5. Calculate the value of equity of Topnotch as at January 1 2015. Assume a two stage MVA where stage
1 covers the period from 2015 to 2017 and stage 2 from 2018 and beyond. Predict a constant growth
of EVAs from 2018 which equals the growth rate of EVAs from 2017 to 2018.
6. Suppose that the valuation of equity by Dividend valuation model will show the same result as the
valuation of your MVA. How large must the growth rate of dividends be for an equivalent result of a
DVM from 2019 onward, if the 2018 dividend paid is equal to 2017 dividend paid?

SOLUTION TO ILLUSTRATION 4 ON EVA

NOPAT 2013 Nm 2014 Nm
PAT 44 55
NON CASH EXPENSE 10 10
INTEREST (1-TAX RATE) 2.60 3.90
56.60 68.90
CAPITAL EMPLOYED 2013 Nm 2014 Nm
At start 223 250
Non capitalised lease 10 10
233 260
WACC 2013 (15 X 0.60) + 9(1 - 0.35) X 0.40 = 11.34%
WACC 2014 (17 X 0.60) + 10(1 - 0.35) X 0.40 = 12.8%
EVA 2013 56.60 - (11.34% X 233) = N30.18m
EVA 2014 68.90 - (12.8% X 260) = N35.62m
The EVA shows that the company had added significant value in both years and achieved a
satisfactory level performance.
B question is on relationship between EVA and NPV
The present value of all EVAs generated over the life of a project, summed together should
approximate the NPV of the project. EVA shows the return in excess of the cost of financing them
just like NPV.
C PART OF THE QUESTION IS ON ADVANTAGES AND DISADVANTAGES OF EVA
ADVANTAGES OF EVA
▪ It is consistent with maximising shareholders wealth
▪ It is easily understood by managers
▪ It can be linked to managerial bonus schemes and motivate managers to take decisions that
increase shareholders value
▪ It makes the cost of capital visible to all managers
▪ It is based on cash flows and is less easy to manipulate than accounting data
▪ It clearly shows if a company is creating or destroying value

DISADVANTAGES OF EVA
▪ It can be difficult to calculate because of numerous adjustments involve.
▪ Economic depreciation is difficult to estimate and conflicts with generally acceptable
accounting principles which may hinder its acceptance

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▪ It is difficult to use for inter firm or inter divisional comparisons because it is not a relative
measure
▪ It is normally historic and so may not be useful for strategic and future decisions
▪ It may favour investments with relatively short time horizon

ILLUSTRATION 6 ON RANGE
Pluto Training was established in 1999 and since that time it has developed rapidly. The directors are
considering either a flotation or an outright sale of the company.
The company provides training for companies in the computer and telecommunications sectors . it offers a
variety of courses ranging from short intensive courses in office software to high level risk management
courses using advanced modeling techniques. Pluto employs a number of in-house experts who provide
technical materials and other support for the teams that service individual client requirements. In recent years,
Pluto has diversified into the financial services sector and now also provides computer simulation systems to
companies for valuing acquisitions. The business now accounts for one third of the company’s total revenue.
Pluto currently has 10 million, 50k shares in issue. Jupiter is one of the few competitors in Pluto’s line of
business. However, Jupiter is only involved in the training business. Jupiter is listed on a small company
investment market and has an estimated beta of 1.5. Jupiter has 50 million shares in issue with a market price
of 580k. The average beta for the financial services sector is 0.9. Average market gearing (debt to total market
value) in the financial services sector is estimated at 25%.
Other summary statistics for both companies for the year ended 31 December 2007 are as follows
COMPANY PLUTO JUPITER
NET ASSETS AT BOOK VALUE (N MILLION) 65 45
EARNINGS PER SHARE (K) 100 50
DIVIDEND PER SHARE (K) 25 25
GEARING (DEBT TO TOTAL MARKET VALUE) 30% 12%
FIVE YEAR HISTORIC EARNINGS GROWTH 12% 8%
(ANNUAL)

Analysts forecast revenue growth in the training side of Pluto’s business to be 6% per annum, but the financial
services sector is expected to grow at just 4%.
Background information:
The equity risk premium is 3.5% and the rate of return on short dated government stock is 4.5%. Both
companies can raise debt at 2.5% above the risk free rate. Tax on corporate profits is 40%.
a. Estimate the cost of equity capital and the weighted average cost of capital for Pluto trading
b. Advise the owners of Pluto trading on a range of likely issue prices for the company.

SOLUTION TO ILLUSTRATION
1. UNGEAR THE BETA OF JUPITER AND FINANCIAL SERVICES SECTOR Beta asset =
1.5 X 88/(88 + 12(1-0.40) =1.3865 for Jupiter
Beta asset = 0.9 x 75/(75 + 25(1-0.40) =0.75 for Financial services

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2. Beta asset for Pluto based on business split = (2/3 x 1.3865) + (1/3 x 0.75) = 1.175
3. Regear beta of Pluto = 70 + 30 (l-0.40)/70 x 1.175 = 1.48
4. Ke = 4.5 + (3.5x1.48) = 9.68%
5. WACC = (0.7 x 0.0968) + 0.3 x (0.025 + 0.045)1-0.40) = 8.04%
RANGE OF LIKELY ISSUE PRICES
NET ASSETS = 45M/ 10M = N4.50/SHARE

DIVIDEND VALUATION MODEL = Do (1 + g)/ke -g = 25(l+0.726)/0.0968 - 0.0726 =

N11.06/share.
g = br = 0.0968 x 75/100 = 7.26%
The range is between N4.50/share to N11.06/share.

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SESSION 18; MERGER AND ACQUISITION

Companies may decide to increase the scale of their operations through a strategy of internal growth by
investing money to purchase or create assets and product lines internally (organic growth) or by buying other
companies thus acquiring readymade tangible and intangible assets and product lines (acquisition).
Organic growth in areas where the company has been successful and has expertise may present few risks but it
can be slow/expensive or sometimes impossible while acquisition requires high premiums that make the
creation of value difficult.
ADVANTAGES OF MERGER AS AN EXPANSION STRATEGY
1. Speed: acquisition of another company is a quicker way of implementing a business plan as it allows
a company to reach a certain optimal level of production much quicker than through organic growth.
2. Lower cost: acquisition may be a cheaper way of acquiring productive capacity than through organic
growth. For instance an acquisition can take place through an exchange of shares with no impact on
the firm’s financial resources.
3. Acquisition of Intangible Assets: such as brand recognition, reputation, customer loyalty and
intellectual property which are more difficult with organic growth.
4. Access to overseas markets: easy breaking into the overseas market is achieved through acquiring a
local firm.
DISADVANTAGES OF MERGER AS AN EXPANSION STRATEGY
1. Exposure to business risk: acquisitions involve large investments by the bidding company and if it is
not viable, then the effect on the acquiring firm may be catastrophic.
2. Exposure to financial risk: some information may have been hidden from the bidding company
during the acquisition process, leading to a less than complete information on the target company.
3. Acquisition premium: is the amount paid over the present market value. This premium is normally
justified by the management of the bidding company as necessary for the benefits. However , too large
a premium may render an acquisition unprofitable.
4. Managerial competence: the management of the acquiring company may not have the experience or
ability to deal with operations on the new larger scale even if the new management is retained.
5. Integration problems: as each company has a different culture, history and way of operations.
The table below summarises the relative merits of both approaches
ACQUISITION ORGANIC GROWTH
Quicker Entry cost may be too high
May be cheaper to buy an existing firm than go Clash of cultures
for a new start up
Lower risk as the target already has goodwill May get presence in places that would not
and a customer base otherwise have been chosen
Could be the best way of getting round barriers Easier to control growth if organic
to entry
One less competitor, when you acquire or merge Easier to introduce new technology and systems
with the competitor.
Target may be undervalued Reputation of the target company? Is not a
problem with organic growth
Possibility of hiding ones identity It may be easier to finance as new jobs may
result in grants

TYPES OF MERGER

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Merger involves two or more companies pooling their interest and having common ownership of the new
company’s assets while acquisition usually involves a stronger company (predator) taking over the assets of a
smaller company (target) and assuming ownership of these assets.
1. HORIZONTAL MERGER is one in which a company acquires another company in the same line of
business. it happens between firms which are formerly competitors and which reduce competition in
the market in which they operate (increase market power). A horizontal merger is said to achieve
horizontal integration.
2. VERTICAL MERGER is a merger between firms that operate at different stages of the same
production chain or firms that produce complementary goods such as a newspaper company acquiring
a paper manufacturer. It is either backward integration when the firm merges with a supplier or
forward integration when the firm merges with a customer. A backward vertical integration is aimed
at controlling the supply chain while forward vertical integration is aimed at controlling distribution.
3. CONGLOMERATE MERGER is a merger where a company acquires another company in an
unrelated line of business for example a newspaper company acquiring an airline. It is aimed at
diversification.
4. CONGENERIC MERGER

EVALUATING THE CORPORATE AND COMPETITIVE NATURE OF A GIVEN ACQUISITION

PROPOSAL
Expansion by organic growth or acquisition should only be undertaken if it leads to an increase in the wealth
of the shareholders (that is when it creates synergies which either increase revenues or reduce cost or when the
management of the acquiring company can manage the assets of the target company better than the incumbent
manager thus creating additional value for the new owners).
ASPECTS THAT WILL HAVE AN IMPACT ON THE COMPETITIVE POSITION OF THE FIRM
AND ITS PROFITABILITY IN A GIVEN ACQUISITION PROPOSAL
1. MARKET POWER: reducing competition in the industry, giving the company ability to charge
higher prices for its products and have greater bargaining power with suppliers. This can be achieved
by horizontal merger.
2. BARRIERS TO ENTRY: this can be achieved through vertical acquisition
3. SUPPLY CHAIN SECURITY: ensuring that there is no disruption in the supply of inputs that will
threaten the company’s ability to produce, sell or retain its competitive position.
4. ECONOMIES OF SCALE: larger scale of operations may lead to reduction in the cost per unit
resulting from increased production (as production increases, cost of producing each additional unit
falls)
5. ECONOMIES OF SCOPE: refers to when it is more economical to produce two or more products
jointly in a single production unit than to produce them in separate firms. Scope economics arise from
the spreading of fixed cost over an expanded product mix and cost complementaries in producing the
different products.
6. FINANCIAL SYNERGY, TAX AND DEBT BENEFITS
7. DISPOSAL OF CASH SLACK: where a cash rich money company seeks a development target. The
target company should have great projects but not funds. Examples exclusive rights to products or use
of assets but no funds to start activities.

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8. ACCESS TO CASH RESOURCES: where a company with a number of cash intensive projects,
products in their pipeline or heavy investment in research and development might seek a company that
has significant cash resources or highly cash generative product lines to support their own needs.
9. CONTROL OF THE COMPANY: where the objective is to find a target firm which is badly
managed and whose stock has underperformed the market. The management of an existing company
is not able to fully utilize the company’s assets potential and the bidding company feels that it has
greater expertise or better management methods. The bidding company therefore believes that the
assets of the target firm will generate for them a greater return than for their current owners (market
valuation of the company is lower than the asset value).
10. ACCESS TO KEY TECHNOLOGY: acquires target companies in order to get rid of the
technology.
CREATING SYNERGIES
The existence of synergies increases the shareholder value in an organization. The identification, quantification
and announcement of these synergies are part of the process as shareholders must be convinced about the
merger. Synergy occurs when two companies are worth more joined together than when separate. (the 2+2=5
concept)
REVENUE SYNERGY
This exists when acquisition leads to higher revenue, higher return on equity or a longer period of growth.
They arise from increased market power, marketing synergies and strategic synergies. Revenue strategies are
difficult to assess as it is difficult to determine customers reaction to new mergers and demand for price
concession from cost savings. Customer relationship management and product technology management are
two core business processes that will deliver revenue synergy.
COST SYNERGY
This results primarily from economies of scale. As the level of operation increases, the marginal cost falls
which is manifested in greater operating margins for the combined entity. Rationalization of shared activities
like combining two sales teams, no need for two head offices.
FINANCIAL SYNERGY
This arises from one or a combination of the following
a. DIVERSIFICATION; is reduction of risk and could be beneficial for private firms or closely held
publicly traded firms.
b. CASH SLACK; arises when a significant excess cash firm acquires a firm with great projects but
insufficient capital leading to increase in the present value of the project.
c. TAX BENEFITS; arises if one of the firms has tax deductions but no profits while the other firm has
income which pays significant taxes (assets of the firm been taken over can be written up to lead to
higher tax savings).
d. DEBT CAPACITY; diversification will lead to an increase in debt capacity and increase in the value
of the firm. Where two firms with no/low debt capacity combine, it could create a company that has
the capacity to borrow money and create value. When two companies in different businesses combine,
their earnings is less variable and may be able to borrow more than individual firms.
DEVELOPING AN ACQUISITION STRATEGY
The main reasons behind a strategy for acquiring a target firm include the fact that the target firm is
undervalued (finding undervalued firms, funds to acquire them and the skill to execute the acquisition) or

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that the predator wants to diversify operations in order to reduce risk (elimination of unsystematic risk and
increasing potential value)
PORTER’S TEST FOR ASSESSING ACQUISITIONS
Porter suggested three tests of any proposed acquisition
1. THE ATTRACTIVENESS TEST; is the target company in an attractive market? This can be
discussed using PEST and PORTER’S 5 forces ANALYSIS.
2. THE COST OF ENTRY TEST; even if the market is attractive, there may be cheaper ways of
entering it. One line of argument is to consider the alternative of organic growth or to see if the target
company is overpriced.
3. THE BETTER OFF TEST; the shareholders have the option of simply buying shares in the target
company without the need for a full merger or acquisition. The acquisition must generate extra
benefits or synergies.
CRITERIA FOR CHOOSING AN APPROPRIATE TARGET FOR ACQUISITION
Acquirers must be able to assess the acquisition from the target company’s point of view as well as from
their own. They must be able to identify and capture new skills in the companies they buy. The criteria that
should be used to assess whether a target is appropriate will depend on the motive for the acquisition.
4. BENEFIT FOR ACQUIRING UNDER VALUED COMPANY; Target firm should trade at
prices below the estimated value (unexploited assets)
5. DIVERSIFICATION: Target firm should be in a business different from the acquiring firm’s
business and correlation in earnings should be low.
6. OPERATING SYNERGY: it should create cost savings through economies of scale or it should
be able to create a higher growth rate through increased monopoly power.
7. TAX SAVINGS: Target Company should have large claims to be set off against taxes and not
sufficient profits. It should provide a tax benefit to the acquirer.
8. DEBT CAPACITY INCREASE: the target firm should have a capital structure such that its
acquisition will reduce bankruptcy risk and will result in increasing its debt capacity.
REASONS FOR HIGH FAILURE RATE OF ACQUISITION IN ENHANCING SHAREHOLDER
VALUE
It has been noticed that shareholders of the acquiring company seldom enjoy any benefits whereas the
shareholders of the target company do. What is the reason for the failure to enhance shareholder value?
1. AGENCY THEORY suggests that takeovers are primarily motivated by the self interest of the
acquirer’s management such as diversification of management’s own portfolio, use of free cash flow
to increase firm size, acquiring assets that increase the firm’s dependence on management. The idea
behind this theory is the fact that acquisition is a process that results in value being transferred
from shareholders of the acquiring firm to the managers of the acquiring firm. The implication
of this theory is that since the target firm knows that the bid is in the interest of management rather
than shareholders, it seeks the opportunity to extract some value that would have gone to management
depending on the bargaining power of the firm.
2. ERRORS IN VALUING A TARGET FIRM: managers of a bidding firm may advise their company
to bid too much as they do not know how to value a recursive problem. The value of an acquisition
cannot be measured independently resulting in a failed merger as the subsequent performance cannot
compensate for the high price paid. A risk changing acquisition cannot be valued without revaluing
your company on the presupposition that the acquisition has gone ahead.

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3. MARKET IRRATIONALITY: if a rationale manager feels that his firm’s stocks are overvalued in
the short run, he has an incentive to exchange the overvalued stocks to real assets before the market
corrects the overvaluation. A merger therefore occurs in order to take advantage of market irrationality
and it is not related to either synergies or better management. Lack of this may lead to a failing merger
even though the acquired firm was bought cheaply through the exchange of overvalued shares.
4. PRE-EMPTIVE THEORY: explains why acquiring firms pursue value decreasing horizontal
mergers even if managers are rationale and are trying to maximize shareholder value. If large cost
savings can be achieved through a merger, many firms will compete for the opportunity to merge with
the target. The winning firm who acquires the target could become a lower cost producer, improve its
product market position, and gain market share from the rivals. If a firm fears that one of its rivals will
gain large cost savings, then it is rational for the firm to pre-empt this merger with a takeover attempt
of its own.
5. WINDOW DRESSING: companies are not acquired for the synergies they may create, but in order
to present a better financial picture in the short term.
6. POOR INTEGRATION MANAGEMENT: effective integration management and recognition that
successful integration takes time are needed for good integration. Where management is poor or there
is an attempt to do too much too soon, potential successful mergers can actually fail.
Inflexibility in the application of integration plans drawn up prior to the event can be damaging.
Management must be prepared to adopt plans in the light of changed circumstances or inaccurate prior
information once the merger has taken place.
7. POOR MAN MANAGEMENT can be detrimental to successful integration. Lack of communication
of goals and future prospects of employees and failure to recognize and deal with their uncertainties
and anxieties can lead to employees being unclear of what is expected of them. Hostilities may
develop between the two groups of staff, with an unwillingness to adapt to new procedures and
practices.
REGULATIONS OF MERGER IN NIGERIA
The regulation process of merger and acquisition in Nigeria is primarily regulated under the Investments and
securities Act 2007 (ISA) and the rules and regulations made pursuant to the ISA (SEC rules). The listing rules
of the Nigerian stock exchange (listing rules) also contain rules that impact merger and acquisition
transactions. The provisions governing schemes of arrangement are contained in the companies and allied
matters act cap c20 laws of the federation of Nigeria 2004 (CAMA).
The key regulator of merger and acquisition in Nigeria is the Securities and Exchange Commission. In addition
there are other specific laws that regulate merger and acquisition whose prior approval is required for a change
of control in the relevant sector.
▪ Banks and other financial institutions act (BOFIA) CAP B3, laws of the federation of Nigeria 2004,
which regulates the financial sector requires the approval of the Central Bank of Nigeria (CBN)
▪ The Nigerian communications act 2003, which regulates the telecommunication industry requires the
approval of the Nigerian Communications Commission (NCC)
▪ The Insurance Act 2003, which regulates the insurance industry requires the approval of the National
Insurance Commission (NAICOM)
▪ The National Broadcasting Commission act, chapter N11, which regulates the broadcasting sector
requires the approval of the National Broadcasting Commission and
▪ The Electric Power sector reform act 2005 which regulates the electricity requires the approval of the
Nigerian Electricity Regulatory Commission.

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A SMALL MERGER is a merger with combined turnover or assets below N250,000,000

(approximately US$1.6 million). A formal approval is not required for a small merger but SEC must
be notified within 6 months of the transaction.
An Intermediate merger is one with combined turnover or assets between N250,000,000 and
N5,000,000,000.
A large merger is one with combined turnover or assets above N5,000,000,000 (approximately
US$32,000,000). A formal approval is required for intermediate and Large merger.
TYPE 1 ACQUISITION are acquisitions that do not disturb the acquirer’s exposure to financial or
business risk. Where the acquisitions affect the firm’s exposure to business risk, it is a type 2
acquisition while type 3 acquisition are acquisitions that affect both financial and business risk.
Mergers in Nigeria are guided by the provisions of CAMA 90 as amended
CONDITIONS FOR THE SCHEME OF MERGER TO BE EFFECTIVE AND BINDING
1. Special resolutions to be proposed at the court ordered meetings duly passed
2. Securities and Exchange Commission must approve the terms and conditions of the scheme as agreed
by majority of the shareholders of both companies
3. It must have been approved by majority (three quarters) in value of the shareholders of each of the two
companies voting either in person or by proxy at their separate meetings convened by the order of the
court.
4. Court must sanction the scheme and confirm the cancellation of the target company, the merger of its
assets, liabilities and undertakings with those of the bidding company as provided in the scheme and
the dissolution of the target company without winding up.
5. Delivery of the office copy of the court order to the registrar general of the corporate affairs
commission.

LEGAL AND PROCEDURAL REQUIREMENT

1) Presentation of a pre merger notice to Securities and Exchange Commission.
2) Preparation of a scheme of arrangement which contains the agreed terms and conditions of merger and
acquisition
3) Forward the scheme to the approving authorities for approval
4) The federal high court summons separate meetings of the shareholders of both companies to consider
the scheme of arrangement
5) Report the outcome of the meeting to the court.
6) Obtain final section from the court to proceed with the merger and acquisition
7) Filling of the court order with the registrar of companies
8) Seal the deal and implement terms –share or cash exchange

FINANCING OF MERGERS
1. CASH can be used without any additional cost and is taxable immediately.
2. ORDINARY SHARES IN THE ACQUIRING COMPANY may be attractive if they are still
interested in equity investments which may be difficult to dispose. The opportunity cost is that the
shares issued for the merger should have been issued for cash.
3. LOAN STOCK OF THE BIDDER would not dilute control thereby entitling the target company
shareholder to a fixed income, fixed repayments and less risk. Its challenges include that the bidding
company is committed to continuous payment default of which may lead to liquidation.
Factors To Consider Before Choosing Cash Exchange Or Share Exchange
PREDATOR COMPANY SHAREHOLDERS

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i) Dilution of EPS- attributable to existing shareholders which might occur if purchase consideration
is in equity
ii) Cost of the company
iii) Control of the shareholders
iv) Authorized share capital
v) Liquidity of the organization
vi) Gearing
vii) Uncertainty over consideration value

TARGET COMPANY SHAREHOLDERS

i) Tax implication
ii) Present income level
iii) Future investment holding in predator company

OTHER PARTIES INVOLVED IN MERGER AND ACQUISITION

▪ Nigeria stock exchange: their approval will be required when new shares have to be issued to replace
those that have been cancelled
▪ Federal board of Inland Revenue for tax purposes especially where there is cash exchange.
▪ Federal ministry of finance: when foreign shareholders are involved
▪ Federal high court to approve all agreements and make them binding on the shareholders
▪ Financial advisers: to advice on the financial implication of the merger
▪ Solicitor to the company- handle all legal issues on behalf of their company relating to merger and
acquisition
▪ Registrar: handles the transfer of shares update register of members, cancel old certificates and issue
new certificates
▪ Tax consultants: handle all tax masters relating to merger and acquisition
▪ Stock brokers: markets the shares, assist in taking the shares to the stock exchange.
▪ Solicitors to the scheme: handle legal issues relating to the whole scheme arrangement

The issue of poorly developed industries, reluctance by business owners to lose control and
low competition rate has accounted for the low rate of merger and acquisition in Nigeria.
The only major merger was that of the banks in 2005 to increase capital base by the
government which could be the major reason why they could withstand the global financial
melt down.

DE-MERGER/DIVESTMENTS/DIVESTITURES: is the breaking down of a company into two or more

separate entities and disposal of unviable ones which arises from the need to concentrate on core activities of
the business so as to create value of the shareholders.
ADVANTAGES
i) Unprofitable subsidiaries are sold off
ii) Enable firms to be more focused
iii) Profit may be realized from subsidiaries disposal
DISADVANTAGES
i) Loss of economies of scale
ii) Lower turnover associated with small company
iii) Higher operating cost as a consequence of low turnover

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iv) Future finance may become very difficult

REVERSE MERGER: occurs when a small company takes over another that is bigger in form of assets and
potentials.
ROLL UP CONCEPT: occurs where many small companies are merged to form a very big company
MEZZANINE FINANCING: Is a finance method that lies between equity and debt which gives the lender
the option to exchange the loans for shares after the takeover. It is usually used by the bidding company.
SELL OFF: Is a form of divestment involving the sale of a part of a company to a third party usually for cash.
It is expected that the disposal will create value. The decision is based on whether the present value of the
stream of future cash flows of the part sold will be less than the value received.
SPIN OFF: Is the creation of a new company where shares are owned by the shareholders of the original
company which makes the disposal of assets. There is no change in ownership of assets as the shareholders
own the same proportion of shares in the new company as the old company. A spin off could arise from a need
to carve out a separate identity for that business or as a need to avoid a takeover by spinning off a valuable part
of the company.
MANAGEMENT BUY OUTS: the company sells a particular part of a business to the management of that
part of the business possibly because the sector does not fit into the overall strategic objective of the company.
Where the management of a buyout is mainly from loans raised by managers from the bank, it is called
LEVERAGED BUY OUT.
VOLUNTARY LIQUIDATION occurs where the company is sold in its entirety. A decision to do this
should be based on value creation for the shareholders that is the valu of the company when liquidated is
greater than the present value of its stream of future cash flows. The idea here is that assets when sold
separately to individual buyers would have higher value than when sold as a whole as in a merger.
EQUITY CARVE OUT : is similar to a spin off but the shares issued in respect of the division go to the
public. The parent company does not relinquish total control as it continues to hold some of the shares of the
subsidiary.
GOING PRIVATE: simply means converting from a public company to a private company which could be
for reasons such as reduced administrative cost, focus on long term economic earnings as against periodic
earnings, incentive to managers to work harder and avoidance of embarrassing questions from stock brokers
and financial analyst when making presentation of facts behind the figures.
BUY INS: arises when a group of individuals unconnected with a company make an offer to purchase a part of
the company. Example where a major owner of a one man business is retiring.
STRATEGIC ALLIANCE/CO-OPERATIVE ARRANGEMENT is entered when a company clearly sees
the synergy/benefits from merging with another company but lacks the resources to execute a strategic merger.
This is different from a merger in the sense that legal and physical existence remains. It could be attained by
either a joint venture or a virtual company.
JOINT VENTURES: is a form of strategic alliance when two or more companies agree to form a separate
company which will be managed in such a way that will achieve their individual corporate objectives.
VIRTUAL COMPANY is one that involves large scale outsourcing of its business activities. It allows a
company to focus on its core activities where it has competitive advantage and outsourcing other business
activities. For example a manufacturing company outsourcing its production activities.
BANK MAIL: Is an agreement between a bank and a company planning a takeover which prevents the bank
from financing any other potential acquirers bid.

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WINNER’S CURSE: is the tendency for the winner in certain competitive budding situations to overpay
whether because of overestimation of intrinsic value emotion or information asymmetries

DEFENSIVE MERGER TACTIC: is a move designed to make a company less vulnerable to the takeover

MERGER TACTICS
Friendly bid – is one in which the management of both companies write out suitable terms agreed by both
companies.
Yellow Knight is a situation where a takeover bid ends up in a merger with the target company.
Hostile bid: Is a bid that a target company resists there by compelling the predator company to persuade the
shareholders
Black knight is a hostile takeover bid by a company in a target company
Gray knight is a company which attempts a takeover bid on a target company capitalizing on the initial
problems faced by past bidders.

INSTRUMENTS OF HOSTILE BIDS

1) Proxy fight: a group of shareholders are persuaded/convinced by the acquiring company to join forces
and gather enough shareholder proxies to win a corporate vote to install new management that is open
to takeover when the company’s board does not approve acquisition.
2) Tender offer: is a general offer made directly to a target firms shareholders in a bid to buy a
substantial percentage of the target company shares or units for a limited period of time. It is usually at
a premium over the prevailing market price.
3) Saturday night special: is a merger tender offer made just before the market doses for weekend and
this takes the target company’s officers by surprise.
4) Corporate raid: is a situation where a bidding company procures the shares of the target company at
a price on the stock exchange that is cheaper than the price that the target company has stated.
5) Down raid: is a situation where a bidding company acquires a substantial amount of shares of a target
company at a price first things in the morning when the market opens.
6) Bear hug offer – is an offer made by one company to buy the shares of another for a much higher per
share price than what the company is worth. This approach is approved when there is doubt that the
target company will sell.
7) Lady Macbeth strategy: is a takeover strategy with which a third party poses as a white knight to
gain trust turns around and joins with the unfriendly bidder.
8) God father offer – is an irrefutable takeover made to a target company by a predator company.
9) Hubris hypothesis: this occurs bidders have an ego which restricts rational decision making. There is
an over cleaning self confidence in bidders that they can utilize the target firms assets to create
maximum value if control is given to them but this theory is not acceptable to the target company.
DEFENSIVE STRATEGIES
This can be divided into pre offer and post offer take over mechanisms
ANTI TAKEOVER DEVICES/REPELLANT/ PRE-OFFER Defenses are those strategies that are put in
place before a takeover bid is made.
They include provisions a company has made to eliminate or discourage takeover bids such as .

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i) Golden parachutes: Are unacceptably high compensation packages that must be paid to managers. If
they are forced to leave the firm
ii) Poison pill: gives the current shareholders the right to purchase additional shares of the target
company at extremely attractive prices. It is also called flip in pill as it is triggered once a specific
level of ownership is exceeded.
iii) Flip over pill: gives the current shareholders of the target company the right to purchase shares of the
acquiring company at a significant discount from the market price.
iv) Poison puts: gives the target company’s bond holders the right to sell their bonds back to the
company at the pre specified price
v) Shark repellants: Involves amending the memorandum (articles of association in such a way that the
takeover becomes extremely difficult such as increasing the margin of majority votes to approve a
takeover
vi) Staggered board of directors: this allows that only a portion of the board’s seats are due for election
each year. This is done to ensure that it would take a longer time to elect enough directors to take
control of the board fair price amendment. Restriction voting rights.
vii) Lobster trap: a provision preventing anyone with more than 10% ownership from converting
securities into voting stock
POST OFFER TAKE OVER DEFENSE MECHANISMS
i) Just reject the offer defense
ii) Litigation: seek government injunction to restrict predator company
iii) Asset revaluation
iv) PAC MAN Defense: is a strategy where the target firm turns the table by bidding for the aggressor.
v) White knight defense: Is a strategy where the target firm seeks third party with a better strategic fit
and offer in lieu of the hostile bidder.
vi) Scorched earth/crown jewel defense: Is a strategy where the target sells off a subsidiary or asset
(which may be the motivation of the merger) to a third party.
vii) Green mail: is the termination of a hostile takeover through a payoff to the acquirer at a premium to
the market price.
viii) Repurchases its own shares back from the acquiring company
ix) Share repurchase: a target company repurchases its shares from any shareholder who is willing to sell.
x) People pill: management team resigns emblock in the event of a takeover, so as to severely harm the
company.
xi) Marcaroni defense: the target company issues large number of bonds with the condition that they
may be redeemed at a high price if the company is taken over. Whenever a takeover bid is made the
redemption price expands like Marcaroni in a port
xii) Appeal to shareholders not to sell their shares by promising better prospects and share appreciation.
xiii) Suicide pill : engage in activities that might actually run the company
xiv) White squire defense: the target firm places its shares in the hands of a friendly firm or investor who
is not interested in acquiring control of the target firm and will not sell out to the predator.
xv) Leveraged buy out: a target company bugs all of its shares and converts to a privately held company.
The management team generally partners with a private equity firm that specializes in buyouts. The
new entity borrows a higher proportion of the overall purchase price, the financial firm contributes as
certain amount of capital while the management teams provides the expertise to run the business in
exchange for a payout percentage

A leverage buyout is a situation in which the firms managers borrow heavily against the asset of the company
to purchase the company themselves.

PARTIES TO A BUYOUT
i) Management team wanting to make the buyout

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ii) Directors of the group who make the divestment decision

iii) Financial backers of the buyout team.
Reasons For Acceptance Of The Buyout Of A Subsidiary
i) The subsidiary may be peripheral to the group’s main stream of activities and no longer fit into the
group’s overall strategy.
ii) The group may wish to sell off a loss making subsidiary and the management may think it can restore
cast fortune.
iii) The parent company needs to raise cash quickly
iv) A group that decided to sell its subsidiary will get the best cooperation from management
v) The subsidiary may be a newly acquired one which the company wishes to dispose part
vi) The best bid may come from management

CALCULATION
1) Determine the existing market value of the target company
2) Determine the existing market value of the predator company
3) Determine the post merger/enlarged value which is dependent on the information given by the
examiner
a. Where synergy is given in absolute terms the market value for enlarged company would be target
company value + predator company + synergy
b. Where information affecting cost structure is given, the new company’s market value would be
combined profit after considering additional information divided by cost of capital
c. Where the emphasis is on dividend then dividend valuation model should be used.

ILLUSTRATIONS ON MERGER AND ACQUISITION

ILLUSTRATION (NOVEMBER 2017 ICAN PAST QUESTION)
Ray plc, is a successful IT services company formed 10 years ago. It was listed on the stock
exchange 3 years ago. The company has a broad customer base mainly consisting of small and
medium sized companies. Ray plc has achieved rapid growth in recent years by obtaining repeat
business from satisfied customers and also by acquiring other IT services companies.
The Directors of Ray plc have identified Hay limited; an unlisted company as a possible
acquisition target. Hay Limited has a number of large multinational clients and, in general, its
clients tend to be larger than those of Ray plc. If successful, the acquisition would go ahead on
January 1,2018.
Forecast financial data for Ray plc and Hay Limited as at December 31, 2017 is summarized
below:
Ray plc Hay plc
Share capital (ordinary N1 N150m N40m
shares)
Market share price N4.90 N/A
N/A: not applicable as unlisted
Additional information:
I. If Hay plc, were to remain an independent company, its directors estimate that reported
profit after tax would be N15 million for 2018 and then grow by 2% yearly in perpetuity.

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II. If the acquisition were to go ahead, Ray plc’s directors estimate that Hay Limited’s profit
after tax would be 5% higher for 2017 than if the company remains an independent
company and that profit after tax would then grow by 3% yearly in perpetuity.
III. The average ungeared cost of equity for the industry is 8%.
IV. Both Ray plc and Hay plc are wholly equity financed
V. Profit after tax can be assumed to be a good approximation of free cash flow attributable
to investors
The directors of Ray plc are considering offering to purchase Hay limited at a price of N7.00 per
share. It is estimated that transaction costs of N8 million would be payable on the acquisition and
that N2 million would be required in the first year to cover the costs of integrating the two
companies.
Required :
a. Calculate
I. The value of Ray plc on December 31, 2017
II. The value of Hay limited on December 31, 2017 before taking the possible
acquisition of the company by Raymond plc, into account.
III. The overall increase in value created by the acquisition of Hay limited by Ray plc
(8 marks)
b. You are required to
I. Explain how value might be created by the proposed acquisition (2 marks)
II. Comment on the difficulties Ray plc, is likely to face in realising the potential
added value after the acquisition.
( 2 marks)
c. Evaluate the proposed offer price of N7.00 per share for Hay Limited from the view point
of
I. Hay Limited’s shareholders
II. Ray plc’s shareholders (8 marks)
(Total 20 marks)

SOLUTION TO ILLUSTRATION 1

a)
Pre-acquisition value:
Raymond Pic N4-90 x 150m = 735
Harold N15m/0.08 — = 250
0.02
Limited
985
Post-acquisition value:
Harold Limited N15mxl.05 = 315.00

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/0.08 - 0.03
Raymond Pic.
735.00
Transaction costs (8.00) (1.85)

1,040.15
Integration costs yv2ml.08
Total value
Pre-acquisition total value (985.00)
Incremental value
55.15

b) i) Value can be created by combining the two companies through the achievement of synergies
and economies of scale. In most business combinations, there are likely to be savings generated from
combining operations and reducing the amount of resources needed to fund central functions such as
human resources, finance and treasury. The cost savings are likely to have an almost immediate
impact on the cash flow and hence are likely to be reflected in 5% growth in free cash flow in the
first year.
Synergies might also arise in respect of the cross-selling of services between the two companies to
their respective client bases. It is possible that the directors of Raymond Pic. anticipate that there are
opportunities to enhance the cash flows of Harold Limited by utilising the expertise of Raymond Pic.
leading to a higher growth rate of 3% a year compared to 2%. ii) Key challenges in realising the
potential added value after the merger are:
Success depends on the extent that Harold's management and staff accept the transfer of ownership
and remain committed to servicing Harold Limited"s clients to the best of their ability. To
overcome this challenge, Raymond Pic. should consider introducing an incentive scheme such as a
bonus payment or employee"s share option scheme;
It also depends on whether Harold's clients are happy with the new arrangement and are confident of
receiving the same level of service as before; and
The reliability of the forecast improvement in earnings and growth is also key to successful
realisation of the potential added value.

c) Consideration paid: H7 x 40 million shares = N280 million

Comparison of shareholders” Harold Limited Total value
wealth before and after the
acquisition: Raymond Pic.
Before the acquisition N735million N250million N985million
After the acquisition N760million M280million N1,040million
Share of synergistic =(Nl,040m - N 280m) (proceeds)
benefits K25million M30million

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Harold Limited^s shareholders perspective: Very attractive. Harold Limitedvvs shareholders can
expect to receive 55% of the synergistic benefits of the merger which does not seem to be a fair split
considering:
Harold Limited is the smaller company and contributing less to the merger; 0 Harold Limitedvvs
shareholders do not carry any of the risks that the synergistic benefits cannot be realized; and
Harold Limited is unlisted and it is therefore very difficult for the shareholders to realise their
investment at all, let alone at such a generous price which is above the company"s own bullish value
estimates derived from discounted cash flow analysis.
Raymond Plc."s shareholders" perspective: Possibly too high a price for comfort. The main reasons
for this conclusion are as follows:
The reverse of the above: Raymond Plc.vvs shareholders take all the risk and contribute most value
to the combined business and yet oniy expect to receive 45% of the increase in value; and
It is likeiy that Harold Limited has a higher business risk than Raymond Pic. despite being in the
same industry because of the different clients profile. If one customer were to be lost by Harold
Limited, then this could have a significant impact on cash flow and hence the variability of Harold
Limited"s cash flows is likely to be higher than for Raymond Pic. Therefore, it is possible that a
higher discount rate should be used to value Harold Limited which would have the effect of reducing
its value.
Conclusion: The price needs to be reduced. The proposed price is not fair to Raymold Plcus
shareholders and Harold Limited is potentially over-valued at a discount rate of 8%.

ILLUSTRATION ON MERGER AND ACQUISITION

Relevant plc and Oracle plc operate in the same field manufacturing children’s clothes and toys
although Oracle plc also has interests in sportswear and equipment. Relevant plc is planning to
take over Oracle plc and the shareholders of Oracle do not see this as a hostile bid.
The following information is available about the two companies
ORACLE PLC RELEVANT PLC
CURRENT EARNINGS N240,000 N650,000
NUMBER OF SHARES 1,500,000 5,000,000
% EARNINGS RETAINED 80% 20%
RETURN ON NEW INVESTMENT 15% 15%
Return required by ordinary shareholders 24% 21%

Dividends have just been paid and the retained earnings have already been reinvested in new
projects. Relevant plc plans to adopt a policy of retaining 35% of earnings after the takeover and
expects to achieve a 17% return on new investment
Savings due to economies of scale are expected to be in the region of N85,000 per annum.
Required return to ordinary shareholders will fall to 20% due to portfolio effects. Neither
company is quoted.
Requirements

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a. Calculate the existing share value of Relevant plc and Oracle plc
b. Find the value of Relevant plc after the takeover
c. Advise Relevant plc on the maximum amount it should pay for Oracle plc

SOLUTION TO ILLUSTRATION ON MERGER AND ACQUISITION

a. Existing values
Existing share price of Relevant pic
Dividend = payout ratio x PAT = 650,000 x 80% = N520,000
Growth = rb = 0.15 x 0.20 = 3%. Ex dividend market value = next year's dividend/ Ke - g =
520,000
(1.03)/ 0.21 - 0.03 = N2,975,556
Existing share price of Oracle pic
Dividend = payout ratio x PAT = 240,000 x 20% = N48,000
g = rb = 0.15 x 0.80 = 12%= market value = 48,000 (1.12)/ 0.24 - 0.12 = N448,000

b. Value of combined company

Earnings of combined company = 650,000(1.03) + 240,000(1.12) + 85,000 =
N1.023,300 Growth of combined company = rb = 0.17 x 0.35 = 6%
New cost of equity = 20%
New dividend = payout ratio x earnings =1,023,300 x 65% = N665,145
Value = Di/ke - g = 665,145/ 0.20 - 0.06 = N4,751,036
c. Maximum amount to be paid N
Value of combined company = 4,751,036
Less value of acquiring company 2,975,556
Maximum amount 1,775,480
d. Reasons for one company to buy another
▪ To save time of setting up a project by allowing instant access to the new market
▪ Economies of scale
▪ To buy out a competitor and thus increase market share
▪ For good products, projects or ideas
▪ For expertise and goodwill
▪ Increase geographical coverage
▪ Asset acquisition especially intangible
▪ Diversification
▪ Tax reasons
▪ New technology
▪ Increased borrowing powers

ILLUSTRATION ON MERGER AND ACQUISITION (MAY 2015 ADJUSTED)

King Plc and Queen plc both manufacture and sell household equipment. The summarized
income statements of the two companies for the year 2014 are as follows
King Plc (N’000) Queen Plc (N’000)
Revenue 37,500 20,000
Operating expenses (20,000) (15,500)

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17,500 4,500
Each company has earned a constant level of profit for a number of years and both are expected
to continue to do so for the nearest future. The policy of both companies is to distribute all
profits as dividend to ordinary shareholders as they are earned. None of the companies has any
fixed interest capital.
Details of the ordinary share capital of the companies are as follows;
ORDINARY SHARE CAPITAL KING PLC (N’000) QUEEN PLC (N’000)
AUTHORISED SHARES (N1 PAR 125,000 50,000
VALUE)
ISSUED SHARES (N1 PAR 50,000 25,000
VALUE)

The ordinary shares of King plc have a current market value of N3.50 each ex-div and those of
Queen plc a current market value of N1.50 each ex div.
The Directors of King plc are considering submitting a bid for the entire share capital of Queen
plc. They believe that if the bid succeeds, the combined sales revenue of the two companies will
increase by N1,500,000 per annum and savings in operating expenses amounting to N1,250,000
per annum will be possible. Part of the machinery owned by King plc would no longer be
required and could be sold for N2,500,000 now.
Furthermore, the directors of King plc believe that the takeover would result in a reduction of the
returns required by the ordinary shareholders at 10%.
a. As a financial consultant to King plc, advise on the maximum price that the company
should be willing to pay for the entire share capital of Queen plc showing clearly the
basis of your advice.
b. Advise on the minimum price Queen plc should accept
c. Show how the entire benefit from the takeover will accrue to all the present shareholders
of King Plc assuming that the takeover price is agreed at half of the figure you advised in
“a” above, and the purchase consideration will be settled by an exchange of ordinary
shares in Queen plc.
d. Show how the entire benefit from the takeover will accrue to shareholders of Queen plc if
purchase consideration will be settled by an exchange of ordinary shares in Queen plc.
e. Discuss briefly any other five factors that the directors and shareholders of both
companies might consider in assessing the acceptability of the proposed takeover.

SOLUTION TO ILLUSTRATION ON MERGER AND ACQUISITION

To calculate the maximum price, the values of both companies before the acquisition must be
computed as well as the value of the combined company after acquisition.

Value of King before the acquisition = market price per share (MPS) x number of shares = 3.50 x
50,000,000 = N175,000,000

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Value of Queen before acquisition = 1.50 x 25,000,000 = N37,500,000

Value of combined company would be revised PAT/ cost of equity whenever there is a change in
cost and revenue.
N'000
SALES (37,500 + 20,000 + 1,500) 59,000
COST (20,000 + 15,500 - 1,250) (34,250)

PBT/PAT 24,750
VALUE = PAT/cost of equity = 24,750/0.10 N247,500
Part of machinery sold now N2,500

Total value of company to infinity = N247,500, 000 + N2,500,000 = N250,000,000

a. Maximum price = value of combined company - value of acquiring company = N250m -
N175m = N75 million
b. Minimum price = value of target company = N37.5 million
a. For the benefit to go to shareholders of King PIc, the whole gain from the merger should be
added to King pic as shown below
N'000
Value after acquisition 250,000
Value of Queen pic 37,500
Value of King pic 212,500
Vps in king pic; 212,500/50,000 N4.25
Number of shares = 37,500/4.25 8,823,529 shares
d.
N'000
Value after acquisition 250,000
Value of Queen pic 75,000 (37,500 + gain 37,500)
Value of King pic 175,000
Vps in king pic; 175,000/50,000 N3.50
Number of shares = 75,000/3.50 21,428,571 shares

e. Other factors to consider are

▪ Reliability of the synergy estimates

▪ Post merger integration problems
▪ Government policy
▪ Impact on staff and company's reputation
▪ Means of financing the merger and acquisition
▪ Impact on control

ILLUSTRATION ON WORK BACK

Heaven limited and Hell Limited are manufacturing companies which are financed entirely by
equity. Each company has earned a constant level of profit for a number of years and no change

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in performance is expected. Details of their profit and cost structure and their share capital and
prices are given in the table below:
INCOME AND COST STRUCTURE HEAVEN HELL
PROFITS AFTER TAX N7,500,000 N3,000,000
VARIABLE COST AS % OF 60 50
REVENUE
FIXED COST AS A % OF REVENUE 20 25
AUTHORIZED SHARE CAPITAL N50,000,000 N30,000,000
N1/SHARE
ISSUED SHARE CAPITAL N20,000,000 N20,000,000
N1/SHARE
MARKET PRICE PER SHARE N3.75 N1.20
The directors of Heaven Limited are considering submitting a bid for the entire share capital of
Hell Limited. They believe that if the bid succeeds, they will be able to increase the sales
revenue of Hell by N1,000,000, reduce the fixed cost of the merger operation by N2,400,000 and
that the variable cost will equal to 56.5% of the total sales revenue of the merged companies. The
expected return from investment by the shareholders remain constant. Corporate tax rate is 40%.
1. Advise Heaven Limited on the maximum price that should be paid for Hell Limited
2. What would be the maximum price that should be paid by Heaven Limited for acquisition
of Hell Limited, if the sales and cost do not change as expected. Is the merger
worthwhile?
3. Advise the shareholders of Hell Limited as to the minimum price they should be prepared
to accept from Heaven Limited.
4. If the agreed price is N30,000,000 which is to be paid by issue of new shares in Heaven
Limited, what will be the ratio at which the new shares will be exchanged for the
ordinary shares of Hell Limited.
5. If the proposals in “d” above are carried out, how much will shareholders of Heaven and
Hell Limited gain from the merger.

SOLUTION TO ILLUSTRATION ON WORK BACK

This is a work back question and so the profit statement of both companies should be computed
based on the percentages given like PBT = PAT/ (1 - TAX RATE) while the sales would be
100/profit % x profit before tax as shown below
The profit statement of the two companies are calculated as;
N HEAVEN N HELL
Revenue 62,500,000 20,000,000
Variable cost 37,500,000 10,000,000
Fixed cost 15,000,000 5,000,000
Profit before tax 12,500,000 5,000,000
Tax 5,000,000 2,000,000
Profit aftertax 7,500,000 3,000,000

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Cost of equity = D/VE = 7,500,000 / 20m X N3.75 = 10%

Value of Heaven = 3.75 x 20m shares = N75 m
Value of Hell = 1.20 x 24m shares = N24 m
VALUE OF COMBINED COMPANY
Revenue (20,000,000 + 1,000,000 + 62,500,000) N83,500,000
Variable cost (56.5%) (N47,177,500)
Fixed cost (15,000,000 + 5,000,000 - 2,400,000) (N17,600,000)
Profit before taxation N18,722,500
Taxation at 40% N7,489,000
Profit after taxation Nil,233,500
Value of combined company = PAT / kE 11,233,500/0.10 = N112,335,000
a. Maximum price = value of combined company - value of acquiring company = 112,335,000 -
75,000,000 = N37,335,000
b. if the synergy is not enjoyed then the value of the company would be combined PAT of the
two companies discounted at the cost of equity; 7,500,000 + 3,000,000 / 0.10 =
N105,000,000. Maximum price = value ofcombined company - value of acquiring company
= 105,000,000 -75,000,000 = N30,000,000
c. Acceptable minimum price = existing value of target company = N24,000,000
d. Share exchange ratio
Post merger value N112,335,000
Less agreed price of Hell N30,000,000
Value of Heaven N82,335,000
Value per share 82,335,000/20,000,000 = N4.12
Number of shares 30,000,000/4.12 = 7,281,553 Shares
Exchange ratio 7,281,553/20,000,000 = 364 shares per 1,000

e. Calculation of gain
HEAVEN HELL COMBINED
AFTER N82,335,000 N30,000,000 JM 112,335,000
BEFORE N75,000,000 N24,000,000 N99,000,000
GAIN N7,335,000 N6,000,000 N13,335,000

ILLUSTRATION ON SHARE/CASH OFFER

Techno plc is a publicly listed company involved in the production of highly technical and sophisticated
electronic components. It has a number of diverse and popular products, an active research and
development department, significant cash reserves and a highly talented management who are very good
in getting products to market quickly.
It intends to go into a new industry which has been expanding rapidly and there are strong indications that
this recent growth is set to continue. However Techno has limited experience in this industry. It believes
that the best and quickest way to expand would be through acquiring a company already operating in the
industry sector
Nokia Limited is a private company operating in the new industry Techno is planning to enter and is
owned by a consortium of business angels and company managers. The owner managers are highly skilled

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scientists who have developed a number of complex products, but have found it difficult to commercialise
them. They have also been increasingly constrained by the lack of funds to develop their innovative
products further.
Nokia managers have indicated their happiness towards the discussions on possibility of Techno acquiring
the company. If Nokia is acquired, it is expected that its managers would continue to run Nokia as part of
the larger combined company.
Nokia is of the opinion that most of its value is in its intangible assets, comprising intellectual capital.
Therefore the premium payable on acquisition should be based on the present value to infinity of the after
tax excess earnings the company has generated in the past three years over the capital employed of the
new industry. However Techno plc is of the opinion that the premium should be assessed on synergy
benefits created by the acquisition and changes in value, due to the changes in the price-earnings ratio
before and after the acquisition.
Given below are extracts of financial information for Techno plc for 2015 and Nokia for 2013, 2014 and
2015:
TECHNO PLC NOKIA LIMITED
2015 Nm 2013 Nm 2014 Nm 2015 Nm
Earnings before tax 1,980 397 370 352
Non current assets 3,965 882 838 801
Current assets 968 210 208 198
Share capital 25k/share 600 300 300 300
Reserves 2,479 183 166 159
Non-current liabilities 1,500 400 400 400
Current liabilities 354 209 180 140
The current average PE ratio for the new industry is 16.4 times and it has been estimated that Techno plc
PE ratio is 10% higher than this. However , it is thought that the PE ratio of the combined company would
fall to 14.5 times after the acquisition. The annual after tax earnings will increase by N140 million due to
synergy benefits resulting from combining the two companies.
Both companies pay tax at 20% per annum and Nokia’s annual cost of capital is estimated at 7% while
Techno’s current share price is N9.24 per share. The new industry’s pre tax return on capital employed is
currently estimated to be 20% per annum. Techno has proposed to pay for the acquisition using one of the
following three methods:
▪ A cash offer is N5.72 for each Nokia Limited share: or
▪ A cash offer of N1.33 for each Nokia limited share plus one Techno plc share for every two
Nokia limited shares : or
▪ A cash offer of N1.25 for each Nokia limited share plus one N100 3% convertible bond for
every N5 nominal value of Nokia limited shares. In six years, the bond can be converted into
12 Techno plc shares redeemed at par.
I. Distinguish between the different types of synergy and discuss possible sources of synergy based
on the above scenario.
II. Based on the two different opinions expressed by Techno plc and Nokia limited, calculate the
maximum acquisition premium payable in each case.
III. Calculate the percentage premium per share that Techno limited’s shareholders will receive under
each acquisition payment method and justify, with explanations, which payment would be most
acceptable to them.

SOLUTION TO ILLUSTRATION

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An acquisition creates synergy benefits when the value of the combined company is more than the
sum of the two value companies (2 + 2 = 5). Synergies are often separated into three types:
▪ Revenue synergies result in higher revenues for the combined entity, higher return on equity
and a longer period when the company is able to maintain competitive advantage. In this
scenario, the following revenue synergies may arise; Techno pic management can help
market Nokia products more effectively by using their sales and marketing talents. Research
and development activity can be combined to create new products using technologies
available and bringing innovative products to the market faster. The services of the scientist
would be retained to drive innovation forward.
▪ Cost synergy result mainly from reducing duplication of functions and related costs and
economies of scale. It may arise in the scenario from the combined entity been able to
negotiate better terms and lower cost. Cost could also be saved from reduction in
duplicating functions
▪ Financial synergy results from financing aspects such as the transfer of funds between
group companies to where it can be utilised best or increased debt capacity. This may be
available because Nokia does not have the funds to innovate new products and Techno has
cash reserves available. As the company increases in size, the debt capacity of the combined
company may increase , giving additional access to finance or decrease in the cost of capital
of the combined company.

B part of the question

Maximum premium based on excess earnings method
This method is similar to the EVA method which measures excess return.
Average pre tax earnings = 397 + 370 + 352 /3 = N373 m

Average capital employed

2015 Nm 2014 Nm 2013 Nm
Shareholders funds 483,. 466 459
Non current liabilities 400 400 400
883 866 859
Average = 883 + 866 + 859/3 = N869.33m EXCESS ANNUAL PREMIUM
Nm
Average pre-tax return as above 373
Pre tax return required on capital employed= 0.20 x 869.33 (174)
Annual excess return 199
Less tax at 20% (39.80)
After tax excess return 159.20
Pv to infinity = 159.20 /0.07 2,274.29
Maximum premium payable is N2,274.29

MAXIMUM PREMIUM BASED ON PE RATIO METHOD

NOKIA LTD PE RATIO = 16.4 X 1.10 = 18

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NOKIA LTD PROFIT AFTER TAX = N397m X 0.80 = N317.6m

TECHNO PLC PROFIT AFTER TAX = Nl,980m x 0.80 = Nl,584m
TECHNO PLC CURRENT VALUE = N9.24 X 2,400 shares = N22,176m
Nokia limited current value = N317.6m x 18 = N5,716.80m
Combined company value = 1,584 + 317.6 + 140) x 14.5 = N29,603.20m
Maximum premium = N29,603.20 - (22,176 + 5,716.80) = Nl,710.40m

C. Nokia current value per share = 5,716.80m/l,200m shares = N4.76/share

Maximum premium % based on PE ratio = Nl,710.40m / N5,716.8m = 29.9% Maximum

premium % based on excess earnings = N2.274.29m / N5,716.8m = 39.8%
▪ CASH OFFER
Premium = (5.72 - 4.76) / 4.76 = 20.2%

▪ CASH AND SHARE OFFER

Premium = techno share price = N9.24,1 for 2 then Nokia share price = N4.62
Cash payment per share = N1.33
Total return = N4.62 + N1.33 = N5.95
Premium % = (5.95 - 4.76)/4.76 = 25%

▪ CASH & BOND OFFER Nominal

value per share = NO.25 Number
of shares = 5/0.25 = 20 shares
Bond value = N100/20 shares =
N5/share Cash payment =
N1.25/share
Total = N6.25 per share
Premium % = (6.25 -4.76)/4.76 = 31.3%
On the basis of the calculations, the cash together with bond offer yields the highest
return in addition to the value calculated above, the bonds can be converted to 12 Techno
pic shares, giving them a price per share of N8.33 (N100/12).

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CHAPTER 19: CORPORATE RESTRUCTURING

This refers to the revamping of the activities of a failing company which is faced with capital imbalance so as
to put the company in the path of success in terms of profitability, liquidity, survival, growth and continuity. A
failing company is a company facing problems relating to profitability, liquidity and is moving toward
discontinuity i.e. its going concern is threatened.

SYMPTOMS OF A FAILURE COMPANY

i) Fixed assets of the company are overvalued
ii) Obsolete assets.
iii) Fixed assets of the company are too weak and old to lead the company in the path of success and gemots
iv) Continuous operating losses being incurred
v) Large proportion of accumulated losses
vi) Poor and bad management
vii) Rapid labour turnover
viii) Inability to meet obligations as at when due
ix) Existence of significant amount of deferred charges, intangible and fictitious assets.
x) The book value of the ordinary shares capital is overstated (loss of capital) d
A capital reduction or reconstruction is a scheme approved by the court in which the nominal value or par
value of the company’s paid up share capital is reduced.

ALTERNATIVES AVAILABLE FOR A FAILURE COMPANY

When a company’s situation is so bad, the following alternatives should could be taken
i) Undertake reconstruction with a view to reposition the company (capital reconstruction)
ii) To amalgamate with financially sound companies (amalgamation)
iii) To make itself available to acquisition by a financially stable company (Absorption)
iv) To wind up the company voluntarily (liquidation).

STATUTORY REQUIREMENTS FOR CAPITAL REDUCTION

i) The company’s articles must authorize such scheme
ii) The shareholders of the company must pass a special resolution approving the capital reduction scheme
iii) The resolution must specify the amount of reduction
iv) The company must obtain a court approval/sanction confirming the scheme
v) The company must register the court approval with the registrar of companies before it can take effect.
vi) The court will make an order confirming the scheme provided it is satisfied that the consent of every
creditor entitled to object to the capital reduction has been obtained or the debt/claim of such creditors
has been discharged determined or secured and the authorized share capital does not full below the
minimum
vii) The court order and the minutes of the meeting of the company where the special resolution was passed
and the scheme was approved shall be registered with corporate affairs commission.
viii) The notice of registration by CAC may be published as the court may direct.

REASON FOR CAPITAL REDUCTION

i) To extinguish or reduce liability on any share of the company in respect of capital not paid
ii) To cancel paid up share capital which is lost or unrepresented by available assets
iii) To pay of any paid up capital which is lost in excess of the company’s needs. It must be noted that
capital reductions is illegal unless it is carried out in the manner prescribed by CAMA 1990 as amended.
CAPITAL RECONSTRUCTION ANSWER PLAN
1) List the reconstruction principles which will be successful if it ensures
a) It raises adequate finance
b)All group is worst off under the scheme
c) It treats all parties fairly
d)Are the new shares fairly priced i.e. is the company viable.

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2) State the reasons why the scheme is required

As a result of the recent considerable losses there are inadequate funds available to finance the
redemption of debentures

3) Does the scheme raise adequate finance?

Cash iiv Cash out repayment
Equity xx Debenture Xx
Debenture xx Creditors (unsecured) Xx
Sale of surplus assets xx Working capital requirements Xx
- Scheme funding Xx
Total raised xx Total required Xx

Total raised xx
Less total required (xx)
Scheme surplus (deficit) xx /( xx)
Current cash balance xx
New cash balance xx

You should state an as estimated of the incremental working capital requirement would be essential where the
examiner is silent.

4) THE CAPITAL REPAYMENT POSITION – PRIORITY ORDER

It is common in exam questions that the fund would not be enough to discharge the unsecured
creditors, so their repayment position will normally improve under a scheme because the cash from
the issue of new equity is used to purchase assets on which they will have a prior claim to
shareholders.

Capital requirement
No liquidation After scheme
N N N N
List realized/breakup value of assets xx xx
New assets purchased - xx
Less secured creditors: debentures (xx) Xx
New debentures - (xx)
Preferential creditors (tax wages (xx) (xx) (xx) (xx)
redundancy)
Funds available to pay unsecured xx xx
Total unsecured creditors (Bank and (xx) (xx)
overdraft)
Fund available to pay shareholders xx xx
Preference shareholders (xx)
Balance funds to ordinary shareholders xx

5) ARE THE NEW SHARES FAIRLY PRICED- COMPANY VALUATION?

Calculate the earnings per share price earnings ratio and the interest cover and also ensure that the share
price is fair to encourage investors to buy.
6) IS THE SCHEME ACCEPTABLE TO ALL PARTIES?
Remember that the company will be liquidated if the scheme is not accepted therefore you must
compare each group upon liquidation and under the scheme in relation to debentures and shares, it may
be worthwhile to note their market value before the scheme.

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7) CONCLUSION
Draw out a sensible conclusion about the scheme justified by your analysis.

ILLUSTRATIONS ON CORPORATE RESTRUCTURING

ILLUSTRATION 1 ON RECONSTRUCTION SCHEME
A company has proposed the following scheme of reconstruction
o Assets are to be revalued as follows:
Property, plant and machinery N980,000
Goodwill Zero
Receivables N290,000
Inventory N350,000

o Ordinary share capital is to be surrendered and reissued 250 for each 1,000 held
o The existing ordinary shareholders are to subscribe new share capital with a nominal value of
N250,000 at a consideration of N750,000
o Preference share capital is to be reduced by 25%
o Debenture holders are to accept shares with a nominal value of N125,000 for debentures
worth N250,000
o The accumulated loss is to be written off
The statement of financial position before the reconstruction is as follows:
N,000 N’000
Property,plant and equipment 1,000 Ordinary share capital 1,500
Goodwill 500 Preference share capital 200
Cash - Accumulated loss (300)
Receivables 300 10% debenture secured on PPE 500
Inventory 400 Bank overdraft 300
2,200 2,200
Execute the scheme of reconstruction.
SOLUTION TO ILLUSTRATION 1
BEFORE N'000 AFTER N'000
Property, plant & equipment 1,000 980
Goodwill 500
Cash 450
Receivables 300 290
inventory 400 350
2,200 2,070
Ordinary share capital 1,500 750
Preference share capital 200 150
Share premium 500
Accumulated loss (300)
Capital reserve (balancing fig) 420
1,400 1,820
10% debenture 500 250
Bank overdraft 300

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2,200 2,070
Workings
■ Ordinary share capital
N'000
Reduction of existing capital (25% x 1,500) 375
New shares subscribed 250
Issued to debenture holders 125
750
■ Cash from new subscription
N'000
Cash to pay overdraft 300
Balance to cash account 450
Amount raised ; share capital N250,000; share premium N500,000 750

ILLUSTRATION 2 ON CORPORATE RECONSTRUCTION

The latest statement of financial position for Olive Inc is summarized below:
N000 N000 N000
Non current assets at net book value 5,700
CURRENT ASSETS
Inventory and work in progress 3,500
Receivables 1,800
5,300
Less current liabilities
Unsecured payables 4,000
Bank overdraft (unsecured) 1,600 5,600
Working capital 300
Total assets less current liabilities 5,400
NON CURRENT LIABILITIES
10% secured debentures 3,000
Net assets 2,400

CAPITAL AND RESERVES

Called up share capital 4,000
Profit and loss account 1,600
2,400

The company’s called up capital consist of 4,000,000 N1 ordinary shares issued and fully
paid. The non current assets comprise of freehold property with a book value of N3,000,000
and plant and machinery with a book value of N2,700,000. The debentures are secured on the
freehold property.
In recent years, the company has suffered a series of trading losses which have brought it to
the brink of liquidation. The directors estimate that in a forced sale the assets will realise the
following amounts

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Freehold premises N2,000,000

PLANT & MACHINERY N1,000,000
INVENTORY N1,700,000
RECEIVABLES N1,700,000
The costs of liquidation are estimated at N770,000. However, trading conditions are now
improving and the directors estimate that if new investment in plant and machinery costing
N2,500,000 were undertaken, the company should be able to generate annual profits before
interest of N1,750,000. In order to take advantage of this, they have put forward the following
proposed reconstruction scheme.
I. Freehold premises should be written down by N1,000,000, plant and machinery by
N1,100,000, inventory and work in progress by N800,000 and receivables by N100,000.
II. The ordinary shares should be written down by N3,000,000 and the debit balance on the
income statement written off
III. The secured debentures would exchange their debentures for N1,500,000 ordinary shares and
N1,300,000 14% unsecured loan stock repayable in five years time.
IV. The bank overdraft should be written off and the bank should receive N1,200,000 of 14%
unsecured loan stock repayable in five years’ time in compensation
V. The unsecured payables should be written down by 25%
VI. A rights issue of 1 for 1 at par is to be made on the share capital after the above adjustments
have been made
VII. N2,500,000 will be invested in new plant and machinery
Required
▪ Prepare the statement of financial position of the company after the completion of the
reconstruction (8 marks)
▪ Prepare a report, including appropriate calculations, discussing the advantages and
disadvantages of the proposed reconstruction from the point of view of:
a. The ordinary shareholders
b. The secured debenture holders
c. The bank
d. The unsecured payables
Ignore taxation (22 marks)

SOLUTION TO QUESTION 2
BEFOR AFTER
E
N'000 a b c d e-g N'000
Non current assets 5,700 (2,100) 2,500 6,100
Current assers
Inventory 3,500 (800) 2,700
Receivables 1,800 (100) 1,700
5,300 4,400
Payables (4,000) 1,000 (3,000)
Overdraft (1,600) 1,600 0
Working capital (300) 1,400

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Total assets less current 5,400 7,500

liabilities
10% debenture (3,000) 3,000 0
14% stock (1,300) (1,200) (2,500)
Net assets 2,400 5,000
Capitai&reserve
Share capital 4,000 (3,000) 1,500 2,500 5,000
Income statement (1,600) 1,600 0
2,400 5,000

B part is a report on the scheme

To : board of directors
From : Management Accountant
Date : 18th November 2015
Subject: proposed capital reconstruction

INTRODUCTION
The purpose of this report is to evaluate the implications of the proposed capital reconstruction of
the company for the various affected parties, including the shareholders, debenture holders,
unsecured payables and the bank. Calculations showing the effect of the reconstruction on the
statement of financial position are included as an appendix to this report.

ORDINARY SHAREHOLDERS
In the event of a liquidation, the ordinary shareholders would be most unlikely to receive anything
for their shares, since the net proceeds of the liquidation would be as follows;
If the reconstruction is undertaken, the existing shareholders will have to provide an additional N1
million of capital in subscribing to the rights issue. They would also have an EPS of 28k and annual
return to shareholders. If the estimates are reliable, then their shares can be disposed. However their
control would shift as they only have 40% shareholding.

SECURED DEBENTURE SHAREHOLDERS

Under the existing arrangements, the amount owing to the debenture holders is N3m. the asset on
which it is secured has reduced to N2 m which means that only N2m is secured and the balance
Nlm is unsecured. They would get 85% of the amount they are been owed.
Under the scheme they would receive share capital of N1.5m making them 60% shareholding and
an unsecured loan of N1.3m,
They would enjoy an interest of N182,000 annually from interest and a dividend of 28k per share.

THE BANK
The bank (overdraft) would only get 55% of their amount if the company gets liquidated that is
N880,000.
Under the scheme, the bank gets N1.2m loan stock and an interest of 168,000 (14% x N1.2m)
which is equivalent to an annual return of 19% which would be favoured by the bank if the
estimates can be relied upon.

Unsecured payables
Under liquidation they get N2.2 million but if the scheme is implemented, they get N3m and a guaranteed
future business

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Conclusion
The proposed scheme appears to hold benefits for all the parties involved. However these benefits will only
be realised if the forecast is correct and the projected returns are realistic

WORKINGS ON LIQUIDATION state

Property 2,000,000
Plant 1,000.000
Inventory 1,700,000
Receivables 1,700.000
Liquidation cost (770,000)
Total 5,630,000
SECURED PORTION OF DEBENTURE (2,000,000)
Net available for unsecured debt 3,630,000
BALANCE OF DEBENTURE (UNSECURED) 1,000,000 gets N550,000 only
BANK OVERDRAFT UNSECURED 1,600,000 gets N880,000
UNSECURED PAYABLES 4,000,000 gets N2,200,000
Unsecured debt will rank same for the debt left 3,630,000/6,600,000 = 55%

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SESSION 20: CORPORATE FAILURE

ILLUSTRATIONS ON CORPORATE FAILURE
ILLUSTRATION 1 (NOVEMBER 2015 ICAN PAST QUESTION)
Corporate failure is never the result of a random set of events. It is normally a reflection of deep seated
corporate shortcomings.
a. identify and discuss the financial symptoms of corporate failure in Nigeria (6 marks)
b. Discuss seven general causes of corporate failure in Nigeria (14 marks)
SOLUTION TO ILLUSTRATION 1
(a) Financial symptoms of corporate failure
i) Declining profitability: Low, negative and/or an adverse trend in operating profitability figures normally
represent a distress situation;
ii) Declining liquidity: Unless timely stemmed, declining profitability inevitably turns into decreased ability to
generate cash and cash crisis.
iii) Declining solvency: Declining profitability sooner or later leads to declining solvency when liabilities
exceed assets. A solvency crisis triggers action by banks and other lenders concerned about lack of cover for
their exposure; and
iv) Inadequate capital: When a company"s capital is not adequate for the business it is engaged in, the
company is likely to fail. In a similar vein, if a companyvvs gearing/leverage ratio is high and level of income
is not enough to meet the interest payments on the debts, that is, when the interest cover and the liquidity is
low, it may lead to problem in meeting the payment of interest on loans.
(b) General Causes of corporate failure in Nigeria
i) Bad management: Management is the process of combining, allocating and utilizing an organizations
input(men, materials and funds) by planning, organizing, directing and controlling for the purpose of
producing output-goods and services- desired by customers in order to accomplish organizational objectives.
Towards achieving this objective, it will be necessary to watch the cost, sales, profit margin etc of the
organization;. '
The end-result of all these management tasks and processes will show in the financial ratios like cash flow to
total debt ratio, return on assets ratio, stability of the earnings and the interest coverage ratio, the retained
earnings to total assets ratio, the current ratio, and the size of total assets which are some of the ratios that
indicate corporate success or failure. From this, it can be safely concluded that how well managers do their
work determines whether a company will fail or not.
ii) Technology: Although investment in technology is a management decision some companies lack the
resources to acquire the right technology for their industry. This sometimes increases their overhead and their
unit cost when compared with their competitors who are able to acquire such modern technology. Since
technology assists in the price of goods and service delivery time, companies that are not able to move with the
new technological developments are bound to lose out even though acquiring new technology goes a little
beyond management decision. Investment in new technology depends on the resource available to the
company.
iii) Frauds: Although many companies invest in internal control to avoid or prevent fraud, it still occurs.
Corporate fraud has assumed an alarming proportion in Nigeria today despite the legal provisions made against
it. It has led to the failure of companies by depleting their resources.

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iv) Political & Environmental factors: These are factors that impact negatively or otherwise on the company
beyond the control and even sometimes the cognitive forecast of its management. It has to do with political
factors such as political turmoil and environmental factors such as the Boko Haram Insurgency.
v) Cost of funds: Companies raise short term funds for working capital from the banks (money market) while
they raise long term funds from the capital market. Since cost of funds in Nigeria is very high firms find it
very difficult to source funds for their operations from banks and this has been having negative effect
on their operations.
a. Inflation: This has made the cost of goods to be high and since the incomes of the consumers
are not moving at the same rate the suppliers increase the price of their products, it has become
difficult for consumers to buy the products. Many companies" warehouses are therefore
overstocked with unsold goods thereby affecting their operational performance.

b. Poor infrastructural facilities: The poor level of infrastructural facilities in the country creates
additional costs for organizations in the form of provision of electricity, water, transportation ,
security, communication, etc.

c. Multiple Taxation: Businesses in Nigeria are exposed to multiple taxation from Local
Government level to Federal Government level thereby creating additional cashflow burden.
Furthermore, a large number of illegal charges are imposed on organizations by corrupt
government officials at the various ports, all of which add to the cost of doing business in the
country.

d. Government Foreign Exchange Policy: This is also an area that contributes to corporate failure
in the country. For example, the recent Central Bank guidelines on foreign exchange is
adversely affecting many industries as they are now having a shortage of foreign currency to
import necessary inputs

ILLUSTRATION 2 ON CORPORATE FAILURE

The following data relates to six public companies
A plc B plc C plc D plc E plc N000 F plc N000
N000 N000 N000 N000
Sales 760,000 360,000 575,000 180,000 480,000 880,000
EBIT 80,000 -40,000 75,000 5,000 30,000 48,000
Working 176,000 16,000 150,000 -10,000 44,000 75,000
capital
Total 500,000 600,000 600,000 250,000 200,000 800,000
assets
Total debt 156,000 290,000 340,000 160,000 40,000 325,000
Retained 104,000 10,000 80,000 15,000 80,000 225,000
earnings
Issued 240,000 300,000 180,000 75,000 80,000 250,000
share
capital N1
shares

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Current N1.50 N0.20 N2.50 N0.40 N4.20 N1.20

market
price per
share
▪ using the Altman Z-score formula for the prediction of bankruptcy, calculate the Z score
for each company and comment on your results.
▪ Outline the usefulness and limitations of the Altman model and outline any other sources
of information you consider might be useful for bankruptcy prediction
Note: the Altman Z score model is as follows Z= 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5
X1 = Working capital to asset
X2 = cumulative retained earnings to total assets
X3 = earnings before interest and taxes to total assets
X4 = Market value of equity to book value of total debt
X5 = sales to total assets

SOLUTION TO ILLUSTRATION 2 ON CORPORATE FAILURE

Z score for A pic; 1.20(0.352) + 1.40(0.208) + 3.3(0.160) + 0.60(2.308) + 1.00(1.520) = 4.146

Z score for B pic; 1.20(0.027) + 1.40(0.017) + 3.3(0.067) + 0.60(0.207) + 1.00(0.600) = 0.559
Z score for C pic; 1.20(0.250) + 1.40(0.133) + 3.3(0.125) + 0.60(1.324) + 1.00(0.958) = 2.651
Z score for D pic; 1.20(-0.04) + 1.40(0.06) + 3.3(0.02) + 0.60(0.1875) + 1.00(0.72) = 0.935
Z score for E pic; 1.20(0.220) + 1.40(0.40) + 3.3(0.150) + 0.60(8.40) + 1.00(4.40) = 10.759
Z score for F pic; 1.20(0.094) + 1.40(0.281) + 3.3(0.06) + 0.60(0.923) + 1.00(1.10) = 2.358
COMPAN Xi x2 x3 x4 X5
Y
A PLC 176/500=0.0352 104/500=0.208 80/500=0.16 360/156=2.30 760/500=1.52
B PLC 16/600=0.027 10/600=0.017 -40/600=-0.067 60/290=0.207 360/600=0.60
C PLC 150/600=0.250 80/600=0.133 75/600=0.125 450/340=1.324 575/600=0.958
D PLC -10/250 = -0.04 15/250=0.06 5/250=0.02 30/160=0.1875 180/250=0.72
E PLC 44/200=0.220 80/200=0.4 30/200=0.15 336/40=8.40 880/200 = 4.4
F PLC 75/800=0.094 225/800=0.281 48/200=0.06 300/325=0.923 880/800= 1.10

COMPANY COMMENT BASED ON THE Z SCORE VALUES

A PLC Z score of 4.146, it is a very iow possibility of failure
B PLC Z score of 0.559, very high potential of failure
C PLC Z score of 2.651, high possibility of failure
D PLC Z score of 0.935, very high potential of failure
E PLC Z score of 10.759, highly reliable with low possibility of failure
F PLC Z score of 2.358, high possibility of failure

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USEFULNESS OF Z SCORES

A current view of the link between financial ratios and business failure would appear to be as
follows:

a. The financial ratios of firms which fail can be seen in retrospect to have deteriorated
significantly prior to failure, and to be worse than the ratios of non- failed firms.
b. No fully accepted model for prediction of future business failures has yet been
established, although some form of Z score analysis would appear to be the most
promising avenue for progress.
c. It cannot be used for companies which lack market value.

It is widely used in the banking sector for risk assessment, loan grading and corporate finance
activities. They are also used by accountancy firms, fund management houses, stockbrokers and
credit insurers
including trade indemnity.
LIMITATION OF CORPORATE FAILURE MODELS

XIII. They relate to the past without considering macro-economic environment

XIV. They are based on accounting conventions and concepts
XV. The publication of accounting data by companies is subject to delay
XVI. The definition of corporate failure is not clear, given that various forms of rescue or
restructuring are possible.
XVII. The model may become less useful as a predictive tool as the measures may be subject to
manipulation if used as objectives
OTHER INDICATORS OF CORPORATE FAILURE/FINANCIAL DIFFICULTIES

XVIII. Other information in the published accounts such as large increases in intangible assets,
worsening net liquid funds position, very large contingent liabilities and important post
balance sheet events.
XIX. Information in the chairman's report and the director's report such as board composition
and qualifications, company's plan
XX. Published information in the press
XXI. External matters such as new legislation, international events, new and better products
being launched on to the market by a competitor, large rise in interest rates and big change
in foreign exchange rates.

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SESSION 21: BOND PRICING

A bond is an instrument requiring the issuer (debtor or borrower) to repay to the lender (investor/holder) the
amount borrowed plus interest over some specified period of time.
Par value of a bond is the face value or stated amount of the bond while the stated annual interest rate on the
bond is known as coupon rate.
A floating rate bond is a bond whose interest rate fluctuates with shifts in the general level of interest rates.
Zero coupon bonds are bonds that do not pay any interest during their life while premium bonds are bonds
having a market value greater than its par value. A callable bond is a bond that gives the issuer the right to
repurchase the bond at a pre-determined price (call price) at a certain time (call date) while a putable bond is
one in which the bond holder has the right but not the obligation, to sell the bond to the issuer at a pre-
determined price.
A discount bond is one in which the market value of the bond is less than the par value but the yield is higher
than the coupon rate.
VALUATION OF BONDS
The price of any asset is equal to the present value of the expected cash-flows from the asset. (the expected
cash flows are annual coupons from year 1 to maturity date and the par value at maturity).
The market value of a zero coupon bond is the present value of the bond’s par value since it only has one cash
flow.
In the bond market, investment decisions are made on the basis of bond’s yield rather than its price because the
bond yield affects the price at which it trades and serves as an important measure of potential or expected
return.
Nominal yield is the coupon rate of the bond while current yield relates the coupon interest to the market value
(current yield = annual coupon / price). Yield To Maturity (YTM) considers both the interest income , capital
gains/losses and also the timing of cash flows received over the life of an issue (it can be called the IRR of a
bond).
YTM has the following assumptions
1. All coupons can be reinvested at the YTM
2. The bond is held to maturity
3. All coupons are received at a prompt and timely fashion
A plot of required rates of return (yields) against maturity is called a yield curve. The normal expectation is
that the yield curve will slope upwards because interest yields are normally higher for longer dated debt
instruments. The opposite may happen when interest rates are expected to rise in the future. When the yield
curve is inverse (sloping downwards), this is an indication that the markets expect short term interest rates to
fall at some time in the future. When the yield curve has a steep upward slope indicates that the markets
expect short term interest rates to rise at some time in the future.
The following points are important about the yield curve
1. Yields are gross yields, ignoring taxation (pre-tax yields)
2. A yield curve is constructed for risk free debt securities such as government bonds.
3. Risk free debt is the debt where the investor has no credit risk whatsoever, because it is certain that the
borrower will repay the debt at maturity.
BOND DURATION

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Duration is a measure of the average life of a bond, defined as the weighted average of the times until each
payment is made. It is the sensitivity of the price of a bond to changes in in interest rate, The higher the
sensitivity, the higher the duration of a bond. Duration can be defined as the time to recover one half of the
project value. It is a concept widely used by analysts in the bond markets to measure how long an investor in
bonds must wait before his investment in the bond is recovered.
MACAULAY DURATION is a concept of duration that looks into the present value of the bond considering
the time value of money. Duration is an indication of the pre-sensitivity of the bond to a change in the market
yield. Duration is calculated using the cash flows from the year that cash flows start to become positive. There
is an inverse relationship between lenders required rate of return and market value. When there is a rise in
interest rate, the fall in the price of the bond is greater for bonds with a higher/longer duration.
Credit risk also referred to as default risk, is the risk undertaken by the lender that the borrower will default
either on interest payments or on the repayment of principal on the due date, or on both. Credit risk arises from
the inability of a party to fulfil its obligation under the terms of a contract. The credit risk of an individual or
bond is determined by the following two factors;
Probability of default is the probability that the borrower or counter party will default on its contractual
obligations to repay its debt.
THE RECOVERY RATE is the fraction of the face value of an obligation that can be recovered once the
borrower has defaulted. When a company defaults, bond holders do not necessarily lose their entire
investment. Part of the investment may be recovered depending on the recovery rate.
LOSS GIVEN DEFAULT (LGD) is the difference between the amounts of money owed by the borrower less
the amount of money recovered.
The EXPECTED LOSS (EL) from credit risk shows the amount of money the lender should expect to lose
from the investment in a bond or loan with credit risk. The expected loss is the product of the loss given
default and the probability of default.
CREDIT RISK MEASUREMENT
The most common approach is to assess the probability of default using financial and other information on
borrowers and assign a rating that reflects the expected loss from investing in the particular bond. This
assignment of credit ratings is done by credit rating companies such as Standard and poor’s, Moody’s investor
services or Fitch. These ratings are widely accepted as indicators of the credit risk of a bond. The table below
shows the credit rating used by Moody’s and Standard and Moody.
STANDARD & POOR MOODY DESCRIPTION OF CATEGORY
AAA Aaa Prime, highest quality, lowest default risk
AA Aa High grade quality
A A Upper medium grade quality
BBB Baa Medium grade quality
BB Ba Lower medium grade quality
B B Speculative
CCC Caa Poor quality, high default risk and highly speculative
CC Ca Highly speculative
C C Lowest grade quality
For standard and poor’s ratings, those ratings from AA to CCC may be modified by the addition of a plus or
minus sign to show relative standing within the major rating categories.

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With Moody’s , numerical modifiers 1,2 and 3 are added to each ratings category from Aa to Caa. Both credit
ratings estimate default probabilities from the empirical performance of issued corporate bonds of each
category.
Sub investment grade bonds or junk bonds is a speculative investment for the lender or holder.
CREDIT RISK is the risk that a party to whom cash is loaned will not be able to service the debt. It is also
called default risk. The credit risk premium is called a spread and is the difference between a debt under
consideration and the risk free rate of return.
The size of the spread allows for additional risk in the debt that is not risk free. The spread is higher for debt
with higher risk for investors or lenders.
CRITERIA FOR ESTABLISHING CREDIT RATINGS
1 FIRM SIZE
2 FINANCIAL GEARING Long term debt/total debt in relation to capital, gearing, working
capital mgt, off balance sheet commitments
3 INDUSTRY RISK Strength of the industry within the country, measured by the
impact of economic forces, demand factors
4 COUNTRY RISK No issuer’s debt will be rated higher than the country of the origin
(sovereign ceiling concept)
5 INDUSTRY POSITION Issuer’s position in the relevant industry compared with
competitors in terms of operating efficiency
6 MANAGEMENT Company’s planning, controls, financial policies and strategies,
EVALUATION overall quality of management and sucession, merger &
acquisition performance, financial result achievement
7 ASSET BACKING Asset management
8 CASH FLOW ADEQUACY Relationship of cash flow to gearing and ability to finance all
business cash needs
9 ACCOUNTING QUALITY Auditor’s qualification of the accounts, accounting policies for
inventory, goodwill, depreciation
10 FINANCIAL FLEXIBILITY Evaluation of financing needs, plans and alternatives under stress,
banking relationship, debt covenant
11 EARNINGS PROTECTION Earnings power including return on capital, pre tax and net profit
margins, source of finance

ILLUSTRATIONS ON BOND PRICING

ILLUSTRATION 1
I. What is the current market value of a bond with a face value of N100,000 and 8% annual coupon,
if the bond has yield to maturity of 10% and a maturity of 5 years.
II. What is the market value of a N1,000,000 par value zero coupon bond with an 8% yield to
maturity due to mature 15 years from today (assuming semi-annual compounding)

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SOLUTION TO ILLUSTRATION 1
The market value of a bond is calculated as the net present value of the inflows from the bond.
The annual interest is 8% x 100,000 = N8,000

Description Year Cash flow N dcf@10% Present value N

Interest 1-5 8,000 3.791 30,328
Face value 5 100,000 0.621 62,100
Net present value 92,428
This is a discount bond because the face value is higher than the market value which arises because
the YTM is greater than the coupon rate.
B PART OF THE QUESTION IS ON ZERO COUPON BOND
Price = face value/ (1 + YTM)n = 1,000,000 /1.0430 = N308,318.67 recall that the bond is semi
annual compounding (twice a year)and so the years would be twice and the yield halved.

ILLUSTRATION 2 on BOND VALUATIONS USING THE YIELD CURVE

A company wants to issue a bond that is redeemable at par in four years and pays interest at 6% of nominal
value.
The annual spot yield curve for a bond of this class of risk is as follows:
MATURITY YIELD
ONE YEAR 3%
TWO YEARS 3.5%
THREE YEARS 4.2%
FOUR YEARS 5%
Calculate the price that the bond could be sold for (amount company could raise) and then calculate the gross
redemption yield (yield to maturity, cost of debt)
SOLUTION TO ILLUSTRATION 2 ON BOND VALUATION USING YIELD
CURVE
The value of a bond is the NPV of its inflows using the annual discount rate based on the yield
curve.
YEAR DESCRIPTION CASHFLOW N DCF@Annual rate PV N
1 Interest 6 3%@yr 1 =0.971 5.83
2 Interest 6 3.5%(2>vr 2 = 0.934 5.60
3 Interest 6 4.2% @ yr 3 = 0.884 5.30
4 Interest 6 5% @ yr 4 = 0.823 4.94
4 Redemption value 100 5% @ yr 4 = 0.823 82.30
Bond price 103.94
Gross redemption yield is the IRR of the bond's cash flows.
year Description Cash flow dcf@6% PV N DCF@4% PV N
N
0 Market value (103.94) 1 (103.94) 1 (103.94)
1 Interest 6 0.943 5.66 0.962 5.77

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2 Interest 6 0.890 5.34 0.925 5.55

3 Interest 6 0.840 5.04 0.889 5.33
4 Interest 6 0.792 4.75 0.855 5.13
4 Redemption 100 0.792 79.20 0.855 85.50
NPV (3.95) 3.32
GRY = LR + (NPVLR / NPVLR + NPVHR) HR - LR = 4 + (3.32/ 3.32 + 3.95)6 -4 = 4.91%

ILLUSTRATION 3 ON YIELD CURVE

There are three bonds in issue for a given risk class. All three bonds pay interest annually in arrears and are to
be redeemed at par at maturity. Relevant information about the three bonds is as follows
BOND MATURITY COUPON RATE MARKET VALUE
A 1 YEAR 6.0% N102
B 2 YEARS 5.0% N101
C 3 YEARS 4.0% N97
Construct the yield curve that is implied by the data above

SOLUTION TO ILLUSTRATION 3 ON YIELD CURVE DERIVATION

▪ Calculate the rate for year 1; INT + RV (1 + R)"1 = Market value;

lOefl+R)"1 = 102 The rate = 102/106 -1 = 3.92%
▪ Calculate the rate for year 2
YEAR Description Cash flow Discount factor PV
1 interest 5 0.962 4.81
2 RV + interest 105 1+ R"2 96.19
Market value 101.00
R=(V 105/96.19) - 1 = 4.48%. note the 96.19 = (101-4.81).
▪ Calculate the rate for year 3 maturity
YEAR DESCRIPTION CASH DCF PV N
FLOW
1 Interest 4 3.92% yr 1 =0.962 3.85
2 Interest 4 4.48% YR 2= 0.916 3.66
3 RV +Interest 104 1+R"3 89.49
Market value 97
R = 3V 104/89.49 - 1 =5.1%
▪ Summarize in a table as shown below
MATURITY YIELD
1 YEAR 3.92%
2 years 4.48%
3 years 5.1%

ILLUSTRATION 4 ON DURATION AND CAPITAL INVESTMENT

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Calculate the NPV and Duration of the project with the information in the table below with a cost of capital of
10%.
year 0 1 2 3 4 5 6
Annual -200,000 -40,000 30,000 120,000 150,000 100,000 50,000
cash flow

SOLUTION TO ILLUSTRATION 4 ON BOND PRICING (DURATION AND MACAU LAY

DURATION)
Duration refers to how long one half of a bond's value can be recovered. It is calculated by
attaching weights to the cash flow or PVs as the case may be. BOND 1

YEA Cashflow N WEIGH EV DCF@10 PV WEIGH EPV

R T % T
1 10 1 10 0.909
9.09 1 9.09
2 10 2 20 0.826
8.26 2 16.52
3 10 3 30 0.751
7.51 3 22.53
4 110 4 440 0.683
75.13 4 300.52
140 500 99.99 348:66
Duration = EV/cash flow = 500/140 = 3.57 years;
Macaulay Duration = EPV/PV = 348.66/99.99 = 3.49 years
▪ BOND 2
YEA Cashflow N WEIGH EV DCF@10 PV WEIGH EPV
R T % T
1 20 1 20 0.909 18.18 1 18.18
2 20 2 40 0.826 16.52 2 33.04
3 20 3 60 0.751 15.02 3 45.06
4 120 4 480 0.683 81.96 4 327.84
180 600 131.68 424.12
Duration = EV/cash flow = 600/180 = 3.33 years;
Macaulay Duration = EPV/PV = 424.12/131.68 = 3.22 years

ILLUSTRATION 5
Julius Berger plc is a major player in the road construction industry with a credit rating of AA. The company
plans to raise N750 million from the bond market. Two different bonds are being considered.
OPTION 1: a 4 year bond with an annual coupon rate of 5%. The bonds will be redeemable at par
Option 2: this is a three year bond, with an annual coupon rate of 4% redeemable at a premium of 5% to
nominal value.
The current annual spot yield curve for Government bonds is as follows:
1 year 3.3%, 2 year 3.8%, 3 year 4.5% and 4 year 5.3%.
The following table of spreads (in basis points) is given for the construction industry

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Rating 1 year 2 year 3 year 4 year

AAA 12 23 36 50
AA 27 40 51 60
A 43 55 67 80
Required
Calculate the theoretical issue prices of the bond and the duration of the bonds.

SOLUTION TO ILLUSTRATION 5 ON JULIUS BERGER

Use the credit rating of the company to determine the spread. The spread is in basis where 100 basis
equals 1%.

Maturity 1 year 2 years 3 years 4 years

Risk free rate 3.3% 3.80% 4.50% 5.30%
AA spread 0.27% 0.40% 0.51% 0.60%
Discount rate 3.57% 4.2% 5.01% 5.90%
BOND 1
YEAR CASH FLOW N DCF PV N
1 5 3.57% YR 1 = 0.965 4.83
2 5 4.2% YR 2 = 0.921 4.61
3 5 5.01% YR 3 = 0.864 4.32
4 105 5.90% YR 4 = 0.795 83.47
97.23
BOND 2
YEAR CASH FLOW N DCF PV N
1 4 3.57% YR 1 = 0.965 3.86
2 4 4.2% YR 2 = 0.921 3.68
3 109 5.01% YR 3 = 0.864 94.18
1001.72

To complete bond duration, we need to compute YTM of the bond. Calculate the IRR of the two
bonds. The YTM is 5.8% and 4.98% for bond 1 and 2. Calculation of bond duration BOND 1

YEAR CASH DCF@5.8% PV WEIGHT EPV

FLOW
1 5 0.945 4.73 1 4.73
2 5 0.893 4.47 2 8.94
3 5 0.844 4.22 3 12.66
4 105 0.798 83.79 4 335.16
97.21 361.49
Duration = 361.49/97.21 = 3.72 years. BOND 2
YEAR CASH DCF@4.98% PV WEIGHT EPV

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FLOW
1 4 0.953 3.81 1 3.81
2 4 0.907 3.63 2 7.26
3 109 0.864 94.18 3 282.54

101.62 293.61
Duration = 293.61 / 101.62 = 2.89 years

ILLUSTRATION 6
GNT co is considering an investment in one of two corporate bonds. Both bonds have a par value of N1,000
and pay coupon interest on an annual basis. The market price of the first bond is N1,079.68. its coupon rate is
6% and it is due to be redeemed at par in five years. The second bond is about to be issued with a coupon rate
of 4% and will also be redeemable at par in five years. Both bonds are expected to have the same gross
redemption yields (yields to maturity). The yield to maturity of a company bond is determined by its credit
rating.
a. Estimate the Macaulay duration of the two bonds GNT Co is considering for investment (9 marks)
b. Discuss how useful duration is as a measure of the sensitivity of a bond price to changes in interest
rates (8 marks)
c. Among the criteria used by credit agencies for establishing a company’s credit rating are the
following; industry risk, earnings protection, financial flexibility and evaluation of the company’s
management. Briefly explain each criterion and suggest factors that could be used to assess it.
(8 marks)

SOLUTION TO ILLUSTRATION 6 ON GNT

To calculate the duration of both bonds, the present value of the cash flows and the selling price of
the bonds need to be calculated first. To obtain the present value of the cash flows, they need to be
discounted by the gross redemption yield. This requires an IRR calculation. The market price of the
first bond which is Nl,079.68, can be used to find the GRY that is common to both bonds.

Year Cashflow Amount N DCF@5 PV N DCF@4 PV N.

% %
0 Market price (1,079.68) 1 (1,079.68) 1 (1,079.68)
1-4 Interest 60 3.546 212.76 3.630 217.80
5 Interest + redemption 1,060 0.784 831.04 0.822 871.32
(35.88) 9.44
IRR = 4 + (9.44)/(9.44 + 35.88) x (5-4) =4.21% = 4.2%
BOND 1
YEAR cashflow amount dcf@4.2% PV WEIGHT EPV
1 interest 60 0.960 57.58 1 57.58
2 Interest 60 0.921 55.26 2 110.52
3 Interest 60 0.884 53.03 3 159.09
4 Interest 60 0.848 50.89 4 203.56

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5 lnt+ RV 1,060 0.814 862.95 5 4314.75

1,079.71 4,845.50

Duration = EPV/PV = 4845.50/1079.71 = 4.49 years BOND 2

YEAR Cash flow Amount dcf@4.2% PV WEIGHT EPV
1 Interest 40 0.960 38.39 1 38.39
2 Interest 40 0.921 36.84 2 73.68
3 Interest 40 0.884 35.36 3 106.08
4 Interest 40 0.848 33.93 4 135.72
5 Int + RV 1,040 0.814 846.66 5 4,233.30
991.18 4,587.17
Duration = EPV/PV = 4,587.17/991.18 =4.63 years.

• The sensitivity of a particular bond to change in interest rates will depend on its redemption date.
Bonds that have a later maturity date are more prices sensitive to interest rate changes. Duration
measures the average time that a bond takes to "payback" its market price. The average time taken to
recover the cash flow from an investment is not only affected by the maturity date of the investment
but also by the coupon rate (which determines the interest payments). We want to be able to compare
bonds quickly- this is when duration is useful. Duration can be used to assess a bond's change in
value following an interest change by using the following formula. Change in bond price =
duration/(l+GRY) X change in yield X current market price of the bond.
The main limitation of duration is that it assumes a linear relationship between interest rates and
price. That is, it assumes that for a certain percentage change in interest rates, there will be an equal
percentage change in price. It assumes a flat yield that is bonds of all maturities have the same yield
to maturity which is contrary to liquidity preference theorem. It assumes instantaneous change in
yield and a parallel change in yield curve.
Industry risk measures the resilience of the company's industrial sector to changes in the economy. In
order to measure this, the following factors could be used;
• Impact of economic changes on the industry in terms of how successful the industry operates under
differing economic outcomes
➢ How cyclical the industry is and how large the peaks and troughs are
➢ How the demand shifts in the industry as the economic changes
• Financial flexibility measures how easily the company is able to raise the finance it needs to pursue
its investment goals. In order to assess this, the following factors could be used
➢ Evaluation of plans for financing needs and range of alternatives available
➢ Relationship with finance providers example banks
➢ Operating restrictions that currently exist in the form of debt covenants
▪ Earnings protection measures how well the company will be able to maintain or protect its earnings
in changing circumstances. In order to assess this, the following factors could be used
➢ Differing ranges of sources of earning growth
➢ Diversity of customer base
➢ Profit margins and return on capital

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■ Evaluation of the company's management considers how well the managers are managing and
planning for the future of the company. In order to assess this, the following factors could be used
1. The company's planning & control policies, and its financial strategies
2. Management succession planning
3. The qualification and experience of the managers
4. Performing in achieving financial and non financial targets

ILLUSTRATION 7
Toltuck Co is a listed company in the building industry which specializes in the construction of large
commercial and residential developments. Toltuck Co had been profitable for many years, but has just incurred
major losses on the last two developments which it has completed in its home country of Arumland. These
developments were an out-of-town retail Centre and a major residential development. Toltuck Co’s directors
have blamed the poor results primarily on the recent recession in Arumland, although demand for the
residential development also appears to have been adversely affected by it being located in an area which has
suffered serious flooding over the last two years.
As a result of returns from these two major developments being much lower than expected, Toltuck Co has had
to finance current work-in-progress by a significantly greater amount of debt finance, giving it higher gearing
than most other construction companies operating in Arumland. Toltuck Co’s directors have recently been
alarmed by a major credit agency’s decision to downgrade Toltuck Co’s credit rating from AA to BBB. The
directors are very concerned about the impact this will have on the valuation of Toltuck Co’s bonds and the
future cost of debt.
The following information can be used to assess the consequences of the change in Toltuck Co’s credit rating.
Toltuck Co has issued an 8% bond, which has a face or nominal value of ₦100 and a premium of 2% on
redemption in three years’ time. The coupon on the bond is payable on an annual basis.
The government of Arumland has three bonds in issue. They all have a face or nominal value of ₦100 and are
all redeemable at par. Taxation can be ignored on government bonds. They are of the same risk class and the
coupon on each is payable on an annual basis. Details of the bonds are as follows:
Bond Redeemable Coupon Current market value ₦
1 1 year 9% 104
2 2 years 7% 102
3 3 years 6% 98
Credit spreads, published by the credit agency, are as follows (shown in basis points):
Rating 1 year 2 years 3 years
AA 18 31 45
BBB 54 69 86
Toltuck Co’s shareholder base can be divided broadly into two groups. The majority of shareholders are
comfortable with investing in a company where dividends in some years will be high, but there will be low or
no dividends in other years because of the cash demands facing the business. However, a minority of
shareholders would like Toltuck Co to achieve at least a minimum dividend each year and are concerned about
the company undertaking investments which they regard as very speculative. Shareholders from both groups
have expressed some concerns to the board about the impact of the fall in credit rating on their investment.
Required:
(a) Calculate the valuation and yield to maturity of Toltuck Co’s ₦100 bond under its old and new credit
ratings. (10 marks)
(b) Discuss the factors which may have affected the credit rating of Toltuck Co published by the credit
agency. (8 marks)
(c) Discuss the impact of the fall in Toltuck Co’s credit rating on its ability to raise financial capital and
on its shareholders’ return. (2 marks)

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SOLUTION TO ILLUSTRATION 7
• Calculate the rate for year 1; INT + RV (1 + R)"1 = Market value; ^(l-fR)"1 = 104
The rate = 109/104 -1 =
4.81% B Calculate the rate for
year 2

YEAR Description Cash flow Discount factor PV

1 interest 7 0.954 6.68
2 RV + interest 107 1+ R~2 95.32
Market value 102
R=(V 107/95.32) -1 = 5.95%. note the 95.32 = (102 - 6.68).

■ Calculate the rate for year 3 maturity

YEAR DESCRIPTION CASH DCF PV N
FLOW
1 Interest 6 4.81% yr 1 =0.954 5.72
2 Interest 6 5.95% YR 2= 0.891 5.35
3 RV +Interest 106 1+R"3 86.93
Market value 98
R = 3V 106/86.93 - 1 =6.83% *
▪ Summarize in a table as shown below
MATURITY YIELD
1 YEAR 4.81%
2 years 5.95%
3 years 6.83%

+ Govt yield Spread old rating Spread new rating

% % % % % %
1 4-81 0-18 4-99 0-54 5-35
2 5-95 0-31 6-26 0-69 6-64
3 6-83 0-45 7-28 0-86 7-69

Valuation of bond under old credit rating

Year Payment Discount factor Discounted cash flow

N N
1 8 1/1-0499 7-62
2 8 1/1-06262 7-09

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3 100 1/1-07283 89-09

Bond valuation

Valuation of bond under new credit rating

Year Payment Discount factor Discounted cash flow ft ft
1. 8 1/1-0535 7-59
2. 8 1/1-06642 7-03
3. 110 1/1-07693 88-08

Bond valuation 102-70

Yield to maturity under old credit rating

Year Payment Discount factor Discounted cash flow Discount factor Discounted cash flow
N 8% N 7% N
0 (103-80) 1-000 (103-80) 1-000 (103-80)
1-3 8-00 2-577 20-62 2-624 20-99
3 102-00 0-794 80-99 0-816 83-23

(2-19) 0-42

Using IRR approach, yield to maturity = 7 + ((0-42/(2-19 + 0-42)) x (8 - 7)) =

7-16% Yield to maturity under new credit rating

Year Payment Discount factor Discounted cashflow Discount factor Discounted cashflow
N 8% N 7% N
0 (102-70) 1-000 (102-70) 1-000 (102-
70)
1-3 8-00 2-577 20-62 2-624 20-
99
3 102-00 0-794 80-99 0-816 83-
23
(1-09) 1-52

Using IRR approach, yield to maturity = 7 + ((1-52/(1-09 + 1-52)) x (8 - 7)) = 7-58%

Market value of ftlOO bond has fallen by ftl-10 and the yield to maturity has risen by
0-42%.

(b) The credit agency will have taken the following criteria into consideration when assessing
Toltuck C's
credit rating:
Country

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Toltuck Co's debt would not normally be rated higher than the credit ratings of its country of origin,
Arumland. Therefore the credit rating of Arumland should normally be at least AA. The rating will
also have depended on Toltuck Co's standing relative to other companies in Arumland. The credit
agency may have reckoned that Toltuck Co's recent poor results have weakened its position.

Industry
The credit agency will have taken account of the impact of the recession on property construction
companies generally in Arumland. Toltuck Co's position within the industry compared with
competitor will also have been assessed. If similar recent developments by competitors have been
more successful, this is likely to have had an adverse impact on Toltuck Co's rating.

Management
The credit agency will have made an overall assessment of management and succession planning at
Toltuck Co. It will have looked at business and financing strategies and planning and controls. It will
also have assessed how successful the management has been in terms of delivering financial results.
The credit agency may have believed the poor returns on recent developments show shortcomings in
management decision-making processes and it may have rated the current management team poorly.
Financial
The credit agency will have analysed financial results, using measures such as return on capital
employed. The agency will also have assessed possible sources of future earnings growth. It may
have been sceptical about prospects, certainly for the short term, given Toltuck Co's recent problems.
The credit agency will also have assessed the financial position of Toltuck Co, looking at its gearing
and working capital management, and considering whether Toltuck Co has enough cash to finance its
needs. The agency will also have looked at Toltuck Co's relationship with its bankers and its debt
covenants, to assess how flexible its sources of finances are if it comes under stress. It may well have
been worried about Toltuck Co's gearing being higher than the industry average and concerned about
the high levels of cash it needs to finance operations. It will also have assessed returns on
developments-in-progress compared with commitments to repay loans. Greater doubt about Toltuck
Co's ability to meet its commitments is likely to have been a significant factor in the fall in its rating.

The agency will also have needed reassurance about the quality of the financial information it was
using, so it will have looked at the audit report and accounting policies.
(c) Toltuck Co may not have increased problems raising debt finance if debtholders do not react in
the same way as the credit rating agency. They may attach different weightings to the criteria which
they use. They may also come to different judgements about the quality of management and financial
stability. Debtholders may believe that the recent problems Toltuck Co has had generating returns
may be due more to external factors which its management could not have controlled. However, it is
probable that the fall in Toltuck Co's credit rating will result in it having more difficulty raising debt
finance.
Banks may be less willing to provide loans and investors less willing to subscribe for bonds. Even if
debt finance is available, it may come with covenants restricting further debt or gearing levels. This
will mean that if Toltuck Co requires substantial additional finance, it is more likely to have to make
a rights issue or issue new equity on the stock market. Shareholders may be faced with the choice of
subscribing large amounts for new capital or having their influence diluted. This may particularly
worry the more cautious shareholders.
Even if Toltuck Co can obtain the debt it needs, the predicted increase in yield to maturity may be
matched by debtholders demanding a higher coupon rate on debt. This will increase finance costs,

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and decrease profits and earnings per share, with a possible impact on share price. It will also mean
that fewer funds are available for paying dividends. Toltuck Co has been faced with difficult
decisions on balancing investment expenditure versus paying dividends and these difficulties may
well increase. Additional debt may have other restrictive covenants. They may restrict Toltuck Co's
buying and selling of assets, or its investment strategy. Restrictions on Toltuck Co's decisions about
the developments it undertakes may impact adversely on shareholder returns.
Loan finance or bonds will also come with repayment covenants. These may require Toltuck Co to
build up a fund over time which will be enough to redeem the debt at the end of its life. Given
uncertainties over cash flows, this commitment to retain cash may make it more difficult to undertake
major developments or pay an acceptable level of dividend.
The fall in Toltuck Co's credit rating may result in its cost of equity rising as well as its cost of debt.
In turn, Toltuck Co's weighted average cost of capital will rise. This will affect its investment choices
and hence its ability to generate wealth for shareholders. It may result in Toltuck Co prioritising
developments offering better short-term returns. This may suit the more cautious shareholders, but
the current majority may worry that Toltuck Co will have to turn down opportunities which offer the
possibility of high returns.

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SESSION 22: DIVIDEND POLICY

Dividend is defined as the benefit investors derive on their stock of investment from the company to
compensate them for the risk they are undertaking and for the time value of their investment.
Dividend policy decision is concerned with the determination of the amount of corporate earnings (earnings
after interest and tax) to be distributed in the form of dividend and how much to be retained within the
company.
It can also be defined as the set of rules which guides management in the distribution of profit to ordinary
shareholders. Dividend policy is aimed at determining the proportion of current income which should be
distributed as dividend.
The objective of dividend policy should be to maximize shareholders return which is dividends and capital
gains. The higher the dividend paid the lower the retained earnings which would be needed to finance
expansion and the higher the retained earnings the lower the dividend payment which is meant to increase the
purchasing power of shareholders
FACTORS AFFECTING DIVIDEND DECISIONS
1. FINANCIAL NEEDS/INVESTMENT OPPORTUNITIES; which may be in conflict with the desires
of shareholders. This refers to profitable investment opportunities which the company could execute
using retained earnings. The dividend policy should consider the effect of not undertaking these projects
at the expense of dividend payments.

2. LEGAL RESTRICTIONS; The dividend policy of the firm has to be in line with the legal framework
and restrictions. The legal rules act as boundaries within which a company can operate in terms of
paying dividend

3. LIQUIDITY; payment of dividend means cash flow. A company may have sufficient profits to declare
dividend but insufficient cash to pay it. The cash position of the organization should be considered in
dividend matters.

4. CONTROL; the objective of maintaining control over the company by existing shareholders may
influence the company’s dividend policy as they may prefer retained earnings to dividend.

5. INFLATION; earnings might have to be retained to ensure the firms survival and capital intact as the
accounting statements are prepared on historical costs

6. TAXATION; the rate of tax may influence the dist4ibution of dividend to shareholders because it is
necessary to make provisions for tax before any determination to pay dividend.

7. PROFITABILITY; the decision to pay dividend absolutely depends on the declared net income before
ordinary shareholders and retained earnings are considered.

8. LOAN AGREEMENT RESTRICTION; lenders may put restriction on dividend payments (covenant)
when the firm is experiencing liquidity or profitability difficulties.

9. GOVERNMENT REGULATIONS; may restrict the amount of dividend payable to a certain

percentage or from a particular profit stage to control the money circulation in the country

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10. DIVIDEND POLICY OF SIMILAR COMPANIES; companies tend to consider what other similar
companies in the industry are paying when deciding on their dividend policy.
11. ACCESS TO THE CAPITAL MARKET; a company that is not sufficiently liquid can pay dividends
if it is able to raise debt or equity in the capital markets. Easy accessibility to the capital market provides
flexibility to the management in paying dividend as well as meeting the corporate obligations.

12. ABILITY TO BORROW; if a firm has the ability to borrow at a comparatively short notice it may be
relatively flexible to pay dividend.

13. INFORMATION CONTENT OF DIVIDEND; dividend paid or proposed is believed to inform the
public on the company’s performance and so the company will consider the message a zero, high or low
dividend will send to the general public in designing its policy.

14. FIRM’S SIZE; a large firm is expected to pay a higher dividend than a smaller one and so failure to do
so might affect the company’s value

15. SHAREHOLDERS PREFERENCE: also plays a significant role on the dividend to be paid.

16. ATTITUDE of the board of directors

FORMS OF DIVIDEND
1. CASH DIVIDEND; involves payment of dividend by cash to shareholders. A company should have
enough cash in its bank account when cash dividends are declared. The cash account and reserves
account of a company will be reduced when cash dividend is paid. It is usually preferred by shareholders
for CERTAINTY.

2. SCRIP DIVIDEND; is the payment of dividend to shareholders by way of additional shares in a

company. It represents a re-capitalization of the company’s capital such that proportional ownership
remains unchanged

It is simply the distribution of shares in lieu or in addition to the cash dividend which increases the number of
shares of the company (increase equity share capital) but reduces the reserves and retained earnings thereby
not affecting the total net worth. It simply represents a recapitalization of the owner’s equity portion.

ADVANTAGES OF SCRIP DIVIDEND

TO SHAREHOLDERS
1. It is not taxable as income like cash dividend
2. It is normally interpreted by shareholders as an indication of higher profitability and may have a
favorable impact on share price
3. Shareholders holding is increased without any additional cost
4. Future dividends may increase where a company with the policy of paying a fixed amount of dividend
per share continues even after the declaration of the bonus.

TO COMPANY

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1. Conservation of cash; company pays dividend without using up cash needed for expansion
2. It is the only alternative to pay dividend under financial difficulty or contractual relations
3. it reduces the market price making it more attractive
4. it decrease the company’s gearing
5. it enhances the company’s borrowing capacity

LIMITATIONS OF SCRIP DIVIDEND TO SHAREHOLDERS

1. it gives no extra or special benefit to shareholders as the proportionate ownership in the company is not
changed
2. it could be deceptive when investors construe additional shares as additional value

TO COMPANY
1. They are more costly to administer
2. The PE ratio as well as share value may go down where the issue is so small that the EPS remains
unaltered

SCRIP ISSUE
This is a conversion of equity reserves into issued share capital. It is also referred to as capitalization of
reserves or bonus issues. It does not bring new funds but has the advantage of making shares cheaper and more
easily marketable

It involves the use of share premium to increase its equity shares which are issued to existing shareholders. The
company’s current profits are not used to support the issue but its existing capital structure.

DIFFERENCE BETWEEN SCRIP DIVIDEND AND SCRIP ISSUE

1. Scrip Dividend uses current year profit to support it while scrip issue uses existing reserves only.
2. Scrip dividend is taxable while scrip issue is not
3. Scrip dividend is optional while scrip issue is free and not optional
4. Scrip dividend is a form of dividend that scrip issue is not

When directors of a company prefer to retain funds within the business but consider that they must pay at least
a certain amount of dividend they offer equity shareholders the choice of a cash dividend or a scrip dividend
.Each shareholder would decide separately which to take .

STOCK SPLIT: - This involves reduction in the par value of a share geared towards increasing the number of
outstanding shares. The proportion ownership of the shareholder remains unchanged. It has same effect with
stock dividend in reducing market price per share thereby serving as a tax benefit to the shareholders.
REVERSE SPLIT: - this involves the reduction in the number of outstanding shares through an increase in
the par value of a firm’s share. They are employed to increase the market price per shares.
SHARE REPURCHASE: - is the purchase by a company of its own shares in the market which can take
place for various reasons and must be in accordance with any requirement of legislation. In many countries,

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firms have the right to buy back shares from shareholders who are willing to sell them subject to certain
conditions.

For a smaller company with few shareholders, it might be that there is no immediate willing purchaser at a
time when a shareholder wishes to sell, for a public company it might be a way of withdrawing from the share
market and going private or to resist a takeover.

ADVANTAGES OF A SHARE REPURCHASE SCHEME

i. it is a method of returning funds to shareholders when no profitable use can be found for them
ii. It can allow a company to buy out dissident shareholders.
iii. From the overall view, it might allow a better distribution of investment funds.
iv. It enables a company to reduce its overall size in response to a restriction in its level of activities
v. Increases the earnings per share through a reduction in the number of shares in issue.
vi. It allows adjustment to capital structure, if this seems to be desirable. Equity can be replaced by debt.
vii. It enables a public company withdraw from the stock market.
viii. It could be used as a take over defense.

DISADVANTAGES OF SHARES REPURCHASE SCHEME

1. It can be hard to arrive at a price that will be fair both to the vendors and to any shareholders who are
not selling shares to the company.
2. It could be seen as an admission that the company cannot make better use of to funds than the
shareholders.
3. Some shareholders may suffer from being taxed on capital gain following purchase of shares
permanently freezes reserves.
4. It allows a company to support its share price and thus creates a false market.
5. The concentration of shareholders may be increased if smaller holders are bought out.

DIVIDEND THEORIES
There are two major theories of Dividend policy
1. Dividend irrelevancy and
2. Dividend supremacy / relevancy theory

DIVIDEND IRRELEVANCY THEORY

In 1961 Modigliani and Miller (M & M) argued against the claim that an active dividend policy should be
pursued as a means of maximizing shareholders wealth. They argued that in a tax free world, shareholders are
indifferent between dividend and capital gain. Stating that the value of a company is determined solely by the
earnings power of its assets and investments.

The bases of their arguments are:

1. If earnings were distributed as dividends each shareholders would gain but would also suffer a
proportionate loss as the company would have to source for funds outside but if earnings is retained it
would lead to the appreciation in the share value.

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2. The consumption preference of stakeholders need not be jeopardized by the company’s dividend policy
and so if a firm pays more cash dividend than needed, the shareholders uses the surplus cash to invest
and if the company refused to pay dividends, the shareholder sells some shares to get cash.
3. There are companies with low dividend payout but high market values and also companies with high
dividend payout but low market values.
4. If a company with investment opportunities decides to pay dividend additional funds from outside would
make for the short fall in funds.
Their arguments are based on the following assumptions:
a. There is a perfect capital market.
b. No floatation or transaction cost
c. No taxation
d. Perfect certainty by every investor as to the future of the companies
e. No risk of uncertainty
f. Company will maintain a fixed investment policy.

DIVIDEND SUPREMACY / RELEVANCY / THEORY

James Walter and M. J Gordon argued that dividends were all that mattered in the determination of share price.
They based their argument on the fundamental theory of share value which states that the market value of a
company’s share depends on the size of dividend, growth rate in dividend and shareholders required rate of
return.

The growth rate in dividend according to Gordon depends on how money reinvested in the company affects the
rate of return (growth rate = return on equity x retention ration).

They assumed that if a firm finances all its investment with retained earnings a constant IRΔ & WACC is
maintained and that all earnings are either paid out as dividend or reinvested internally immediately.

Ke = D/MV - Mv = D/Ke

Ke = do (I + g) + g - Mv = do (I + g)
Mv Ke – g.
The Dividend supremacy theory is supported by the following arguments

a. INFORMATION VALUE ARGUMENT: - which states that the Dividend policy has image making
potential which creates a positive or negative information which is capable of influencing the market
price of the company.

b. CERTAINTY ARGUMENT: - states that investors believe that dividends reduce the risk of
uncertainty compared to capital gains and so the payment or non payment of dividend may influence the
market price.

c. CLIENTELE ARGUMENT: - states that the dividend policy of a firm attracts an identifiable class of
investors to it and so any diversion might influence the share value.

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d. TAXATION ARGUMENT: - The tax rate on dividend income is different from capital gains and so is
likely to influence the kind of investors in a company which may in turn influence the share price in line
with the investor’s preference.

e. CAPITAL RATIONING ARGUMENTS: - the payment of dividend when cash flow available is not
enough to finance viable investments may affects the share value of the company i.e. shareholders
wealth where the opportunity cost of foregoing the project exceeds the dividend paid.

f. ASYMMETRIC INFORMATION: - states that managers and shareholders have different and
incomplete information. Managers do not know how shareholders will react to dividend change likewise
shareholders do not know how managers are performing inside and sol dividends acts as a bridge to the
communication gap.

g. SIGNALLING PROPERTIES OF DIVIDEND: DIVIDENDS are represented as signals from

managers to shareholders and financial markets. Dividend announcement signals the companies’
prospects to the public.

h. BIRD IN HAND ARGUMENT: arises from the existence of uncertainty. This says that investors
prefer a naira dividend that is certain to a naira capital gain which is uncertain meaning that a company
with high pay out ratio is referred to as less risky and so higher confidence by investors which may
affect the share value

ALTERNATIVE DIVIDEND POLICIES

ACTIVE DIVIDEND POLICY: is a policy where dividend is accorded priority before the company will
commit itself to its capital needs. This means that retained earnings for viable projects can only be considered
when dividend has been settled.

It could be a:
STABLE DIVIDEND POLICY: is a policy where a fixed dividend per share is paid annually
CONSTANT PAYOUT RATIO is where a constant proportion of its earnings available for equity is paid out
as dividends.
PASSIVE DIVIDEND POLICY is a policy where dividends are only considered when earnings have been
retained for all viable investment opportunities. It is also called the residual theory of dividends which believes
that dividend should be secondary to be considered after setting out money aside for all viable investment
projects.
HYBRID DIVIDEND THEORY: is a policy which tries to combine the active and the passive. This is not
practical and so it is advisable a firm invests in profitable projects to earn a higher return than the individual
shareholders can in their alternative investment opportunities.
RETAINED EARNINGS: is surplus cash that has not been needed for operating costs, interest payments, tax
liabilities, asset replacement or cash dividend. It belongs to shareholders and regarded as equity financing. A
company may have substantial retained profits in its balance sheet but no cash in the bank and will not
therefore be able to finance investment from retained earnings.

ADVANTAGES

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1. It is a flexible source of finance.

2. It involves no change in shareholding pattern
3. No dilution of control
4. No issue costs

DISADVANTAGES
1. Shareholders may interpret it wrongly
2. It is deceptive to take retained profits as cost free method

DIVIDEND POLICY
Dividend decision is one of the three main finance decisions of any firma and it involve the determination of
the proportion of a company’s earnings to pay out or retain. It is described as current earnings paid or
distributed by companies to their shareholders as a return on their investment.

There are two schools of thoughts about whether or not dividend policy affects the value of a firm. The first
school of thought argues that dividend policy affects the value of the firm (dividend supremacy) while the
second school believes otherwise (dividend irrelevance)

DIVIDEND SUPREMACY/RELEVANCE
WALTER’S MODEL
Professor James E. Walter argues that the choice of dividend policies almost always affects the value of the
firm. His model shows the importance of the relationships between the firm’s rate of return (r) and its cost of
capital (k) in determining the dividend policy that will maximize the wealth of shareholders. The model is
based on the following assumptions:
i) Internal financing: No debt or new equity is issued as all investments are financed through retained
earnings
ii) Constant rate of return and cost of capital
iii) 100% payout or retention – all earnings of the firm are either distributed as dividend or re-invested
internally immediately
iv) constant earnings per share and dividend per share
v) infinite time – the firm has a very long or infinite life
Walter formula to determine the market price per share is as follows.
P = DIV + r (EPS – DIV) /K
K K
P = market price per share, DIV = Dividend per share,
EPS = Earnings per share = r = firm’s rate of return, K = firms cost of capital or capitalization rate.
The equation above reveals that the market price per share is the sum of the present value of two
sources of income
i) Present value of the infinite stream of constant dividends (DIV/K) and
ii) Present value of the infinite stream of capital gains (r (EPS –DIV)/k)/K
When the firm retains a perpetual sum of (EPS – DIV) at r rate of return the value of the share will be
the present value of all dividends plus the present value of all capital gains.

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P= DIV + (r/K) (EPS – DIV)

K
In demonstrating how dividend policies affect a firm’s value Walter classified all firms into 3
categories

1 Growth firms Internal rate more than opportunity cost Ability to reinvest earning at a rate higher
of capital (r>k) optimum payout is zero than expected by shareholders. (retain all
earnings) to maximize value MPS increases as
payout reduce
2 Normal firms Internal rate of return equals opportunity Dividend policy has no effort on market value
cost of capital (r=k) No unique optimal per share
payout
3 Declining Internal rate of return less than No profitable investment opportunities as rate
firms opportunity cost of capital (r=k) of return on investment is less than required
optimum payout ratio is 100% by shareholders. Distribute all earnings

Dividend policy in Walter’s model depends on the availability of investment opportunities and the relationship
between the firm’s internal rate of return and its cost of capital thus a financing decision which makes payment
of cash dividend a passive residual.

CRITICISM
i) No external financing
ii) Constant return
iii) Constant opportunity cost of capital

DIVIDEND RELEVANCE: GORDON’S MODEL

Myron Gordon developed a model relating the market value of the firm to dividend policy based on the
following assumptions.
i) All equity firm – the firm is an all equity firm and has no debt
ii) No external financing : is available retained earnings would be used to finance any expansion
iii) Constant return and constant cost of capital
iv) Perpetual earnings
v) Corporate taxes do not exist
vi) Cost of capital is greater than growth rate k > br=g
vii) Constant retention i.e. growth rate (g = br) is constant forever.

According to Gordon’s dividend capitalization mode the market value of as share is equal to the present value
of an infinite stream of dividends received by the shareholders.
Po = DIV1 + DIV2 DIV
I+K (1+K)2 (1+k)

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Which can be written as Po = DIV (1+ g) = DIV1

k–g k-g
Substituting EPS (1- b) for DIV and br for g
Po = EPS (1- b) = (1-b ) Ra
k – br k-br

Gordon’s conclusion on the relationship between dividend policy and value of the firm is similar to that of
Walters model. Market price increases as retention ration increases for growth firms while the market price
reduces as retention ratio increases for declining firms but the market value of the share is not affected by
dividend policy in a nominal firm.
DIVIDEND IRRELEVANCE MM HYPOTHESIS
According to Miller and Modighiani (M & M) under a perfect market situation the dividend policy of a firm is
irrelevant as it does not affect the value of the firm. They argue that the value of a firm depends on the firm’s
earnings that result from its investment policy. Thus when investment decision of the firm is given dividend
decision (the split of earnings between dividends and retained earnings) is of no significance in determining
the firm’s value. A firm in a perfect capital market may face one of the following situations.
1) Firm has sufficient cash to pay dividend: i.e. shareholders get cash in their hands, but the firms asset
reduce (cash balance declines). What shareholders gain in the form of cash dividends, they lose in the
form of their claims on the (reduced asset) no net gain or loss and so firms value remains unaffected.
2) Firm does not have sufficient cash to pay dividends and therefore issues new shares to finance the
payment of dividend: Existing shareholder get cash in the form of dividend but suffer an equal amount
of capital loss since the value of their claims to assets reduce) shareholders wealth unchanged) the new
shareholders part with cash to the company in exchange for new shares at a fair price. This is simply a
transfer of part of the claim of existing for cash. There is no net gain or loss and so value of firm remains
unaltered.
3) Firm does not pay dividends: a shareholder can create a “home made dividend” by selling part of
his/her shares at the market/fair price in the capital market for obtaining cash. The shareholder could
have less number of shares but increased cash with a nil gain or loss leaving the firms value unaltered.
The summary of the M & M hypothesis is that shareholders do not necessary depend on dividends for
obtaining cash. In the absence of taxes floatation cost and difficulty in selling shares they can get cash
by devising a “home made dividend without any dilution in their wealth.
They based their argument on the following assumptions
i) Perfect capital market where investors are rationale, no floatation cost and information is freely
available to all
ii) No taxes
iii) Fixed investment policy
iv) No risk i.e. investors are able to forecast future prices and dividend with certainty and one discount rate
is appropriate for all securities and all time periods (r = k = kt for all t)
v) Investment programme can be financed either by retained earnings or issues of new shares or both.

r = DIV1 + (P1 – P0) (1) Po = Purchase price at time O

Po P1 = Purchase price at time 1
 Po = DIV1 + P1 = DIV + P1 DIV = DPS at time 1

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(1+ r) (1 + k) n =Number of shares outstanding

VALUE OF FIRM WHEN NO DIV NEW FINANCING

V= npo = n(DIV1 + P1)_ (2)
1+K

VALUE OF FIRM WHEN NEW FINANCING EXIST

npo = nDIV1 + (n+m) P1 – mp1 (3)
1+K m = number of new shares
Amount of new share issued will be
Mp1 = I1 – (X1 – nDIV1) = I1- X1 + nDIV1 (4)
I1 = Total amount of investment during first period
X1= Total net profit of firm during period

npo = nDIV1 + (n+m) p1 – (I1 – X1 + nDIV1) (combining 3 and 4)

1+k
npo = (n+m) p1 – I1 – X1) (collecting like terms)
1+k

A firm which pays dividends will have to raise funds externally to finance the investment plans which
buttresses MM’s argument that dividend policy does not affect the wealth of its shareholders as the dividend
paid by a firm’s as advantage is offset by external financing.

ILLUSTRATION ON DIVIDEND POLICY

ILLUSTRATION 1
The rate of return of A Plc and B Plc is 15% and 8% respectively with a cost of capital of 10%. The profit
after tax of A plc is N1,000,000 and it has 100,000 shares while B plc has a profit after tax of N1,200,000
and 100,000 shares.
I. Using Gordons model determine the price of both companies if the payout ratio of A plc is 40% and
B 60%. Explain if A plc or B plc is a growth or declining firm.
II. Using walters model, determine the price of both companies, explaining if the company is a growth or
declining firm. Advise on the best appropriate payout ratio.
III. A company has a net profit of N1,000,000, one million issued shares, cost of capital is 10%, dividend
is N5 per share, market price per share is N100 . using M & M model calculate the share price of this
company at the end of the year if
a. The company does not pay divided
b. The company pays a dividend of N5 per share

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c. How many shares must be issued by the company if it intends to pay dividend of N5 per share and
meet up with its investment.
IV. Write short notes on the following
I. Traditional theory of dividend policy
II. Residual theory of dividend policy
III. Modigliani and miller theory of dividend policy
IV. Static trade off theory of financing investments
V. Pecking order theory
VI. Market timing theory of financing investments

SOLUTION TO ILLUSTRATION 1
GORDONS MODEL: p = EPS(l-b)/ k - br = for A = 10(l-0.60)/0.10 - (0.60 x 0.15) = N400
For B = 12(1-0.40)/ 0.10 - (0.60 x 0.08) =N138.5
A is a growth firm as it has a return higher than cost of capital while B is a declining firm.
Walter model: p = div +r/k (EPS - DIV)
K
So p would be N150 for A and the appropriate pay out ratio shouid be 0% for a growth firm and
100%
for a declining firm.
According to M&M = PI = p0(l+k) - div = 100 (1.10) -0 = 110
If dividend is paid = 100(1.10) - 5 = N105
Mpl = investment - (net profit - total dividend) where m is number of new
shares M = 2,000,000 - 1,000,000 + 500,000 /105 =
▪ Traditional theory of dividend policy states that dividend payment determines the clientele
and so should be paid as it affects the value of the firm
▪ Residual theory of dividend policy states that dividend should only be paid after all viable
decisions have been considered
▪ M&M theory states that a dividend payment has no impact on the value of an organization.
▪ Static trade off theory states that there is an optimal capital structure with an optimal
gearing level which every company will try to achieve. The higher the profit, the higher the
gearing level. There is a positive correlation between profitability and gearing level
▪ Pecking order states that companies show preference for finance sources based on risk as
there is no optimal level of gearing. Companies would use retained earnings, then debt,
preference shares before new equity. There is a negative correlation between profitability
and gearing level as successful companies would use more of retained earnings.
▪ Market timing theory states that finance choices is driven by opportunities in the capital
market Due to asymmetric information. Companies will make a new issue of shares when
they feel that the share price is overvalued and share repurchase when they feel that the
share price is undervalued. A company does not have optimal level as finance choices are
driven by market opportunities and timing.

ILLUSTRATION 2
The managing Director of Smart plc wishes to provide an extra return to the company’s shareholders and has
suggested making either
▪ A 2 for 5 bonus issue (capitalization issue) in addition to the normal dividend
▪ A 1 for 5 scrip dividend instead of the normal cash dividend
▪ A 1 for 1 share (stock) split in addition to the normal dividend
SUMMARISED STATEMENT OF FINANCIAL POSITION AT THE END OF LAST YEAR

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Nm
Non current assets 65
Current assets 130
Less current liabilities (55)
140
Financed by
Ordinary shares (50 kobo par value) 25
Share premium account 50
Revenue reserves 40
Shareholders fund 115
11% debenture 25
140
The company’s shares are trading at 300k cum div and the company has N50 million of profit from this year’s
activities available to ordinary shareholders of which N30 million will be paid as dividend if options I or III are
chosen. None of the N40 million revenue reserves would be distributed. This year’s financial accounts have
not yet been finalized.
a. For each proposal, show the likely effect on the statement of financial position at the end of this year,
and the likely effect on the company’s share price.
b. Discuss reasons why a company might wish to undertake a scrip dividend or a share stock split

SOLUTION TO ILLUSTRATION 2
STATEMENT OF FINANCIAL POSITION

BONUS ISSUE Nm SCRIP DIVIDEND SHARE SPLIT Nm

Nm
Net assets 135 165 135

Ordinary shares 35 30 25
Share premium 40 75 50
Revenue reserves 60 60 60
135 165 135
▪ 2 for 5 bonus issues require the issue of 20 million new shares with a par value of 50k each.
It is most likely that the share premium account will be used for the bonus issue as the use of
revenue reserves would restrict the company's future rights to pay dividend
▪ 1 for 5 scrip dividend requires the issue of 10 million new shares with a par value of 50k
each. A transfer equal to the market value of the new shares has been made from the profit or
loss account to the ordinary shares (N5m) and share premium (N25m)
▪ 1 for 1 share split requires the issue of 50m new shares, all shares now having a par value of
50 kobo. The revenue reserves and share premium account are not affected
▪ The net assets increase from last years position by N20m when a dividend is paid and by
N50m when dividend is not paid.
▪ Share price will likely fall to the extent that shareholders wealth remains unchanged if market
is efficient and the bonus issue, share split or scrip dividend are believed to convey
significant new information on the assumption that the market has full information on the
new profit and dividend
▪ Bonus issue = 50m X 300k + {20m x 0) / 70m = 214kobo cum div or 171 kobo ex div
▪ Scrip issue = 50m x 300k + (10m x 0)/60m = 250 kobo

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▪ Share split = 50m x 300k + (50m x 0) / 100m = 150 kobo

▪ The expected share price will differ from the computation above if the market does not have
the information or does not believe in the offer

B part of the illustration

Reasons why a Scrip dividend or share split may be taken

1. A scrip dividend preserves liquidity as no cash may leave the company
2. Both measures create cheaper shares and may increase marketability of the shares
3. Both measures may be used as a means of signalling investors of the company's future
prospects
4. Both measures broaden share ownership of a company.

ILLUSTRATION 3
There is a serious debate on the issue of dividend policy, dividend capacity and other related issues. You have
been called upon as the newest Chartered Accountant in the company to throw more light on the following
issues
a. Difference between dividend relevancy and dividend irrelevancy theory
b. Briefly explain dividend capacity stating four practical influences on dividend policy
c. Advise on the pattern of dividend payments would be recommended in a perfect capital market
d. What factors regarding investors preferences would need to be taken into account by firms operating
in the real world.
e. Differentiate between scrip dividend, cash dividend and bonus issue.

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CHAPTER 23: SOURCE OF FINANCE

Financing Decision identifies the different sources of funds, the cost associated with each source, the
characteristics of each source and the availability of each source.
Source of finance is categorized into three (3) major groups;
▪ Short term sources repayable within one year
▪ Medium term sources repayable between one and five years (1-5 years)
▪ Long term sources repayable from 5 years to infinity

SHORT TERM FUNDS

They are suitable for funding shortages in working capital and include

BANK CREDIT/OVERDRAFT
This is a facility which grants customers the right to overdraw their accounts up to a certain limit with interest
charged on a day to day overdrawn position. Bigger and well known customers may be charged a little over the
bank’s base rate (prime rate) with the interest charged being tax deductible.

Bank overdrafts are usually unsecured but under certain conditions may require collaterals. It is usually
available for one year although it may be rolled over with its major cost as the interest charge. It should be
noted that while a short term loan is charged on the whole amount overdraft interest is charged only on the
daily debit or overdrawn balances.

COMMERCIAL PAPER
This is a document issued by an issuing house on behalf of the company. The issuing house (merchant bank)
does not guarantee the notes but assists in finding investors to buy them. The investors effectively lend directly
to the company issuing the notes with the issuing house charging a commission for its service.

Commercial papers usually carry a stated coupon rate whose maturity ranges between 30- 270 days. The cost
of a commercial paper is made up of the coupon rate and the issuing house commission (usually 0.5% flat on
amount raised)

TRADE CREDITS
This refers to credit from suppliers which could be very expensive if it includes a cash discount that is rejected.
It has the advantage of being readily available without formal arrangement and can be rolled over.
Its cost include the cost of not taking a discount
= ___% age discount__ X ______________365_________________
100%- % age discount max payment period - max discount period
Other costs associated with trade credits include pressure from suppliers and reduction in credit rating for
delayed payment beyond the due date.

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FACTORING
This is the raising of funds on the security of the company’s debt so that the cash is received earlier than if the company
waited for the debtors to pay. It could be service factoring where the factor buys the company’s invoiced debt thereby
taking over debt collection and debtor accounting. The procedure involves the company selling goods to the debtor and
selling the debt to the factor who may make an initial payment to the company of about 90% of the debt total value
while the factor receives a commission for the collection of the debt from the debtors. A factoring company provides
immediate cash and also takes care of the collection of the debts as well as the sales administration of debts for a fee.
Factoring arrangement could be with or without recourse. Factoring with recourse means the factor is not
liable for any bad debts but without recourse means the factor is liable for any bad debts arising as a result of
the transaction.
The costs associated with a factor include commission on initial amount provided and the commission on the
service provided.
Factoring has been categorized into two major types
Service factoring where the factor buys from the company its invoiced debt i.e. take over debt accounting and
collection while payment is made when debt matures and
Service and finance factoring where the factor provides immediate finance as well as the accounting services
for an additional finance charge.
The demerits of factoring include the fact that the debtor is aware of the factor and it provides no significant
increase in cash resources available to the company. It could also send a wrong signal of the company’s going
concern position.
INVOICE DISCOUNTING
This involves selling debts to an agent who makes an initial payment of an agreed percentage of the face value
of the debt sold. The agent buys the debt and appoints the company as an agent to collect the debts. No
accounting services available. The cost associated is the difference between the face value and the amount the
agent is paying.

BILLS DISCOUNTING
A bill of exchange is usually prepared by the supplier of goods /creditor for endorsement or acceptance by the
customer/debtor. The supplier can receive immediate cash after the goods have been dispatched by discounting
the bill with a bank/discount house. The cost is the difference between the face value and the discounted value.
ACCRUALS
Tax and Wages accrued may cost the company penalties/fines as well as dampen employees morale thereby
leading to absenteeism, reduced efficiency and so on. This source of finance should only be used only as a
source of last resort..
ACCEPTANCE CREDIT/BANKERS ACCEPTANCE
This is similar to a commercial paper but the bank guarantees to liquidate the debt on maturity in case of a
default. They are issued for periods varying between 2months and 1year with the provider of the fund
evaluating the bank’s credit worthiness and reputation.
FRANCHISING

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This is a method of expanding a business on less capital than otherwise needed. A Franchisee pays a
franchisor for a right to operate a local business under the franchisor’s trade name. The franchisor charges the
franchisee an initial franchise fee to cover set up cost, relying on the subsequent regular payments by the
franchisee for operating profit (which will be a % of the franchisee’s turnover). The advantages are that the
capital outlay needed to expand the business is reduced substantially and the business image is improved upon
while the franchisee obtains ownership of the business for an agreed number of years and avoids some of the
mistakes of many small businesses.
MEDIUM TERM SOURCE OF FINANCE
Bank term loan: This is similar to a bank overdraft but carries a higher interest and charge and covers a
longer period. A bank loan requires a higher collateral security and is repayable after a specific period of time.
Venture capital: this is a significant early stage financing of new and young enterprises seeking to grow
rapidly. It involves management of the client’s enterprises. Venture capital refers to the commitment of
capital for the formation and setting up of small scale enterprises specializing in new ideas or new technologies
with growth potential.
FEATURES OF VENTURE CAPITAL
EQUITY PARTICIPATION: The venture capitalist participates by either direct purchase of shares, options
or convertible securities with the objective of making capital gains by selling off the investment once the
enterprise becomes profitable.
LONG TERM INVESTMENT: it is not repayable on demand and it takes 5 – 10 years before profit is made.

PARTICIPATION IN MANAGEMENT: the venture capitalist supports the entrepreneur by actively

involving in marketing, technology development, planning and management skills as a member of the board.

STAGES OF VENTURE FINANCING

Seed money for supporting a concept/ idea

EARLY STAGE FINANCING Start up capital for initial production & marketing
Research and development cost

Second stage financing for working capital and

EXPANSION FINANCING initial expansion
Development & bridge financing for facilitating
public issue

Turnaround financing of sick unit

ACQUISITION/BUY-OUT Acquisition of another firm for growth
FINANCING Management buy out financing to enable group
growth

Venture capitalist are high risk investors who require a high return which is achievable by managing the risk
return ratio in investing only in businesses that fit their investment criteria after having completed due
diligence. They look at the business location size of the investment, stage of the company, industry

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specialization, investment structure, quality and depth of management, corporate governance practices and
their exit plan.
Process of venture capital financing
• DEAL ORIGINATION: which could be through the following;
• Referral system—trade partners, industry associations and friends
• Active search---network, trade fair, conferences and seminars
• Intermediaries
• INITIAL SCREENING OF ALL PROPOSALS
• DUE DILIGENCE/ DETAILED EVALUATION of the business plan and quality of the entrepreneur
as well as the risk analysis and product characteristics. The business plan must be prepared to convince
the venture capitalist explaining the nature of the business , what it wants to achieve and how it is going
to do it . The business plan should be challenging but achievable with simple language and technical
details explained.
• DEAL STRUCTURING: this is the process of negotiation between the entrepreneur and venture
capitalist on due covenants and earn out arrangements.

Covenants refer to the right by the venture capitalist to control the company and change management if
needed and make other strategic decisions while earn out arrangement specifies the entrepreneurs equity
share and objectives to be achieved.

• POST INVESTMENT ACTIVITIES: the venture capitalist partners with the entrepreneur in running
the business through board membership
• EXIT PLAN :the venture capitalist can sell their equity share through initial public offering, acquisition
by another company, or purchase by the promoters or even outsiders

PROJECT FINANCING
This is a scheme of financing a particular economic unit in which a lender is satisfied by looking at the cash
flows and the earnings of that economic unit as a source of funds from which a loan can be repaid and the asset
of the economic unit as a collateral for the loan.

It is a source of financing in which the project, assets, contract, inherent economies and cash flows are
separated from their promoters or sponsor to permit credit appraisal and loan to the project independent of
sponsors that is the assets of the project serve as collateral for the loan while all loan repayments are made out
of project cash flow.

This is a self-liquidating facility with the following characteristics such as the financial standing of borrower is
not important, proceeds from project should be sufficient to repay the capital together with the interest and the
project financed serves as security

EQUIPMENT LEASING

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This is a financial arrangement to finance the purchase of an asset through a finance company/ leasing
company/ bank. It could be a finance lease where the risk and benefits of ownership are substantially
transferred to the lessee or operating lease where the risk and benefits remain with the lessor or a sales and
lease back where an asset previously owned by a company is disposed off and immediately repossessed
through a leasing contract

HIRE PURCHASE/ VENDOR CREDIT

This is an arrangement under which the hirer in return for the use of an asset undertakes to make periodic
payments to the owners of the asset and is assumed to be the owner after the payment of the last installment.

MORTGAGE
This is a financing means by which a company borrows money by mortgaging on the freehold property.
Insurance companies, Investment companies and pension funds are good examples of companies prepared to
lend on such basis. The principal and interest is spread over a long period of time with the interest rate in
excess of the base interest rate.

LONG TERM SOURCES OF FINANCE

1) Equity capital
2) Preference share capital
3) Debenture stock capital

EQUITY CAPITAL
The owners of this capital are the owners of the business. Shareholders have preemptive rights to anything of
value that the company may wish to distribute as well as the ultimate control of the company’s affairs. This
right could also be called subscription privilege or right as it gives existing shareholders the right to new issue
of shares before outsiders.

Shareholders bear a huge portion of the entire risks associated with the company hence they expect a higher
return than most other fund providers. The ordinary shareholders have voting power of rights attached to their
investment.

Ordinary shareholders could take the form of preferred, deferred or founders ordinary shares. Preferred usually
receive a fixed dividend before ordinary shareholders while deferred ordinary shareholders are usually residual
recipients after all claims including preferred ordinary shares have been settled. Deferred shares could be given
to the promoters of the company.
RAISING OF EQUITY CAPITAL
The methods of raising equity include
1) STOCK EXCHANGE INTRODUCTION: this is a method of getting permission to deal i.e.
introducing the shares of the company to the market. The company after quotation will have access to
finance in the capital market in the future

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2) OFFER FOR SALE: the shares are offered to the public including the existing shareholders through
the agency of an issuing house. At the end of an offer for sale the nominal share capital of the
company remains unaltered and the proceeds of the sale goes to the vendor (existing shareholders) and
not the company. This is the method used by bureau of public enterprise to sell the federal government
shares in the privatized enterprises.

3) OFFER FOR SUBSCRIPTION: the company offers fresh issue of shares through the agency of an
issuing house with the aim of raising supplementary capital for the company. The proceeds of the
issue go to the company and the number of shares outstanding at the end of the exercise will increase.
It could be an Initial public offering where it is the first sale of shares to the public or a seasoned
equity offer. I t could be called a hot issue where it is in high demand and sells at a premium over the
public offering price on the first day of trading while the illegal practice of soliciting for orders to buy
a new issue before the registration is approved by SEC is known as Gun jumping.

4) OFFER FOR SALE BY TENDER: the company offers the shares for sale at a minimum price level.
Applications are then requested at a price higher or equal to the minimum price from all investors
from which an average price based on the company’s objective is chosen. The p[rice selected is
known as the striking price.

5) PLACING OF SHARES- shares are offered to a specific group of investors usually insurance
companies, pension funds, or any other institutional investor

RIGHT ISSUES: ADVANTAGES OF RIGHT ISSUE

i) Control is maintained through the pro ratio issue of shares
ii) It involves less floatation cost
iii) It is more likely to be successful

DISADVANTAGES
i) There will be decline in wealth it issues is ignored by investors
ii) Companies whose shareholding is concentrated in the hands of financial institutions may prefer a public
issues to dilute holdings.

PREFERENCE SHARES
A preference share is considered to be a hybrid security since it as many features of both ordinary shares and
debentures. The dividend to preferences shareholders is not tax deductable and non payment of its does not
force the company to solvency and may not have a fixed maturity date just like the ordinary share while its
similarities to the debentures include that the dividend is fixed, they do not have voting rights they have claims
on income and assets prior to ordinary to ordinary shareholders and they do not share in the residual earnings.

ADVANTAGES OF PREFERENCE SHARE

Riskless leverage advantage: It provides financial leverage advantage since preference dividend is a fixed
obligation. This advantage occurs without a serious risk of default as non payment of dividend does not force
the company to liquidation.

Dividend postponability: Preference share provides some financial flexibility to the company since it can post
pone payment of dividend unlike interest.

Fixed dividend: The preference dividend payment are restricted to the stated amount i.e. no participation in
excess profits.

Limited voting rights: preference shareholders do not have voting rights except in case dividend arrears exist.

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DISADVANTAGES OF PREFERENCES SHARES

i) Non deductibility of dividends: the dividend is not tax deductible
ii) Commitment to pay dividend: Nonpayment of preference dividend may adversely affect the image of
the company, equity holders cannot be paid any dividend unless preferred shareholders are paid
dividend.

DEBT FINANCE/DEBENTURE /LOAN STOCK

Sometimes business may need long term funds but may not wish to issue equity capital either because the
company does not want to involve outside shareholders or because debt is cheaper, easily available or because
it provides tax relief on interest payments.

FACTORS INFLUENCING THE AMOUNT OF DEBT CAPITAL

i) Loan covenants – Which prohibit or restrict further debt
ii) The security – Availability of suitable tangible assets may restrict further finance
iii) Memorandum and articles of association – may restrict the level of debt which can be undertaken
iv) Cash flows- Insufficient liquidity will restrict borrowing limits
v) Future prospect- level and quality of future profits assist in the credit rating of a company
vi) Reputation of principles

Debt capital of a company may consist of either debentures or bonds which are issued to the public for
subscription or term loan which are obtained from the banks and financial institutions.

The term bonds describes various forms of long term debt a company may issue such as loan notes or
debentures which may be redeemable or irredeemable. It could be floating rate zero coupon or convertible loan
stock.

A debenture is a long term promissory note for raising loan capital where the firm promises to pay interest and
principal as stipulated. It is a long term fixed income, financial security. Debenture holders are creditors of the
firm it has the following features.

1. Interest rate is fixed and known indicating the percentage of the per value of the debenture that will be
paid annually. It is tax deductible.
2. Maturity of a debenture indicates the length of time until the company redeems the debentures. It is
usually issued for specific period of time.
3. Security – Debentures are either secured or unsecured. Credit rating of the bond shows the chances of
timely payment of interest and principal by the borrower.

AAA highest safety BBB - low safety C – substantial risk

AA high safety BB inadequate safety D in default
A adequate safety B – high risk

When an organization is seeking loan finance, lenders consider several factors concerned with the returns
receivable and the risk of default.

Purpose- growth potential, strategy and managerial ability to put the plan into effect

Amount – to ensure that it is not more than what is needed for that particular purpose. This consideration is
linked with customers’ wealth and ability to repay .

Repayment – terms of repayment are dear and borrowers will be able to obtain sufficient income to make the
necessary repayment.

Term if the loan term is appropriate and consistent with the income stream.

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Security: as for adequate collateral.

Factors to be considered by a bank in deciding whether or not to lend money

i. Character of the borrower – Past records, analyse company’s financial position, the company’s article of
association.
ii. The margin of profits : Is the profit enough to warrant the risk
iii. The purpose of the borrowing affects both the interest rate and the banks decision as the bank will
consider the legality of the project and the risk
iv. The amount of the borrowing
v. Repayment terms

ADVANTAGE OF DEBT TO THE COMPANY

2. Debt has a lower direct cost than equity because it is less risky to the investor and it is tax deductible
3. Issue cost of debt are cheaper then equity shares
4. there is no dilution of ownership

To the lender
ii. It earns the lender interest a steady stream of predictable income
iii. It provides business contact for the lender which may allow the marketing of other services.

TO THE SHAREHODER
i. Increase returns to shareholders due to its cheap cost
ii. Ownership is not diluted.

DISADVANTAGES OF DEBT FINANCE

To the company
i. Increases financial risk as well as cost of equity
ii. When much, increases the risk of bankruptcy and significant cost to avoid it
iii. The debt normally has to be repaid at the end of its term
iv. Assets of the company may be pledged as security
v. Interest rate risk borrowing at floating rate and interest rates rice.

LENDER
i. The company may default on its interest or repayment
ii. There is no extra benefit if the company does well
iii. Interest rate risk – risk of lending at fixed interest when interest rates rise

TO SHAREHOLDER
i. Presence of debt make returns more volatile (financial risk) which attracts a compensating increase in
shareholders required return
ii. Increase in bankruptcy cost it debt is high.

ISLAMIC FINANCE
Islamic Finance has the same purpose as other sources of finance except that it operates in accordance with the
principles of Islamic law (Sharia). It covers the following key principles:
a. Complete absence of Interest (riba)
b. Sharing of profits and losses

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c. Finance is limited to islamically accepted transactions; that is no investment in alcohol,

gambling, etc.
d. Money is viewed as a means of exchange and therefore interest cannot be charged on
loans
e. Engaging in speculation is not allowed.
SOURCES OF FINANCE WITHIN THE ISLAMIC BANKING MODEL
SN FINANCE TYPE DESCRIPTION
1 MURABAHA (Trade It is a form of trade credit or loan where the financial
finance) institution purchases an asset and sells it to the business at
an agreed mark up for the future payment. No interest
2 MUSHARAKA (Venture It is a relationship between two or more partners, who
capital) contribute capital to a business. Profits are shared in
proportion agreed in the contract, while losses are shared
according to capital contributions. The investment manager
and the finance provider participate in managing and
running the venture.
3 MUDARABA (equity It is a special kind of partnership where one partner gives
finance) money to another for investing in a commercial enterprise.
The investment comes from the first partner, while the
management and work is an exclusive responsibility of the
other (mudarib). Profits are shared between the partners in
the proportion agreed in the contract and losses borne by
providers of finance
4 SUKUK (debt finance) Islamic bonds are linked to an asset such that the sukuk
holder will participate in the ownership of the company
issuing the sukuk and has a right to profits but will equally
bear their share of any losses
5 IJARA

ADVANTAGES OF ISLAMIC FINANCE

Islamic finance operates by the underlying principle that there should be a link between the economic activity
that creates value and the financing of that economic activity. The main advantages are:
▪ It allows access to a source of worldwide funds as it is appealing to all companies that want to invest
ethically (muslim and non muslim alike)
▪ Gharar (uncertainty, risk of speculation) is not allowed, reducing the risk of losses.
▪ Excessive profiteering is also not allowed, only reasonable mark-ups are allowed
▪ Banks cannot use excessive leverage and are therefore less likely to collapse
▪ It encourages all parties to take a longer term view and focus on creating a successful outcome for the
venture, which should contribute to a more stable financial environment.
▪ It emphasizes on mutual interest and co-operation, with a partnership based on profit creation through
ethical and fair activity benefiting the community as a whole.
DISADVANTAGES OF ISLAMIC FINANCE
▪ There is no international consensus on sharia interpretations’ particularly with innovative financial
products which may not be acceptable in some markets
▪ There is no standard sharia model for the Islamic finance market meaning that documentation is tailor
made for the transaction leading to higher transaction cost than for the conventional finance
alternative.

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▪ Islamic finance institutions are subject to additional compliance work due to the need to comply with
normal financial laws and sharia restrictions
▪ Islamic banks cannot minimize their risk in the same way as conventional banks as hedging is
prohibited.
▪ Some Islamic products may not be compatible with International financial regulations
▪ Corporations may not be able to prove that contracts are effectively debt and they therefore may not
attract a tax shield leading to higher cost of capital.
▪ It may become complicated for companies to balance the interest of the financial institutions with
those of other stakeholders as the Islamic bank take an active role on some contracts.
▪ They are slower to react to market changes and may lack short term flexibility.

ILLUSTRATIONS ON SOURCE OF FINANCE

ILLUSTRATION 1 ON FINANCE SOURCES
A. What is Islamic finance, explain five different contracts under Islamic finance. What are the
advantages and disadvantages of Islamic Finance.
B. Interest rates depend on the term to maturity of the asset. The term structure of interest rates refers to
the way in which the yield on a security varies according to the term of the borrowing. Explain
reasons why the yield curve will normally be upward sloping. Clearly give reasons why the yield
curve might slope downwards.
C. What is yield to maturity.
D. Briefly explain venture capital, business angels, private equity and asset securitization as sources of
finance.
E. Prepare a briefing document for a board of directors discussing issues that might influence a
company’s capital structure strategy.

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FINANCE FOR SMALL AND MEDIUM SIZED ENTITIES

Small and medium sized entities can be defined as having three characteristics
a. Firms are likely to be unquoted
b. Firms are owned by a small number of individuals
c. They are micro businesses that are normally regarded as those very small businesses that act as a
medium for self-employment of the owners.
This sector accounts for between a third and a half of sales and employment in the UK. It is particularly
associated with the service sector and service niche. They are more adaptable if market conditions change.
According to a study by the US Small Business Association only two thirds of small business start-ups survive
for two years and less than half make it to four years after commencing trading.
PROBLEMS OF FINANCING SME’S
1. SME’S may not know about the sources of finance available
2. Money for investment that SME’s can obtain comes from the savings of individuals in the economy
and so would be affected by Government policy such as tax policy and interest rate policy. Tax policy
including concession given to businesses to invest and taxes on distributions (the higher the tax on
dividend mean less income for investors) and a high interest rate policy makes borrowing for SME
expensive but supply of funds is greater as higher rates give greater incentive to investors to save.
3. They face competition for funds as investors have opportunities to invest in all sizes of organization
both overseas and in government debt
4. SME’S face the problem of uncertainty as they have neither the business history nor longer track
record that larger organizations possess and so banks use credit scoring systems to control exposure.
This means that SME’s need to provide a lot of information as well as how they intend to provide
security for sums advanced
5. Terms of loan (interest rate, term, security, repayment details) will depend on risk involved and the
lender would want to monitor their investment
6. The banks will be unwilling to increase loan funding without an increase in security given or increase
in equity funding which might not be available to SME’S
7. Maturity gap arises as it is difficult for SME’s to match assets and liabilities (which makes it difficult
to obtain medium term loans)
SOURCES OF FINANCE FOR SME’s
1. OWNER FINANCING refers to finance from owners personal resources or those of family
connections . it is the initial source of finance as external funding is difficult to obtain
2. EQUITY FINANCE can be obtained through private placement of shares. It should be noted that
equity gap (difficulty in raising equity) arises if the business has few tangible assets. Surveys have
shown that the amount of equity invested by owners in a business after start up and retained earnings
are relatively low compared with other sources of finance. A major problem with obtaining equity
finance can be the inability of small firms to offer an exit route to investors who wish to sell their
stake (this can be solved by share repurchase but where is the cash or obtain a listing)
3. BUSINESS ANGEL FINANCING refers to wealthy individuals or group of individuals who invest
directly in small businesses prepared to take high risks in the hope of high returns. It is difficult to set
up and is informal in terms of a market’. It is a patient source of finance and need no detailed
information about the company. The amount available is limited and large sums may be from the
consortium of business angels.
4. VENTURE CAPITAL
5. LEASING

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6. FACTORING
CAPITAL STRUCTURE OF SMEs
There is a lack of separation between ownership and management and lack of equity finance. Owners
preference and market considerations are significant as well as the lifecycle of the firm
GOVERNMENT AID FOR SMEs
Availability of government assistance is country specific, in the UK the small firms loan guarantee scheme,
grants and enterprise capital funds.
SMALL FIRMS LOAN GUARANTEE SCHEME was introduced by the Government in 1981 with the aim
of assisting small businesses to get a loan from the bank when the banks are unwilling. This assistance would
be available, the borrower’s annual revenue must not exceed a limit and the business must be less than five
years. Under the amended scheme in 1993, the bank can lend up to $250,000 without security over personal
assets or a personal guarantee being required. However all available business assets must be used as security if
required. The government will guarantee 75% of the loan, while the borrower must pay an annual 2% premium
on the guaranteed part of the loan.
GRANTS is a sum of money given to an individual or business for a specific project or purpose which covers
only part of the total cost involved. Grants to help with business development are available from a variety of
sources such as the government , European union, regional development agencies, business link, local
authorities and some charitable organizations. These grants may be linked to business activity or a specific
industry sector or some geographical areas.
ENTERPRISE CAPITAL FUNDS (ECFs) were launched in the UK in 2005. They are designed to be
commercial funds, investing a combination of private and public money in small high growth business. It is
just a variant of small business investment company (SBIC) that has operated in USA since the 1950s which
supported fedex, apple, intel and AOL.
For investments below £500,000 most SMEs can access an informal funding network of their friends, families
and business angels. Once companies require funding above £2 million they are usually quite established,
generating revenues and therefore perceived as lower risk and are able to secure funding from institutional
investors. The gap between these two finance situations is known as the equity gap.
ECFs provide government match funding for business angels and venture capitalist to help small and medium
sized business bridge the equity gap. Each ECF will be able to make equity investments of up to £2 million
into eligible SME’s that have genuine growth potential but whose funding needs are not currently met.
FACTORS TO CONSIDER WHEN DECIDING ON THE MIX OF SHORT, MEDIUM OR LONG
TERM DEBT FINANCE FOR SMALL AND MEDIUM ENTERPRISES
1. The term of the finance that is the term should be appropriate to the asset being acquired. As a
general rule, long term assets should be financed from long term finance sources and vice versa.
2. FLEXIBILITY ; the flexibility of the source of finance should be considered as the shorter the
finance, the more flexible it would be.
3. REPAYMENT TERMS: sufficient funds should be available to meet repayment schedules laid
down in loan agreement
4. COSTS: the cost of the various terms of debt should be considered (short term or long term)
5. AVAILABILITY: refers to the ease of accessing the various forms of debt
6. EFFECT ON GEARING : the impact of the finance on the gearing ratio of the organization
PRACTICAL FACTORS THAT RESTRICT AMOUNT OF DEBT THAT CAN BE RAISED

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1. Previous record of the company

2. Restrictions in memorandum and articles
3. Restrictions of current borrowing
4. Uncertainty over project
5. Security or insufficient assets to provide the necessary security

ILLUSTRATION ON FINANCE FOR SMALL AND MEDIUM SIZED

ENTITIES

ILLUSTRATION 1 (MAY 2017 ICAN PAST QUESTION)

LL Plc is a large engineering company. Its ordinary shares are quoted on the stock exchange. LL plc’s
board is concerned that the company’s gearing level is too high and that this is having a detrimental impact
on its market capitalization. As a result, the board is considering a restructuring of LL plc long term funds,
details of which are shown here as at 28 February, 2017.
Total par value ₦m Market value
Ordinary share capital (50k) 67.5 N2.65/share ex div
7% preference share capital (N1) 60.0 N1.44/share ex div
4% redeemable debentures (N100) 45.0 N90% ex-int
The debentures are redeemable in 2022. LL plc’s earnings for the year to28 February 2017 were N32.4
million and are expected to remain at this level for the forseeable future. Retained earnings, as at 28
February 2017 was N73.2 million.
The board is considering a 1 for 9 rights issue of ordinary shares and this additional funding would be used
to redeem 60% of LL plc’s redeemable debentures at par. However some of LL plc’s directors are
concerned that this issue of extra ordinary shares will cause the company’s ordinary share price and its
earnings per share to fall by an excessive amount, to the detriment of LL plc’s shareholders. Accordingly,
they are arguing that the rights issue should be designed so that the EPS is not diluted by more than 5%.
The Directors wish to assume that the income tax rate will be 21% for the forseeable future and the tax
will be payable in the same year as the cash flows to which it relates.
Required
1. Calculate LL plc’s gearing ratio using both book and market values (5 marks)
2. Discuss with reference to relevant theories, why LL plc’s board might have concerns over the
level of gearing and its impact on LL plc’s market capitalization (6 marks)
3. Assuming that a 1 for 9 rights issue goes ahead, calculate the theoretical ex rights price of LL
plc’s ordinary share and the value of a right (3 marks)
4. Discuss the Directors’ view that the rights issue will cause the share price and the EPS to fall by
an excessive amount to the detriment of LL plc’s ordinary shareholders. Your discussion should
be supported by relevant calculations.
ILLUSTRATION 2 ON SOURCE OF FINANCE
T plc is a medium sized manufacturing company which is considering a 1 for 5 rights issue at 15%
discount to the current market price of N4 per share. Issue costs are expected to be N220,000 and these
costs will be paid out of the funds raised. It is proposed that the rights issue fund raised will be used to
redeem some of the existing debentures at par. Financial information relating to the company is as follows;
STATEMENT OF FINANCIAL POSITION

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N’000 N’000 N’000

Non –current Assets 6,550
Current Assets
Inventory 2,000
Receivables 1,500
Cash 300 3,800
10,350
EQUITY AND LIABILITIES
Ordinary shares (par value 50k) 2,000
Reserves 1,500
Shareholders fund 3,500
12% debentures 2015 4,500

Current Liabilities
Trade creditors 1,100
Overdraft 1,250 2,350
Net assets 10,350
Other information include
Price earnings ratio of T PLC 15.24
OVERDRAFT INTEREST RATE 7%
INCOME TAX RATE 30%
SECTOR AVERAGES; Debt equity ratio (book value) 100%
Interest cover 6 times
Required
a. Ignoring issue cost and any use that may be made of the funds raised by the right issue; calculate:
I. The theoretical ex-rights price per share
II. The value of rights per existing per share
b. What alternative actions are open to the owner of 1,000 shares in T plc as regards the rights issue.
Determine the effect of these actions on the wealth of the investor
c. Calculate the current earnings per share and the revised earnings per share if the rights issue funds are
used to redeem some of the existing debentures
d. Evaluate whether the proposal to redeem some of the debentures would increase the wealth of the
shareholders of T plc. Assume that the price earnings ratio of T plc remains constant.
e. Discuss the reasons why a rights issue could be an attractive source of finance for T plc. Your
discussion should include an evaluation of the effect of the rights issue on the debt equity ratio and
interest cover.
ILLUSTRATION 3
Flour Mills Limited is an all equity financed company with 10 million issued shares, the current share price
being N2.80. it is considering a major expansion which will require N6 million of new finance and it has
decided to use 1 for 4 rights issue to raise money. The project is expected to yield a net return of N700,000 in
one year time. An annual growth rate of 5% is expected in the return of the new project. The details of the
above project is not yet known in the capital market but will become known before the shares commence
trading ex-rights. Current dividend per share is 42 kobo.
Required
a. Calculate
I. The share price immediately prior to them be traded ex rights (cum rights price)

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II. The ex-rights price assuming no other information will affect the company except the
expansion
III. The price of the rights per share or in total
b. Show that an investor holding 10, 000 shares in Flour Mills Limited would be indifferent to the choice
between taking up the rights and selling the rights.
c. How many rights should be sold by the investor in ‘b’ above, in order that he does not have to spend
or take any receipt of any cash balance of the rights issue?
d. Enumerate the circumstances in which it would be beneficial for shareholders to take up their rights
rather than sell their options in whole or in part.
e. What factors in practice determine the ex-rights price
f. Discuss the advantages and disadvantages of raising additional equity finance by means of a rights
issue rather than by a new public issue of shares.
g. Describe the various types of cost to be incurred by Flour mills in making its rights issue.

ILLUSTRATION 4
The Directors of Big Mouth Limited are considering whether to undertake a major expansion which would
involve an immediate outlay of N1.5m and which the directors would expect to generate additional
earnings available for dividend of N153,000 after one year.
The additional earnings would be expected to grow thereafter at a compound annual rate of 4% and to
continue indefinitely. Details of the expansion have not yet been made public.
The company is financed entirely by equity capital. It has issued a 5 million N1 ordinary shares each of
which has a current market value of N2.26 cum div. The company is due to pay an annual dividend of 14k
per share within the next few days. Many years, the company’s annual dividend has increased at a
compound annual rate of 6% and this rate of increase is generally expected to continue. The rate of growth
of the existing total dividend would not be affected by the expansion been considered. The directors are
considering two ways of financing the possible expansion.
1. A rights issue of one new share for every five held at a price of N1.50 per share
2. A public issue of ordinary shares
In either case, the new shares would rank for dividend one year after issue. One of the directors has
suggested that the company should raise only N1 million of the finance required by an issue of new shares,
the remaining N500,000 being provided by a reduction in the current dividend. Assume that if the
expansion were undertaken, the directors expectations would be communicated to and believed by the
stock market and that the market would perceive the risk of the company to be unaltered
a. Prepare calculations showing whether the expansion is worthwhile
b. Estimate the new ex div market price per ordinary shares, if the expansion is undertaken and financed
by the proposed rights issue
c. Calculate the number of new shares to be issued and the price at which they should be issued, if a
public issue is made and if the total benefit from the expansion is to go to existing shareholders
d. Demonstrate that the total benefit from the expansion goes to existing shareholders under each of the
two financing options.
ILLUSTRATION 6 ON TENDER ISSUE
1) Differentiate between offer for sale and offer by subscription issue of shares
b) AZ ltd is offering 800 million shares to the public through an offer for sale by tender. Issue cost is
expected to be 10 million. The company intends to use the proceeds to finance its expansion into Ghana.
Collation of application received shows the following

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Tender price per share (N) Share (Qty) applied for

5.00 500million
6.00 300million
7.00 200million
8.00 120million
9.00 60million
10.00 50million

Required
i. Briefly describe an offer for sale by tender stating any advantage or disadvantage associated with it
ii. How many shares will need to be issued to raise the maximum amount possible?
iii. How much will be raised if the company issues exactly 800 million shares
iv. How much shares will be issued and how much will be refunded to a shareholder that had applied for
300,000 shares at N9.00 and who has paid N2.7 million. If the company intend to raise the maximum
funds possible
v. Would your answer in “IV” above different if the company intend to issue exactly 800 million shares?
vi. Using the pecking order theory concept briefly why the price of a share will fall after announcement
of new issue of shares.

282
RELEVANT APPROACH TO PORTFOLIO THEORY

This topic review looks at Markowitz portfolio theory and optimal portfolio choice. It
tries to help us understand the relationship between portfolio risk and correlation
between the investments in keeping a portfolio. It also discusses the concepts of
diversification, correlation, indifference curves, expected return and the efficient
frontier.

Modern Portfolio Theory {MPT} or Mean Variance Analysis is the mathematical

framework for assembling a portion of assets such that the expected return is
maximized for a given level of risk. it is a formalization and extension of diversification
in investing, the idea that owning different kinds of financial assets is less risky than
owning only one type.

Its key insight is that an asset’s risk and return should not be assessed by itself, but
by how they contribute to portfolio’s overall risk and return. It uses the variance of
asset prices as a proxy of risk.

A Return is a reward that investors expect for providing funds and keeping those funds
invested, plus a return for the compensation for risk. As a basic rule, an investor will expect a
higher return when the investment risk is higher.

Investment risk refers to the risk associated with investing funds in shares or bonds. The
risks associated with bonds are the fact that the bond issuer may default in paying the
interests on the bonds or the principal at maturity; or there may be a change in the market
rates of interest which may affect the bond value negatively.

The risks associated with equity shares are the fact that the company might go into
liquidation or the company profits might fluctuate and the dividends too. The investment risk
when a company invests in a new project is the risk that actual returns from the investment
will be different from the expected return. Some types of investment are riskier than others,
because of the nature of the industry and markets. When business risk is higher, returns are
less predictable or more volatile, and the expected returns should be higher to compensate
for the higher business risk.

Risk can be measured statistically either from an analysis of historical returns achieved in
the past, or from probability estimates of returns in the future. The volatility is measured as
either the variance or standard deviation of expected returns.

GRACE MAKES THE DIFFERENCE 1

RELEVANT APPROACH TO PORTFOLIO THEORY

An investor can reduce the investment risk (volatility of expected returns) by diversifying
his investments and holding a portfolio of different investments. A portfolio of different
investments can reduce the variation of returns from the total portfolio, because if some
investments provide a lower-than-expected return, others will provide a higher-than-expected
return. The unsystematic and company related risk can be reduced by diversification into
various securities and assets whose variability is different and offsetting or put in different
words which are negatively correlated or not correlated at all.

Markowitz postulated that diversification should not only aim at reducing the risk of a security
by reducing its variability or standard deviation, but by reducing the covariance or interactive
risk of two or more securities in a portfolio. The theory of portfolio diversification attaches
importance to standard deviation, to reduce it to zero, if possible, covariance to have as much
as possible negative interactive effect among the securities within the portfolio and coefficient
of correlation to have -1 {negative} so that the overall risk of the portfolio as a whole is nil or
negligible.

Similarly, a company could reduce the investment risk in its business by diversifying, and
building a portfolio of different investments. There is an argument that there is no reason
for a company to diversify its investments, because an investor can achieve all the
diversification, he requires by selecting a diversified portfolio of equity investments.

An investment portfolio consisting of all stock market securities excluding risk free securities
weighted according to the total market value of each security is called the market portfolio.

Risk aversion refers to the fact that individuals prefer less risk to more risk for a given level
of expected returns and will only accept a riskier investment if they are compensated in the
form of greater expected return. The fact that individuals buy some sort of insurance, whether
auto, health or homeowners indicates that they are generally risk averse.

PORTFOLIO THEORY is concerned with how investors should build a portfolio of

investments that gives them a suitable balance between return and investment risk. It gives
a theoretical basis for CAPM.

GENERAL ASSUMPTIONS OF PORTFOLIO THEORY

1. Investors are rational and behave in a manner that will maximise their utility.
2. Investors have free access to fair and correct information on returns and risk.
3. The markets are efficient and absorb information quickly and perfectly.

GRACE MAKES THE DIFFERENCE 2

RELEVANT APPROACH TO PORTFOLIO THEORY

4. Investors are risk averse and try to minimize their risk while maximizing return
5. Investors base decisions on expected returns and variance or standard deviation of
these returns from the mean.
6. Investors choose higher returns to lower returns for a given level of risk

EXPECTED RETURN, VARIANCE AND STANDARD DEVIATION ON SINGLE

INVESTMENT

Expected return is the average return expected on an investment or portfolio based on the
returns for the security in each state and the probability of their outcomes.

The variance and standard deviation of returns are common measures of investment risk
which determine the variability of a distribution of returns about its mean or expected value.
Variance is calculated as the sum of probability (actual return – expected return)2 = P(r
- ṝ)2 while standard deviation is the square root of variance.

CALCULATION OF EXPECTED RETURN FROM A SINGLE INVESTMENT

From the table below, compute the expected return, variance and standard deviation.

STATE PROBABILITY EXPECTED RETURN

EXPANSION 0.25 5%
NORMAL 0.50 15%
RECESSION 0.25 25%

SOLUTION

STATE PROBABILITY RETURN % Expected return % P (R – Er)2

EXPANSION 0.25 5 1.25 0.25{5 – 15}2 = 25
NORMAL 0.50 15 7.5 0.50{15 – 15}2 = 0
RECESSION 0.25 25 6.25 0.25{25 – 15}2 = 25
15 Variance = 50%
Standard deviation = Ꝩvariance = Ꝩ50 = 7.07%

Expected return is return multiplied by probability.

PORTFOLIO THEORY

Portfolio theory is concerned with how investors should build a portfolio of investments that
give them a suitable balance between return and investment risk. Portfolio theory provides a
GRACE MAKES THE DIFFERENCE 3
RELEVANT APPROACH TO PORTFOLIO THEORY

theoretical basis for the capital asset pricing model, which is an important model in financial
management.

PORTFOLIO RETURN: TWO ASSET PORTFOLIOS {Portfolio with two investments}

The return of a portfolio is equal to the weighted average of the returns of individuals assets
(or securities) in the portfolio with weights being equal to the proportion of investment value
in each asset.

The expected rate of return on a portfolio or portfolio return is the weighted average of the
expected rates of return on assets in the portfolio.

Return on a portfolio = (WA x RA) + (WB X RB)

WA is the proportion or percentage of total portfolio value invested in security A =

amount invested in A / Total investment or portfolio value

WB is the proportion or percentage of total portfolio value invested in security B =

amount invested in B / Total investment or portfolio value

RA and RB represent expected return on amount invested in A and B respectively.

The weight is based on value and not quantity.

In a 2 Asset portfolio, WA + WB = 100% which is WA + WB = 1. This becomes relevant

where the weights in a scenario are unknown for both securities.

ILLUSTRATION 2 ON EXPECTED RETURN ON A PORTFOLIO

An investor holds the following portfolio which is invested in three stocks: Total, GTB and
MTN.

SECURITY NUMBER OF SHARE PRICE EXPECTED

SHARES RETURN
TOTAL 15,000 ₦20 8%
GTB 10,000 ₦30 10%
MTN 40,000 ₦10 12%
Calculate the expected return on this portfolio.

SOLUTION

Rp = (WA RA) + (WBRB) + (WCRC)

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RELEVANT APPROACH TO PORTFOLIO THEORY

Rp = (0.30 x 8) + (0.30 x 10) + (0.40 x 12) = 10.2%

SECURITY NUMBER OF SHARE PRICE VALUE WEIGHT

SHARES
TOTAL 15,000 ₦20 300,000 0.30
GTB 10,000 ₦30 300,000 0.30
MTN 40,000 ₦10 400,000 0.40
1,000,000

ILLUSTRATION 3

An investor requires 25% return from his portfolio of 2 investments. If the return from the first
investment is 30% and the second investment is 20%. How much from the available finance
of N100,000 should be invested in each investment.

SOLUTION

Let A represent first investment and B represent second investment

WA + WB = 1

WA = 1 - WB

Rp = {WARA} + {WBRB}

25 = {WA X 30} + {WB X 20}

25 = 30{1 – WB) + 20WB

25 = 30 – 30WB + 20WB

30WB – 20WB = 30 – 25

10WB = 5

WB = 5/10 = 50%

WA = 1 – 0.50 = 0.50 = 50%

This implies 50% should be invested in both securities.

ILLUSTRATION 4

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RELEVANT APPROACH TO PORTFOLIO THEORY

ABC plc has 3 investments in its portfolio {A, B & C} with 15%, 25% and 30% returns
respectively. The board has decided that 20% of its total investment would be on Agricultural
companies of which company B falls under.

Required

a. Advise the company on how the portfolio should be constructed so as to get a total return
of 20% from the portfolio.

b. Would the answer above be different if the return expected from the portfolio was 13%;
explain your answer.

SOLUTION

RP = {WARA} + {WBRB} + {WCRC}

WA + WB + WC = 1

WA + WC = 1 – 0.20

WA + WC = 0.80

WA = 0.80 – WC

RP = {WARA} + {WBRB} + {WCRC}

20 = (0.80 – WC)15 + {0.20 X 25} + {WC X 30}

20 = 12 – 15WC + 5 + 30WC

20 -12 – 5 = -15WC + 30WC

3 = 15WC

WC = 3/15 = 0.20

WA = 0.80 – 0.20 = 0.60

60% IN A, 20% in B and 20% in C

B PART OF THE ILLUSTRATION

RP = {WARA} + {WBRB} + {WCRC}

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RELEVANT APPROACH TO PORTFOLIO THEORY

13 = (0.80 – WC)15 + {0.20 X 25} + {WC X 30}

13 = 12 – 15WC + 5 + 30WC

13 -12 – 5 = -15WC + 30WC

-4 = 15WC

WC = -4/15 = - 0.27

WA = 0.80 – (- 0.27) = 1.07

107% IN A, 20% in B and -27% in C

This means that an investor can short sell C by 27%.

COVARIANCE AND CORRELATION COEFFICIENT

Covariance = correlation coefficient x standard deviation of X x standard deviation

of Y

Correlation coefficient = covariance / standard deviation of X x standard deviation of

Y

There are two important statistical measures used to describe the association between two
variables. They are Covariance and Correlation coefficient. The portfolio variance or standard
deviation {Risk} depends on the co-movement of returns on two assets. {Covariance
measures the co-movement of returns on two or more assets.

Covariance measures the extent to which two variables move together over time. A positive
covariance means that the variables tend to move together in same direction. Negative
covariance means that the two variables tend to move in opposite directions while a
covariance of zero means that there is no linear relationship between the two variables. A
covariance of zero between two assets implies that knowing the return for the next period on
one of the assets tells you nothing about the return of the other asset for the period.

STEPS IN CALCULATING CO-VARIANCE

▪ Determining the expected returns on assets or investments

▪ Determine the deviation of possible returns from the expected returns for each asset.

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RELEVANT APPROACH TO PORTFOLIO THEORY

▪ Determining the sum of the product of each deviation of returns of two assets and
respective probability.

COVAB = sum of P{RA – ERA}{RB - ERB) where

P is probability; RA & RB refer to returns on A and B: ERA & ERB represent expected
return value (mean) on A and B.

The magnitude of the covariance depends on the magnitude of the individual stock’s
standard deviations and the relationship between their co-movements. The covariance
is an absolute measure and is measured in return units squared. Covariance can be
standardized by dividing by the product of the standard deviation of the securities being
computed.

CORRELATION COEFFICIENT

Correlation is a measure of the linear relationship between two variables. The correlation
coefficient ranges between -1.0 to +1.0. A correlation coefficient of +1.0 implies a perfectly
positive correlation while a correlation coefficient of -1.0 indicates a perfectly negative
correlation.

This standardized measure of CO-movement is called Correlation and is computed as :

CovAB / σA X σB where σA & σB represents the standard deviation of A and B. The
correlation coefficient has no units . it is a pure measure of the co-movement of two stock
returns and is bounded by -1 and +1.

• A correlation coefficient of +1 means that returns always change proportionally in the

same direction. They are perfectly positively correlated.
• A correlation coefficient of -1 means that the returns always move proportionally in the
opposite direction. They are perfectly negatively correlated.
• A correlation coefficient of zero means that there is no linear relationship between the
two stock returns. They are uncorrelated.

As the correlation between the two assets decreases, the benefits of diversification increase
because the separate movements of each stock serve to reduce the volatility of the portfolio.

Correlation coefficient is calculated as {Where the two securities are X and Y}

When there is no probability; n∑xy - ∑x∑y / √{∑𝒙2 – [∑x]2}{∑𝒚2 – [∑y]2}

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RELEVANT APPROACH TO PORTFOLIO THEORY

Where there is probability: n∑pxy - ∑px∑py / √{∑𝒑𝒙2 – [∑px]2}{∑𝒑𝒚2 – [∑py]2}

PORTFOLIO RISK: TWO ASSET PORTFOLIO

Portfolio risk depends on the correlation between the securities as the standards deviation of
portfolio X and Y is considerably lower than the weighted standard deviation of these
individual securities due to the diversification effect. This shows that investing wealth in more
than one security reduces portfolio risk. However, the extents of the benefits of portfolio
diversification depend on the correlation between returns on securities.

The portfolio variance or standard deviation depends on the co-movement of returns on two
assets is measured by the co-variance of returns.

To calculate co-variance

i) Determine the expected return on assets

ii) Determine the deviation of possible returns from the expected return for each
asset.
iii) Determine the sum of product of each deviation of returns of two assets and
respective probability.
Covariance XY = Standard deviation X x Standard Deviation Y x Correlation XY

COV XY = x y CORxy

Correlation is a measure of the linear relationship between two variables.

Correlation X, Y= Covariance XY = COV xy

Standard deviation of X} x {standard deviation y } x y

The value of correlation is called the correlation co-efficient which would be positive, negative
or zero/neutral and ranges between -1.0 and + 1.0

(A x WA) 2 + (B X WB) 2 + 2WA WB COV AB

P =

A 2 WxA2 + B 2 WB2 + 2WA WB A B COr AB

P =

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RELEVANT APPROACH TO PORTFOLIO THEORY

A = Standard deviation of the returns from investment A

B = Standard deviation of the returns from investment B
WA = Proportion of investment A in the portfolio
WB = Proportion of investment B in the portfolio
CorAB = Correlation between A and B
COVAB = Covariance between A and B

When correlation is +1.0, the risk is σp = σAwA + σBWB. There is no advantages of

diversification when the returns of securities have perfect positive correlation.
Where correlation is -1.0, the portfolio risk is given by σp = σAWA - σBWB

MINIMUM VARIANCE PORTFOLIO

It is the best combination of two securities so that the portfolio variance is minimum. It is
also called optimum portfolio. The weights can be calculated using the formula below:

Weight of A = σ2B – CovAB / σ2A + σ2B – 2COVAB

ILLUSTRATION 5

Calculate from the data below,

▪ The variance and standard deviation of returns on the two securities

▪ The covariance of returns on those securities
▪ The correlation coefficient of the returns from the securities from the covariance
▪ The correlation coefficient from the raw data

SEASON PROBABILITY Return from Security A Return from security B

Summer 0.3 25% 28%
Winter 0.5 22% 18%
Spring 0.2 12% 15%
SOLUTION

SECURITY A

RETURN PROB ER R – ER = DEV A P {R – ER}2

25 0.3 7.5 4.1 0.3 (4.1)2 = 6.08
22 0.5 11 1.1 0.5(1.1}2 = 1.13
12 0.2 2.4 -8.9 0.2(-8.9}2 = 15.84
20.9 Variance = 23.05

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RELEVANT APPROACH TO PORTFOLIO THEORY

Standard deviation = Ꝩ23.05 = 4.8%

SECURITY B

RETURN PROB ER R – ER; DEV B P {R – ER}2

28 0.3 8.4 28 – 20.4 = 7.6 0.3 {7.6}2 = 17.33
18 0.5 9.0 18 – 20.4 = - 2.4 0.5 {-2.4}2 = 2.88
15 0.2 3.0 15 – 20.4 = -5.4 0.2 {-5.4}2 = 5.83
20.4 Variance = 26.04
Standard deviation = Ꝩ26.04 = 5.1%

CO-VARIANCE

DEV A DEV B PROB COVARIANCE = P X DEV A X DEV B

4.1 7.6 0.3 9.35
1.1 - 2.4 0.5 -1.32
-8.9 -5.4 0.2 9.61
17.64

COVARIANCE = CORRAB X σA x σB

CORRAB = Covariance / σA x σB

CORRAB = 17.64 / 4.8 x 5.1 = 0.721

CORRELATION COEFFICIENT FROM THE RAW DATA

Where there is probability: ∑pAB - ∑pA∑pB / √{∑𝒑𝑨2 – [∑pA]2}{∑𝒑𝑩2 – [∑pB]2}

{ 444} – {20.9 X 20.4}

Ꝩ{458.3 – (20.9)2} X {442.2 – (20.4)2}

= 444 – 426.36 /Ꝩ21.49 X 26.04 = 17.64 / Ꝩ559.6 = 17.64 /23.66 = 0.746

P A PA A2 PA2 B PB B2 PB2 PAB

0.30 25 7.5 625 187.5 28 8.4 784 235.2 210
0.50 22 11.0 484 242 18 9.0 324 162 198
0.20 12 2.4 144 28.8 15 3.0 225 45 36

20.9 458.3 20.4 442.2 444

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RELEVANT APPROACH TO PORTFOLIO THEORY

ILLUSTRATION 6 ON PORTFOLIO AND CAPM

The management of YOU plc is evaluating two projects whose returns depend on the future
state of the economy as shown below:

Probability IRR of project A IRR of project B

30% 27% 35%
40% 18% 15%
30% 5% 20%
a. Explain how a portfolio should be constructed to produce an expected return of 20%
b. Calculate the correlation between project A and Project B and assess the risk of the
portfolio in (a) above
c. Calculate the minimum risk portfolio of the portfolio in (a) above and the expected
return and risk of the resulting portfolio
d. Briefly discuss the key limitations of portfolio theory in the analysis of physical
investment decisions in practice

SOLUTION

RETURN OF PROB ER R – ERA RETURN OF ER R-ERB

A B
27 0.30 8.1 10.2 35 10.5 12.5
18 0.40 7.2 1.2 15 6 -7.5
5 0.30 1.5 -11.8 20 6 -2.5
16.8 22.5
RP = WARA + WBRB

WA + WB = 1;;;;; WA = 1 – WB

20 = (1 – WB)16.8 + {WB X 22.5}

20 = 16.8 – 16.8WB + 22.5WB

20 – 16.8 = 22.5WB – 16.8WB

3.2 = 5.2WB

WB = 3.2 / 5.2 = 0.62 = 62%

WA = 1 – 0.62 = 0.38 = 38%

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RELEVANT APPROACH TO PORTFOLIO THEORY

COVARIANCE

Correlation = covariance / σA x σB = 43.5 / 8.57 x 8.44 = +0.6

PROB DEV A DEV B COV VAR A = P(R – ER)2 VAR B = P(R – ER)2
0.30 10.2 12.5 38.25 0.30 {10.2}2 =31.1 0.30 {12.5}2 =46.88
0.40 1.2 -7.5 -3.6 0.40 {1.2}2 = 0.58 0.40 {-7.5}2 = 22.5
0.30 -11.8 -2.5 8.85 0.30{-11.8}2 = 41.77 0.30{-2.5}2 = 1.88

43.5 Variance = 73.45 Variance = 71.26

Standard dev = 8.57 Standard dev = 8.44

σp = Ꝩ(WAσA)2 + (WBσB)2 + 2WAWBCOVAB

σp = Ꝩ( 0.38 X 8.57)2 + (0.62 X 8.44)2 X {2 X 0.38 X 0.62 X 43.5} = Ꝩ10.61 + 27.38 +

20.50 = 7.65%

MINIMUM PORTFOLIO = Weight of A = σB2 – CovAB / σA2 + σB2 – 2COVAB

WA = 8.442 – 43.5 / 8.572 + 8.442 - (2 x 43.5)
WA = 27.73 / 57.68 = 0.48 = 48%
WB = 1 – 0.48 = 0.52 = 52%

ILLUSTRATION 7

You are considering investing in either or both GTB and Zenith shares and you are given
the following information:

SECURITY POSSIBLE RATES OF PROBABILITY OF

RETURN OCCURRENCE
GTB 30% 0.3
25% 0.4
20% 0.3
ZENITH 50% 0.6
40% 0.4
I. Calculate the expected return for each security separately and for a portfolio
comprising 60% GTB and 40% zenith shares assuming positive correlation between
both securities
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RELEVANT APPROACH TO PORTFOLIO THEORY

II. Calculate the expected risk of each security separately and of the portfolio as defined
above (risk is measured by the standard deviation)
III. Outline the objectives of portfolio diversification and explain in general terms why the
risk on individual securities may differ from that of portfolio as a whole

SOLUTION
In a question of this nature, sort the individual investments first before dealing with the
portfolio.
GTB
R PROB ER P{R – ER}2
30 0.30 9.0 0.30{30 – 25}2 = 7.5
25 0.40 10.0 0.40{25 – 25}2 = 0
20 0.30 6.0 0.30{20 – 25}2 = 7.5
25 15
Return is 25% and Standard deviation = Ꝩ15 = 3.87%

ZENITH
R PROB ER P{R – ER}2
50 0.60 30 0.60{50 – 46}2 = 9.6
40 0.40 16 0.40{40 – 46}2 = 14.4

46 24
Return is 46% and Standard deviation = Ꝩ24= 4.9%
RETURN ON A PORTFOLIO
RP = WARA + WBRB Where A is GTB and B is Zenith
RP = (0.60 x 25) + (0.40 x 46) = 33.4%

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RELEVANT APPROACH TO PORTFOLIO THEORY

SECURITY POSSIBLE RATES OF PROBABILITY OF

RETURN OCCURRENCE
GTB 30% 0.3
25% 0.4
20% 0.3
ZENITH 50% 0.6
40% 0.4

RISK OF PORTFOLIO
Whenever the probabilities are different, the risk on the portfolio should be calculated as the
standard deviation of the portfolio considering the various alternative combination and joint
probability. 60% OF A AND 40% OF B
RA RB RP = WARA + WBRB JOINT PROB Expected return = P(R – ER)2
prob x return
30 50 (0.60 X 30) + (0.40 X 0.3 X 0.6 = 6.84 0.18{38 – 33.4}2
50) = 38 0.18 =3.81
30 40 (0.60 X 30) + (0.40 X 0.3 X 0.4 = 4.08 0.12{34 – 33.4}2
40) = 34 0.12 = 0.04
25 50 (0.60 X 25) + (0.40 X 0.4 X 0.6 = 8.4 0.24{35 – 33.4}2
50) = 35 0.24 = 0.61
25 40 (0.60 X 25) + (0.40 X 0.4 X 0.4 = 4.96 0.16{31 – 33.4}2
40) = 31 0.16 = 0.92
20 50 (0.60 X 20) + (0.40 X 0.3 X 0.6 = 5.76 0.18{32 – 33.4}2
50) = 32 0.18 = 0.35
20 40 (0.60 X 20) + (0.40 X 0.3 X 0.4 = 3.36 0.12{28 – 33.4}2
40) = 28 0.12 = 3.5

33.4 9.23
Return on portfolio is 33.4% and the Standard deviation = Ꝩ9.23 = 3.04%

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RELEVANT APPROACH TO PORTFOLIO THEORY

SYSTEMATIC AND UNSYSTEMATIC RISK

Unsystematic risk arises from the unique uncertainties of individual securities. It is also called
unique risk.

Unsystematic risk is a risk unique to individual investments or securities, which can be

eliminated through diversification while Systematic (or Market) risk is a risk that cannot be
diversified because it affects the market as a whole, and all investments in the market in the
same way.

Examples of unsystematic risk includes ; strike declared by the company workers, a

formidable competitor enters the market, a company loses a big contract in a bid, the
government increases custom duty on the material used by the company, company’s
inability to obtain adequate quantity of raw material and others

When you diversify across assets that are not perfectly correlated, the portfolio’s risk is less
than the weighted sum of the risks of the individual securities in the portfolio. The risk that
disappears in the portfolio construction process is called the asset’s unsystematic risk (also
called unique, diversifiable or firm specific risk).

The risk that is left, cannot be diversified away, since there is nothing left to add to the
portfolio. The risk that remains is called the systematic risk (non-diversifiable risk or market
risk)

Systematic risk arises on account of the economy-wide uncertainties and the tendency of
individual securities to move together with changes in the market. It is also known as market
risk.

Examples of systematic risk include government changes the interest rate policy, the
government resorts to massive deficit financing, the inflation rate increases,
government relaxes the foreign exchange controls, government reduces capital gains
tax.

TOTAL RISK

Total Risk of an individual security is the variance or standard deviation of its return. It consists
of two parts ; systematic risk and unsystematic risk. Total risk is not relevant for an investor
who holds a diversified portfolio.

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RELEVANT APPROACH TO PORTFOLIO THEORY

IMPLICATION OF SYSTEMATIC AND UNSYSTEMATIC RISK

▪ Investors expect a return on investment that is higher than the risk free rate of return
unless they invest 100% in risk-free investments.
▪ The higher expected return is to compensate investors for the higher investment risk
▪ By diversifying in a wide range of different securities, investors can eliminate
unsystematic risk as good performing and bad performing investments will cancel one
another.
▪ In a well-diversified portfolio, the unsystematic risk is therefore zero. Investors should
therefore not require any additional return to compensate them for unsystematic risk.
▪ The only risk for which investors should want a higher return is systematic risk. This is
a risk that the market as a whole may not perform as expected.
▪ Firms that are very responsive to market or systematic changes such as luxury goods
producers are said to have high systematic risk while firms with little response to
market changes such as utility companies are said to have low systematic risk.
▪ Total risk (measured by standard deviation) can be broken down into its component
parts: unsystematic risk and systematic risk.
▪ Systematic risk is represented with beta factor while unsystematic risk is represented
with alpha value.

ILLUSTRATION 8 (ICAN NOVEMBER 2017 QUESTION 7)

a. In the context of the selection and holding of investments, discuss each of the following
scenarios:
I. An investor holding only one security needs to be concerned with unsystematic
risk of that security (3 marks)
II. However, an investor who holds a number of securities should take account of total
risk (3 marks)
III. An investor should never add to a portfolio, investment that yields a return less
than the market rate of return (3 marks)
b. The equity beta of KT plc is 1.2 and the alpha is 1.4. explain the meaning and
significance of these values to the company
(6 marks)

(Total 15 marks)

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ASSUMPTIONS OF CAPITAL MARKET THEORY

1. Investors can borrow or lend any amount at the risk-free rate

2. Investors have similar expectations on the risk/return distribution from company
securities
3. All investors have the same one period time horizon.
4. All investments are infinitely indivisible
5. There are no taxes or transaction costs
6. There is no inflation, and interest rates do not change
7. The capital markets are in equilibrium

EFFICIENT PORTFOLIO AND EFFICIENT FRONTIER

Where portfolios have different return and different risks, an Efficient portfolio is one
that has the highest return AND the lowest risk

Efficient frontier is a curve that shows returns on all efficient portfolios.

Market portfolio is a portfolio of all risky investments traded in the stock market {except
risk free securities} and is located where the indifference curve meets the efficient
frontier.

A portfolio is considered to be efficient if no other portfolio offers a higher expected return with
the same or lower risk or if no other portfolio offers lower risk with the same or higher return.
In simple terms an efficient portfolio is one that gives the highest return at a given level
of risk or the lowest risk at a given level of return.

A graph of returns and risks of all possible portfolios with different proportion of the assets are
represented as an area. The top boundary of the area (where portfolios are mean variance
efficient that is maximum return and minimum risk) is known as the efficient frontier.

The Efficient frontier represents the set of portfolios that will give you the highest
return at each level of risk (or alternatively, the lowest risk for each level of return).

Indifference curves refer to all curves on the Return-Risk graph where all combinations of risk
and expected return are all preferred by investors.(higher expected return and less risk).
Rational investors will select a portfolio for investment that lies on an indifference curve as far
to the left hand side as possible.

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The optimal or market portfolio is the portfolio that is most preferred of the possible
portfolios and is located at the point where the investor’s highest indifference curve is tangent
to the efficient frontier (that is the point where an indifference curve is as far to the left as
possible touches the efficient frontier)

The market portfolio is a portfolio of all investments traded on the stock market, in quantities
that reflect their relative overall market value but excluding risk free investments. It is a
portfolio consisting of every risky asset and so is completely diversified.

CAPITAL MARKET LINE (CML)

CML is a graphical representation of all the portfolios that optimally or efficiently combine risk
and return. It is a theoretical concept that gives optimal combinations of a risk-free asset and
the market portfolio. It is superior to the efficient frontier in the sense that it combines the risky
assets with the risk-free assets.

Capital market Line is a straight line graph that shows the risk and returns of different
proportions of investment in a risk free asset and an asset with risk (the market portfolio).
CML can also be defined as a line that joins the risk-free asset and the market portfolio
showing all combinations of risk free investments and market portfolio investments that
investors may select.

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RELEVANT APPROACH TO PORTFOLIO THEORY

Risk-free asset or security is a security with zero variance or standard deviation with no risk
of default. The government treasury bills or bonds are approximate examples of risk free
security. Adding a risk free asset to the Markowitz portfolio construction process extends
portfolio theory into capital market theory. The introduction of a riskfree asset changes
the Markowitz efficient frontier from a curve into a straight line called the capital market
line (CML).

The slope of the CML is the Sharpe ratio of the market portfolio. The sharpe ratio shows the
average return earned in excess of the risk-free rate of return compared to the total amount
of risk borne. It shows how the return of an asset compensates the investor for risk taken.
{ER – Rf / σ}

The risk associated with a portfolio increases as the portfolio moves up the CML and vice
versa.

MORE ON THE CAPITAL MARKET LINE EXPLANATION

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FORMULA FOR RETURN AND RISK ON A CML

There are two major investments in a CML; Risk-free securities and the market portfolio.

Wm + Wrf = 1

Wrf = 1 - Wm

ERP = (1 – WM)RF + WMRM = RF (1 – WM) + WM(RM – RF)

Where ERP is return on portfolio in a capital market line

RF is risk free rate

WM is the percentage of total portfolio invested in portfolio of risky assets

(1 – WM) is percentage of total portfolio invested in the risk free asset.

Risk of portfolio = Ꝩ(WAσA]2 + [WBσB]2 + 2WAWBCOVAB

Let A represent risk free security which has a standard deviation of 0, this also
makes the covariance 0 leaving Risk of portfolio = ꝨWBσB2 {let B represent the
market}.

Risk of the portfolio on a CML is now = WMσM

The risk free asset has no risk and hence is not considered when calculating the portfolio risk.

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ILLUSTRATION 9

An investor has one third of her funds invested at the risk free rate and the remainder in a
market portfolio of equities. The market portfolio has an expected return of 15% and a
standard deviation of 12%. The investor’s portfolio lies on the capital market line and the risk
free rate is 9%. Calculate the risk and expected return on the portfolio.

SOLUTION

Let A represent the risk free asset and B the market portfolio

Rp = WARA + WBRB = {1/3 X 9} + [2/3 X 15] = 13%

σp on a CML = WBσB = (2/3 x 12) = 8%

ILLUSTRATION 10

B has a portfolio which lies on the capital market line {B can borrow at the risk free rate which
is 9%}. The market portfolio has an expected return of 15% and a standard deviation of 12%.
B’s expected return on the total portfolio is 18%.

a) Calculate the percentage of total amount that needs to be invested in the market and
the risk-free asset.
b) Calculate the total risk on the portfolio.

SOLUTION

Let A represent the risk free asset and B the market portfolio

WA + WB = 1 and so WA = 1 – WB

Rp = WARA + WBRB = (1 – WB)9 + 15WB

18 = 9 – 9WB + 15WB

18 – 9 = 15WB – 9WB

9 = 6WB

WB = 9/6 = 1.5 = 150%

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RELEVANT APPROACH TO PORTFOLIO THEORY

WA = 1 – 1.5 = -0.5 = -50%

RISK OF THE PORTFOLIO ON THE CML

σP = WBσB = 150% X 12 = 18%

DECISION CRITERIA IN PORTFOLIO THEORY

The portfolio with the highest return and lowest risk should be chosen as the optimal portfolio
when making decisions in portfolio theory.

Where no portfolio can give the highest return and lowest risk, the coefficient of variation
should be used to determine the optimal portfolio. Coefficient of variation is the total risk per
return of the portfolio {Total risk / expected return}. The portfolio with the lowest coefficient of
variation is chosen as optimal.

CAPITAL ASSET PRICING MODEL (CAPM)

CAPM is an equilibrium model that predicts the expected return on a stock, given the expected
return on the market, the stock’s beta coefficient and the risk-free rate. It is a model used to
determine a theoretically appropriate required rate of return of an asset to make decisions
about adding assets to a well-diversified portfolio. It takes into account the assets sensitivity
to non-diversifiable risk {systematic risk or market risk} often represented by Beta.

CAPM establishes a relationship between investment risk and expected return from individual
securities. CAPM assumes that investors hold diversified portfolios and are therefore
concerned with systematic risk only and not unsystematic risk.

A security might have a higher systematic risk than the market portfolio. This means that the
security should rise by a larger amount for any increase in average market return and vice
versa.

A security might have a lower systematic risk than the market portfolio, so that when the
average market return rises, the return from the security will rise by a smaller amount.

Risk free return is the theoretical rate of return of an investment with zero risk. It represents
the interest an investor would expect from an absolutely risk-free investment over a specified
period of time. The real risk-free rate of return can be calculated by subtracting the inflation

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RELEVANT APPROACH TO PORTFOLIO THEORY

rate from the yield of the treasury bond matching your investment duration. A risk-free security
has no systematic risk because returns on these securities are unaffected by changes in
market conditions.

ASSUMPTIONS OF CAPM

1. Investors can borrow and lend at the risk -free rate. This is the assumption that makes
the CML straight.
2. The market is efficient
3. Investors are risk averse
4. There are no transaction costs.
5. All investors have same or homogeneous expectations about the returns and risk of
securities
6. All investors decision are based on a single time period.
7. Individuals pay tax on dividend income and capital gains tax on realized gains.

BETA FACTOR OF A SECURITY

The systematic risk for an individual security is measured as a beta factor. This is a
measurement of the systematic risk of the security, in relation to the systematic risk of the
market portfolio as a whole. The beta factor for the market portfolio itself is 1.0.

The beta factor for risk free securities is zero as they have no systematic risk.

Beta factor is calculated as covariance of the returns of the investment and market
returns/variance of the market. Βeta (β) = COVSM / VARM

where COVSM = correlationSM X σS X σM and VARM = σM X σM

FORMULA FOR THE CAPM

R = RF + β(RM - RF)

R is return on the security

Rf is risk free rate

RM is market returns

Rm – RF is market risk premium

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RELEVANT APPROACH TO PORTFOLIO THEORY

Beta factor is β

The above formula implies that the expected return from an individual security will vary as the
market return fluctuates. The size of rise or fall in expected return will depend on the beta
factor of the individual security and the size of the change in the returns from the market as a
whole.

BETA OF A PORTFOLIO

This is the weighted average of all the beta factors in the portfolio.

βP = (WA X βA) + (WB X βB)

SECURITY MARKET LINE (SML)

SML is derived from the CML. It is a line drawn on a chart that serves as a graphical
representation of CAPM which shows different levels of systematic or market risk of various
marketable securities plotted against the expected return of the entire market at any given
time. It is also called “Characteristic line”

SML is a graph that shows the required return from any investment or portfolio given its level
of systematic risk ( beta factor). Actual returns from investments can be compared to the
required returns from the SML to determine whether the investment is under or overvalued.

▪ An asset with an estimated return greater than its required return from the SML is
undervalued; we should buy more of such assets. (falls above the SML)
▪ An asset with an estimated return less than its required return from the SML is
overvalued; we should sell more of such assets. (falls below the SML)
▪ An asset with an estimated return equal to its required return from the SML is properly
valued; we are indifferent between buying or selling such assets and may just hold it.
(falls on the SML)

CML uses total risk and so only efficient portfolios will plot on the CML while SML uses
systematic risk (beta factor) and so all properly priced securities and portfolios of
securities will fall on the SML

Securities below the SML are overpriced or overvalued , and securities above the SML are
underpriced or undervalued. Investors will buy the underpriced securities and sell the

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RELEVANT APPROACH TO PORTFOLIO THEORY

overpriced securities until no excess return opportunities exist. When all excess return
opportunities have been eliminated, all securities will lie on the SML.

MORE ON THE SML

ALPHA FACTOR

ALPHA Factor is that abnormal return that arises when shares yield more or less than their
expected return based on CAPM. It is a temporary return for unsystematic risk arising due
to the inefficiency of the CAPM. The company is advised to take steps on the securities before
normalcy returns.

SECURITY EXPECTED REQUIRED ALPHA COMMENT

RETURN RETURN VALUE
(CAPM)
A 20 15 +5 The security is undervalued as
the actual return is understated

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RELEVANT APPROACH TO PORTFOLIO THEORY

by the market. The company is

advised to buy more of such
securities with positive alphas.
B 20 23 - 3 The security is overvalued as
the market rates it higher than
its expected return. The
company is advised to sell more
of such securities with negative
alphas
C 20 20 0 The security is properly priced
as it has a zero alpha value.
Companies are advised to hold
such securities.

TIPS FOR CAPM AND PORTFOLIO THEORY CALCULATION

➢ FOR PORTFOLIO THEORY, choose the portfolio that has the highest return and
the lowest risk using the formulas stated above.
➢ FOR CAPM, choose the portfolio that has the highest positive alpha factor. The
expected return on the security is compared to the required return based on
CAPM to get Alpha value

ASSUMPTIONS OF CAPM

▪ There exists a perfect capital market in which all investors have access to all available
information about the financial markets.
▪ There is uniformity of investors expectations
▪ There is only one time period
▪ Investors are rationale

ADVANTAGES OF CAPM

▪ It provides a measurable relationship between risk and return

▪ It can be used to estimate the cost of capital for securities
▪ It considers systematic risk in its computation
CHALLENGES OF CAPM
▪ It may be difficult in practice to estimate the risk free rate, beta factor and market
returns.

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RELEVANT APPROACH TO PORTFOLIO THEORY

▪ It focuses on systematic risk only

ARBITRAGE PRICING THEORY (APT)

The CAPM is a single factor model which calculates the return on an investment by relating
the market risk premium to the systematic risk of the investment. The CAPM is not always
able to account for the difference in assets’ returns using their betas, which paved a way for
the development of an alternative approach, called the Arbitrage-Pricing -Theory {APT}, for
estimating the assets’ expected returns. APT unlike CAPM believes there are a number of
industry-specific and macro-economic factors that affect the security returns. {this implies that
a number of factors measure the systematic risk of the asset under APT unlike CAPM that
believes there is only one factor that measures the systematic risk}

APT calculates the return on an investment by relating it to other factors aside the market
such as company size, interest rate changes, inflation, oil prices fluctuations and others. APT
describes the method of bringing a mispriced asset in line with its expected price. {an asset
is said to be mispriced if its current price is different from the predicted price as per the model.

R = RF + β1(R1 – RF) + β2(R2 – RF) + β3(R3 – RF)………..

Where β1,2,& 3 are beta factor of all the factors and {sensitivity of the asset’s return to the
changes in the factor}.

R1, 2 & 3 are the risk premium attached to the factors. {compensation over and above the risk
free rate}

{ICAN PAST QUESTION MAR/JULY 2020} ILLUSTRATION 11

Topnotch shares have an expected rate of return of 12%, with a standard deviation of
32.65%. The expected rate of return is derived from three equal possibilities

I. That the actual return will be the same as the expected rate of return;
II. That the actual rate of return will be higher than the expected rate of return by x%
III. That the actual rate of return will be lower than the expected rate of return by x%
a.You are required to calculate the two probable actual rates of return under (ii
and iii) above (7 marks)
b. You are required to explain

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RELEVANT APPROACH TO PORTFOLIO THEORY

I. What information is conveyed to a potential investor by the standard

deviation statistic:
II. What factors would be taken into an account by an investor when deciding
whether to add to his portfolio; Topnotch shares or another security having
lower values for standard deviation and expected rate of return (5 marks)
c. Given that the correlation coefficient of the return on Topnotch shares with the
return on the market portfolio is 25% and that the standard deviation for the
market portfolio is 13.5%. you are required to calculate the beta factor for
Topnotch security and to interpret the result you obtain. (4 marks)
d. Given that the risk-free rate of return is 8% and using any relevant information
supplied in parts (a – c) above, you are required to calculate the expected rate
of return on the market portfolio. (4 marks)

(20 marks)

SOLUTION

Return prob Expected return Variance = P(R-ER)2

12 0.33 3.96 0.33{12 – 12}2 = 0
12 + X 0.33 3.96 + 0.33X 0.33{12 + X – 12}2 = 0.33X2
12 – X 0.33 3.96 – 0.33X 0.33{12 – X - 12}2 = 0.33X2

12 0.66X2
Variance = standard deviation = 32.652 = 1066.023
2

0.66X2 = 1,066.023 ; X2 = 1,066/0.66 = 1,615

X = Ꝩ1,615 = 40

Probable return = 12 + 40 = 52% or 12 -40 = -28%

B PART OF THE QUESTION

▪ The standard deviation statistic shows the total risk faced by a security or portfolio.
This implies that it reflects the measure of dispersion or variance of the actual return
from the expected return for that investment.
▪ The main objective of portfolio theory is to reduce risk and maximise the returns. The
investor should consider the relationship (correlation) the security has with the existing
investment and the impact on the risk and return of the portfolio.

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RELEVANT APPROACH TO PORTFOLIO THEORY

C PART OF THE QUESTION

Beta factor = cov / var = 110/182 = 0.60

Cov = correlation x standard deviation of market x standard deviation of security = 25% x 13.5
x 32.65 = 110

Var = standard deviation of market2 = 13.52 = 182

The beta factor implies that the security is less risky when compared to the market, so if the
market increases by 10% for instance this security will increase by 6% [0.6 x 10%}.

D PART OF THE QUESTION

RP = Rf + B(Rm – Rf)

12 = 8 + 0.6{Rm – 8}

12 = 8 + 0.6Rm – 4.8

12 – 8 + 4.8 = 0.6Rm

Rm = 8.8 / 0.6 = 14.67%

ILLUSTRATION 12

Mr Investor maintains a portfolio of equity investments in ten listed companies. He is

considering an investment in one of two companies, Bratim plc and Unique plc, each of
which would then represent 10% of the enlarged portfolio. He is unsure which investment
provides the better fit with his existing portfolio of shares and has employed the services
of an investment analyst to aid him in his decision. The analyst has produced the following
data and conclusions:

BRATIM UNIQUE MARKET Existing

portfolio
Expected return 20% 20% 25% 18%
Standard deviation of returns 25% 30% 20% 15%
Correlation coefficient with 0.7 0.4
market returns
Correlation coefficient with 0.1 0.15
Existing portfolio returns
Risk free rate is 10%.
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RELEVANT APPROACH TO PORTFOLIO THEORY

Conclusion: both investments give the same expected return (20%). Bratim plc has the
lower risk (as measured by standard deviation) and therefore is the better investment. Mr
Investor has approached you, since he does not completely trust the analyst’s judgement.
His main criticisms are

▪ I can just about understand expected returns, but what are standard deviation and
correlation coefficient all about and why are they relevant?
▪ This analyst chap has produced lot of figures, but does not seem to have used
most of them

Requirements

a. Explain in similar terms for Mr Investor’s benefit, the significance of standard deviation
and correlation coefficient.
b. Using portfolio theory, determine which of the two investments is to be preferred.
c. Using CAPM, which investment should be chosen
d. Explain the basis of the calculations above and comment on your findings
e. Assuming that the market value of the shares in Mr Investor’s existing portfolio is in
equilibrum. Calculate the beta factor of the portfolio and hence the correlation
coefficient of portfolio returns and market returns
f. What does the result of “e” suggest regarding Mr Investor’s assertion that he has a
well diversified portfolio of investments.

ILLUSTRATION 13 ON CAPM & PORTFOLIO

You have purchased the following data from an investment bank.

COMPANY Forecast total equity Standard deviation of Covariance with

return total equity return market return
A 16.88% 6.3% 32%
B 12% 4.8% 19%
C 14% 4.7% 24%
D 21.5% 6.9% 43%
The market return and market standard deviation are 14.5% and 5% respectively, and the
risk free rate is 6%. Returns and all other data relate to a one year period.

Required

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Estimate the alpha value for each of these companies shares and explain what use alpha
values might be to financial managers.

ILLUSTRATION 14 ON PORTFOLIO THEORY AND CAPM

Risk free Associates have three new projects under consideration

a. Library
b. Computer annex
c. Photocopy station

Each project will cost N500,000 and only N1,000,000 has been budgeted for capital
investment. As a result, a choice has to be made as to which are the best two investments to
undertake.

Details of the three projects are as follows:

PROJECT Expected return Standard deviation Beta value

Library 20% 10% 1.60
Computer annex 15% 8% 0.80
Photocopy station 18% 9% 0.95

Correlation coefficient

Library and computer annex +0.60

Library and photocopy station +0.70
Computer annex and photocopy station +0.90
The risk free interest rate is 10% and the market return is 17%

▪ Use portfolio theory to analyze the investment decision facing the Risk free Associates
▪ Use the CAPM to re-analyze the company’s investment decision.

ILLUSTRATION 15

PORTFOLIO EXPECTED RETURN Standard deviation of return

on market portfolio
A 11 6.7
B 14 7.5
C 10 3.3
D 15 10.8

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RELEVANT APPROACH TO PORTFOLIO THEORY

The expected rate of return on the market portfolio is 8.5% with a standard deviation of 3%.
The risk free rate is 5%. Identify which of the projects could be regarded as efficient.

EXAM QUESTIONS

ILLUSTRATION 1 {Q4NOVEMBER 2019 ICAN PAST QUESTION}

You are the portfolio manager of an asset management company. A client has approached
you for the creation of his portfolio. The client is considering three stocks; A, B and C. your
research department has provided you with the following annualized details concerning the
three stocks and the market index.

ASSETS EXPECTED STANDARD DEVIATION BETA

RETURN (%) (%)
Stock A 12.8 17.8 0.75
Stock B 15.2 25.4 1.12
Stock C 5.6 12.6 0.22
Market index 15.0 21.2 1.00
Risk free rate is 3%.

Required :

A. Explain which of the three stocks A, B and C will lie on the capital market line (CML)
{2 marks}
B. Using the security market line {SML}, which of the three stocks is the most attractive
to buy. Show all relevant calculations. {4 marks}
C. Using the CAPM theory and the above tabulated data, calculate the correlation
coefficient with the market index for each of the three stocks {2 marks}
D. Your client wants to invest 10% in stock B and the rest in stock A and C as suggested
by you. Also he wants to have a market exposure of 1 {i.e a portfolio beta of 1}.
Calculate what will be the investments in the other two assets to reach the client’s
objective. Also calculate the expected return of the resulting portfolio (Assume you can
sell short any quantity of any stock} {4 marks}
E. Now assume the client wants to invest only in stock B and the risk-free asset. He wants
portfolio’s standard deviation of 10%. Calculate what the weight on stock B should be
in order to achieve the stated objective {3 marks}
F. The equity beta of Zinta plc, another client of yours is 0.95 and the alpha value is 1.5%.
explain the meaning and significance of these values to the company. (5 marks)

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RELEVANT APPROACH TO PORTFOLIO THEORY

20 Marks

SOLUTION
A. CML deals with only efficient portfolios and so none of the stocks would lie on it.
B. SML deals with CAPM and so to determine the security to buy, we would need to
calculate the alpha value. Note investors are advised to buy securities with positive
alpha value {under valued securities}

Security Expected return Required return = Rf + Alpha

B{Rm – Rf} value
A 12.8 3 + 0.75{15 – 3} = 12 +0.8 Buy more
B 15.2 3 + 1.12{15 – 3} = 16.44 -1.24 Sell
C 5.6 3 + 0.22{15 – 3} = 5.64 -0.04 Sell
C. B = cov / var
Cov = correlation x σm x σs / Var = σm x σm
B = correlation x σm x σs
σm x σm
correlation = B x σm / σs
Security correlation = B x σm / σs
A 0.75 x 21.2 / 17.8 = 0.89
B 1.12 x 21.2 / 25.4 =0.94
C 0.22 x 21.2 / 12.6 = 0.37
D. Note that 10% investment in B represents the weight of B
WA + WB + WC = 1
WA + 0.10 + WC = 1
WA + WC = 1 – 0.10 = 0.90
WA = 0.90 – WC
Bportfolio = {WABA + WBBB + WCBC}
1 = (1 – WC]0.75 + [0.10 X 1.12] + [WC X 0.22]
1 = 0.75 – 0.75WC + 0.112 + 0.22WC
1 = 0.75 – 0.53WC + 0.112
0.53WC = 0.75 + 0.112 – 1
0.53WC = -0.138
WC = -0.138 / 0.53 = - 0.26
WA = 0.90 – WC = 0.90 – [- 0.26] = 1.16
Invest 116% in A, 10% in B and -26% in C to get a beta factor of 1

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The expected return on the portfolio will be same at the expected return from the
market because the beta factor is 1.
E. Portfolio risk in a CML = WBσB
The assumption here is that A represents the risk free asset that has a standard
deviation of zero and B represents the other/ market portfolio.
10 = WB X 25.4
WB = 10/25.4 = 39%
Invest 39% in B and the balance 61% in the risk free asset.
F.

ILLUSTRATION 2 {Q4 MAY 2019 ICAN PAST QUESTION}

The managers of pension fund follow an active portfolio management strategy. They
try to purchase shares and bonds that show a positive abnormal return {positive
alpha factor in the case of shares}. The pension fund is required by law to hold at least
40% of its investment in bonds. N100m is currently available for investment.

Three shares and three bonds are being considered for purchase.

The required return on bonds may be measured using a model similar to the capital asset
pricing model, where beta is replaced by the relative duration of the individual bond (D1)
and the bond market portfolio (Dm) i.e D1/Dm.

Shares Expected Return Standard Correlation coefficient of

% deviation of returns with the markets
returns
Equity 10.5 15 1
market
A plc 11.0 25 0.76
B plc 9.5 18 0.54
C plc 13.5 35 0.63

Bonds Duration (years) Coupons (%) Redemption yield (%)

Bond market 7.5 - 5.8
Federal Govt 1.5 8 4.5
D plc 8.6 6 5.3
E plc 14.2 9 7.2
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RELEVANT APPROACH TO PORTFOLIO THEORY

Note: Assume risk free rate of 4% per year.

Required :

a) Evaluate whether or not any of the shares or bonds is expected to offer a positive
abnormal return. {10 marks}
b) The pension fund currently has the maximum permitted investment in shares and
wishes to continue this strategy. It has a market value of N1,000 million and a beta of
0.62.
Required :
Calculate the required return from the pension fund if any shares and bond with
positive abnormal returns are purchased. State clearly any assumptions that you make
{4 marks}
c) Discuss possible problems with the pension funds investment strategy (6 marks) {total
20 Marks}

SOLUTION

SHARES

COY Expected return Required return Alpha value comment

A plc 11.0 12.3 - 1.3 Overvalued’sell
B plc 9.5 8.2 +1.3 Undervalued;buy
C plc 13.5 13 .6 - 0.1 Overvalued; sell

Required return = Rf + B{Rm – Rf}

B = correlation x σs / σm

A = 0.76 x 25 / 15 = 1.27

B = 0.54 x 18/15 = 0.65

C = 0.63 x 35 / 15 = 1.47

B = correlation x σs / σm R = Rf + B{Rm – Rf)

A A = 0.76 x 25 / 15 = 1.27 R= 4 + 1.27 {10.5 – 4} = 12.3

B B = 0.54 x 18/15 = 0.65 rR = 4 + 0.65{10.5 – 4} = 8.2

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RELEVANT APPROACH TO PORTFOLIO THEORY

C C = 0.63 x 35 / 15 = 1.47 R = 4 + 1.47{10.5 – 4} =13.6

BONDS

Determine using CAPM

BOND Expected Return Required Return Alpha value Comment

FED Govt 4.5 4.4 +0.1 Undervalued’ Buy
D plc 5.3 6.0 -0.7 Overvalued ‘ Sell
E plc 7.2 7.4 - 0.2 Overvalued ‘ sell

Calculation of required return and beta factor

BOND BETA = D1/Dm R = Rf + B{Rm – Rf}

FED GOVT 1.5 / 7.5 = 0.2 R = 4 + 0.2 (5.8 – 4} = 4.4
D PLC 8.6 / 7.5 = 1.1 R = 4 + 1.1 (5.8 – 4} = 6.0
E PLC 14.2 / 7.5 = 1.9 R = 4 + 1.9 (5.8 – 4} = 7.4
B plc shares and the Federal Government Bond have positive Alpha values

B PART OF THE ILLUSTRATION

Required Return on the portfolio is calculated using the Beta of the portfolio. It is assumed
here that the return of the market is that of the shares of 10.5%.

R = RF + BP {Rm – Rf} = 4 + 0.61 {10.5 – 4} = 7.96 = 8%

Beta of Portfolio

INVESTMENT VALUE Nm BETA AVERAGE BETA

Existing 1,000 0.62 620
B PLC 60 0.65 39
FED GOVT Bond 40 0.2 8
1,100 667
Beta portfolio = 667 / 1,100 = 0.61

Beta Portfolio = WABA + WBBB + WCBC

C PART OF THE QUESTION

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RELEVANT APPROACH TO PORTFOLIO THEORY

The strategy of the organization is to purchase undervalued securities (with positive alpha
values}. The problem with this strategy includes but not limited to

1. If the market is efficient, there would be no undervalued securities.

2. The company must have a comprehensive information system to identify undervalued
securities and have funds to acquire them when the opportunity arises.
3. The basis of comparison is CAPM which has a lot of unrealistic assumptions in practice
4. The strategy of the company does not align with the objective of investing 40% in
bonds.

QUESTION 3 {MAY 2018 ICAN PAST QUESTION}

Sunmola Funds [SF] Plc has a portfolio of short-term investment in the shares of four
quoted companies.

Company Holding
Tomiwa (T) 100,000 shares
Pascal (P) 155,000 shares
Binta (B) 260,000 shares
Yetunde (Y) 420,000 shares
You have the following additional information:

Company Beta Market value per share Expected total return on

(Kobo) investment p.a (%)
T 1.55 280 21.0
P 0.65 340 12.5
B 1.26 150 18.0
Y 1.14 9.5 18.5
The market risk premium is 10% per year and the risk free rate is 6% per year.

Required :

a. Estimate the Beta of SF’s Plc’s short-term investment portfolio {4 marks}

b. Recommend giving your reasons, whether the composition of SF plc’s short-term
investment portfolio should be changed using relevant calculations. {10 marks;
Hint: Consider the alpha values of the shares and the propriety of investing short-
term funds in equity}

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RELEVANT APPROACH TO PORTFOLIO THEORY

c. Explain three factors that a financial manager should take into account when
investing in marketable securities. (6 marks) {Total 20 Marks}

ILLUSTRATION 4 (ICAN NOVEMBER 2017 QUESTION 7)

In the context of the selection and holding of investments, discuss each of the following
scenarios:

a. An investor holding only one security needs be concerned with unsystematic risk of
that security (3 marks)
b. However, an investor who holds a number of securities should take account of total
risk (3 marks)
c. An investor should never add to a portfolio, investment that yields a return less than
the market rate of return (3 marks)
c. The equity beta of KT plc is 1.2 and the alpha is 1.4. explain the meaning and
significance of these values to the company
(6 marks)

(Total 15 marks)

ILLUSTRATION 5 (ICAN NOVEMBER 2016 )

a. Capital Asset Pricing Model (CAPM) is an equilibrium model of the trade off between
expected portfolio return and unavoidable risk. What are the basic assumptions on
which this model is based? (6 marks)
b. Currently, the rate of return on the Federal Government bond redeemable at par in the
year 2018 is 5%. The securities of four companies Akira plc, Bamboo plc, Courage plc
and Divine plc have expected return of 12%, 9.5%, 10.5% and 13% respectively. The
average expected return on market portfolio is 10% subject to a 6% risk (standard
deviation). Other relevant information relating to the four securities of the companies
is as stated below

SECURITIES STANDARD DEVIATION CORRELATION

COEFFICIENT
Akira plc 0.080 0.975
Bamboo plc 0.075 0.640
Courage plc 0.090 0.740
Divine plc 0.150 0.680
You are required to show which of the companies is/are overvalued (9 marks)
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RELEVANT APPROACH TO PORTFOLIO THEORY

ILLUSTRATION 6

A portfolio consists of shares in the following companies

COMPANY Percentage of Market price per Annual return per

portfolio share share
Wapco 15% 250k 40k
Aiico 20% 375k 52.5k
Nimco 25% 180k 36k
Arm 40% 500k 60k
The market rate of return is 16% and the risk free rate of return is 11%

I. Calculate the beta factor of each shares in the portfolio

II. Calculate the beta factor for the portfolio as a whole
III. Calculate the expected return on the portfolio as a whole
IV. Explain the role of the beta factor in the process of portfolio selection.
SOLUTION
Return = annual return per share / market price = 40 / 250 = 0.16 = 16%
R = Rf + B{Rm – Rf} = 16 = 11 + B{16 – 11}
16 = 5B + 11
B = 16 – 11 / 5 = 1.00
ILLUSTRATION 7

An investor in an equilibrum market has 50% of his wealth in a risk free asset and 50% in
the four assets below:

COMPANY Expected return Beta asset Invested in Asset

Wapco 7.6% 0.2 10%
Aiico 12.4% 0.8 10%
Nimco 15.6% 1.2 10%
Arm 18.8% 1.6 20%
I. Calculate the current beta and expected return of your portfolio
II. Assume that you want an expected return of 12% and intend to obtain it by selling
some of the risk free asset and using the proceeds to buy the market portfolio.
Calculate the set of weights in the revised portfolio

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RELEVANT APPROACH TO PORTFOLIO THEORY

III. If you hold only the risk free asset and the market portfolio, what set of weights would
give you an expected return of 12%
IV. Explain the significance if any , of the beta concept to investors in quoted securities.
SOLUTION
An Equilibrum market is one where the securities are properly priced that is expected return
is equal to the required return. The beta of the risk free asset is assumed to be zero.
SECURITY WEIGHT BETA Weighted Beta
A 0.10 0.2 0.02
B 0.10 0.8 0.08
C 0.10 1.2 0.12
D 0.20 1.6 0.32
RF 0.50 0 0
0.54

To get the required return or expected return from the portfolio, the risk free rate and the
market return must be calculated using any two of the securities.
R = Rf + B (Rm – Rf)
A ; 7.6 = Rf + 0.2 {Rm – Rf} ; 7.6 = Rf + 0.2Rm – 0.2Rf; 7.6 =0.8Rf + 0.2Rm-----{Eq 1}
B : 12.4 = Rf + 0.8 {Rm – Rf); 12.4 = Rf + 0.8Rm – 0.8Rf ; 12.4 = 0.2Rf + 0.8Rm---{Eq 2}
Using elimination method, make one of the variable same, to eliminate Rf, we multiply the
whole of equation 2 by 4
Adjusted Eq 2 = 49.6 = 0.8Rf + 3.2Rm
Eq 1 7.6 = 0.8Rf + 0.2Rm
Difference 42 = 0 + 3.0Rm
Rm = 42 / 3 = 14%
Substitute the Rm into any of the equations to get Rf
7.6 = 0.8Rf + (0.2 x 14)

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7.6 – 2.8 = 0.8Rf

Rf = 4.8/0.8 = 6%
R = Rf + Bp {Rm – Rf} = 6 + 0.54{14 – 6} = 10.32%
B PART OF THE ILLUSTRATION
SECURITY WEIGHT Return Weighted return
A 0.10 7.6 0.76
B 0.10 12.4 1.24
C 0.10 15.6 1.56
D 0.20 18.8 3.76
Rf 0.50 – X 6 3 – 6x
E {Rm} X 14 14x
10.32 + 8x
10.32 + 8x = 12
8x = 12 – 10.32
X = 1.68 / 8 = 0.21
21% should be invested in the market portfolio while {50 – 21%} 29% should be invested
in the risk free asset and other assets remaining constant for the return to be 12%
C PART OF THE QUESTION
Let A represent Rf and B represent market portfolio
RA = 6% {RF} and RB = 14% {Rm}
WA + WB = 1 and so WA = 1 – WB
RP = {WARA} + {WBRB}
12 = {1 – WB)6 + {WB X 14}
12 = 6 – 6WB + 14WB
12 – 6 = 8WB
WB = 6/8 = 75%
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WA = 25% {1 – 0.75}
ROLE OF BETA FACTOR
1. Help investors manage their systematic risk
2. Helps investors know the suitability of assets to add or remove from the portfolio
3. It also acts as a performance measurement tool for the portfolio
4. It helps the investor determine the appropriate return expected for the risk in project

ILLUSTRATION 8

Topnotch shares have an expected rate of return of 12%, with a standard deviation of 32.65%.
The expected rate of return is derived from three equal possibilities

IV. That the actual return will be the same as the expected rate of return;
V. That the actual rate of return will be higher than the expected rate of return by x%
VI. That the actual rate of return will be lower than the expected rate of return by x%
e. You are required to calculate the two probable actual rates of return under (ii
and iii) above (7 marks)
f. You are required to explain
III. What information is conveyed to a potential investor by the standard
deviation statistic:
IV. What factors would be taken into an account by an investor when deciding
whether to add to his portfolio Topnotch shares or another security having
lower values for standard deviation and expected rate of return (5 marks)
g. Given that the correlation coefficient of the return on Topnotch shares with the
return on the market portfolio is 25% and that the standard deviation for the
market portfolio is 13.5%. you are required to calculate the beta factor for
Topnotch security and to interpret the result you obtain. (4 marks)
h. Given that the risk free rate of return is 8% and using any relevant information
supplied in parts (a – c) above, you are required to calculate the expected rate
of return on the market portfolio. (4 marks)

(20 marks)

QUESTION 9

a. What does beta measure, and what does beta of 0.90 mean. (3 marks)
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b. What factors determine the level of beta which a company may have. (5 marks)
c. TRITUONE plc is an all equity company whose shares have a beta value of 1.2. The
managing director has commented that the actual share price behaviour is frequently
inconsistent with that value of beta. Three examples are given:

CASE 1

In a month, when a dividend of 15k per share was paid, the share price and stock market
all share index values were:

Share Price Index

At the start of month 100k 300
At the end of month 93k 315
Return based on opening and closing price levels (7%) 5%

CASE 2

In a month, when a 1 for 2 bonus issue was made, but no dividend was paid, the share
price and stock market all share index values were:

Share Price Index

At the start of month 200k 400
At the end of month 120k 360
Return based on opening and closing price levels (40%) (10%)

CASE 3

In many months, when no dividends were paid or bonus issues etc made, the actual share
price movement was considerably different from, and sometimes in the opposite direction
to, that expected of a share with a beta of 1.2.

You are required to comment on each of the cases, explaining the extent to which the
share price behaviour is in reality inconsistent with the beta value given.

For cases 1 and 2, show the end of month share price which would have occurred if share
price behaviour had in those circumstances been exactly as expected given a beta of 1.2
(12 marks)

(20 marks)
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CURRENCY RISK MANAGEMENT

TREASURY FUNCTION AND MANAGEMENT

TREASURY FUNCTION; the treasury department in a modern enterprise is responsible for making sure
that cash is available in the right amounts, at the right time and in the right place.
Treasury Management is defined as the corporate handling of all financial matters, the generation of
external and internal funds for the business, the management of currencies and cash flows, and the complex
strategies, policies and procedures of corporate finance.
Treasury is the function concerned with the provision and use of finance and thus handles the acquisition
and custody of funds. The Treasury department has a role in all levels of decision making within the
company. It is involved with strategic decisions (dividend policy & raising of capital), tactical decisions
(risk management) and operational decisions (investment of surplus funds)
ROLE OF THE TREASURER

1. Corporate Financial Objectives; is focused on policies, aims and strategies and setting up systems
2. Liquidity management entails making sure that the company has the liquid funds it needs, and
invests any surplus funds, even for very short terms. This includes working capital management,
money transmission management, banking relationships, money management and investment.
3. Funding management is concerned with assessing the various sources of finance, types of finance,
security required for the finance, funding policies, funding proceedures, where the funds are
obtainable, length of time funds available and cost of the finance (interest rate).
4. Currency management involves monitoring exposure policies & procedures, exchange dealing
and exchange regulations.
5. Corporate finance functions which include raising share capital, obtaining a stock exchange
listing, project finance & joint ventures, dividend policies, business reconstructions.
▪ Produce regular cash flow forecasts to predict surpluses and short falls
▪ Arrange short term borrowing and investment when necessary
▪ Deal with entity’s banks
▪ Finance the business on a day to day basis
▪ Advise senior managers on long term financing requirements
▪ Advise on foreign exchange transactions
▪ Risk management such as foreign exchange or currency risk, interest rate risk, credit risk or market
risk. (credit risk is a risk that a debt will not be paid when due while market risk is the risk of
adverse movement in the market price of assets)

Cash Management Function; this involves managing cash receipts, cash payments and net cash balances.
This can be done by pooling and netting of cash flows to avoid interest charges on deficit accounts.
CENTRALISED TREASURY DEPARTMENT
This is the establishing of a single treasury department in the head office which acts as the bank to the group
by taking most decisions on borrowing, , investment of cash surplus, currency management and financial
risk management. They have the job of ensuring that individual operating units have all the funds they need
at the right time.
ADVANTAGES OF CENTRALISED TREASURY MANAGEMENT

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▪ It avoids having a mix of cash surpluses and overdrafts in different local bank accounts and
facilitates bulk cash flows, so that lower bank charges can be negotiated.
▪ Cash is managed by specialist staff as the organization will be able to employ experts with in depth
finance skills, knowledge of dealing in futures, taxation, transfer prices, eurocurrency markets and
so on.
▪ Larger volumes of cash are available to invest, giving better short term investment opportunities.
▪ It increases the negotiating power of the treasury department with banks and third parties as any
borrowing can be arranged in bulk.
▪ Foreign currency risk management is likely to be improved through netting and matching amongst
subsidiaries.
▪ It ensures attention is focussed on group profit performance through good cash funding, investment
and foreign currency management.
▪ It provides a means of exercising better control through the use of standardized procedures and risk
monitoring.
▪ It allows for easy pooling of all cash deficits and surpluses from different accounts into a central
bank account
▪ Cash can easily be channelled to where it is needed and overdraft interest minimised
▪ It lowers the total amount of cash kept aside for precautionary purposes

ADVANTAGES OF DECENTRALISED TREASURY DEPARTMENT

▪ Sources of finance can be diversified and can be matched with local assets
▪ The decentralised treasury function may be more responsive to the needs of individual operating
units
▪ It enables for greater autonomy to subsidiaries and divisions because of the closer relationships
they will have with the cash management function.

FACTORS TO CONSIDER IN CHOOSING IF A TREASURY DEPARTMENT SHOULD BE A

PROFIT CENTRE OR COST CENTRE
1. Competence of Staff: there is a need to see if staff has sufficient expertise in the area of treasury
management. It should only be run as a profit centre if they are well skilled as mistakes in this field
may be costly.
2. Controls : if there are adequate controls in place to prevent costly errors and over exposure to risk,
it can be run as a profit centre and vice versa.
3. Information : does the department have access to detailed and up to date market information? If
they do, the department can be run as a profit centre and vice versa
4. Attitudes to risk: will their attitude to risk management fit with that of the board of directors? A
profit centre would be ideal if they fit.
5. Internal charges: is there an agreement or basis for charging other departments for their services?
A profit centre will be ideal if setting the transfer price is simple and objective.
6. Performance evaluation: departmental managers appraisal should be effective and this is
influenced by the factors the managers have control over.

TREASURY DEPARTMENT AS A PROFIT CENTRE;

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The treasury department is usually run as a cost centre if its main focus is to keep costs within budgeted
spending targets and a profit centre if there is high level of foreign exchange transactions or the business
wishes to make speculative profits.
Treasury department run as a profit centre is with the aim of motivating management and has the following
benefits such as potential for additional profits, efficient operation and a realistic transfer of cost to business
units at the market value.
The challenges with running the department as a profit centre include potential for huge losses due to
speculative deals, additional administrative cost and additional cost of management time in terms of
negotiating transfer prices.
The possible risks of operating a Treasury Department include
▪ The risk that the treasury department will raise finance for the entity in an efficient or inappropriate
way
▪ It may fail to manage the financial risks of the entity sufficiently
▪ It may employ dealers for foreign exchange or investing surplus funds. The dealers may exceed
their trading limits or make mistakes when dealing.
▪ The treasury department may earn only a low return on their investment or surplus funds

TREASURY POLICY
All treasury departments should have a formal statement of treasury policy and detailed guidance on treasury
procedures. The aims of a treasury policy are to establish direction, specify parameters, exercise control and also
provide a clear framework and guidelines for decisions.
The guidance needs to cover the roles and responsibilities of the treasury function, the risks requiring management ,
authorization and dealing limits.
Risks guidance should cover identification and assessment, criteria for risk (tolerable and unacceptable level),
management guidelines and reporting guidelines on bank exposure, investment management, liquidity management,
funding risk, currency and interest rate risk & counter party exposure.

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CURRENCY RISK
1, TRANSACTION RISK

It is a SHORT TERM RISK that a company may pay higher or receive lower from a fixed invoice transaction
simply because the exchange rate is fluctuating. This risk affects cash flow and so needs to be hedged
(minimizing the impact on the organization).

It is the risk of adverse exchange rate movements occurring in the course of normal international trading
transactions. This arises when the prices of imports or exports are fixed in foreign currency terms and
there is movement in the exchange rate between the date when the price is agreed and the date when
the cash is paid or received in settlement.

Transaction risk is the risk that, for any future transaction in a foreign currency, the amount received or
paid in domestic currency might be different from the amount originally expected because of movements
in exchange rate between the date of the initial transaction and the date of settlement.

2. TRANSLATION RISK is the risk that the organization will make exchange losses when the
accounting results of its foreign branches or subsidiaries are translated into the home currency.
Translation losses can result from restating the book value of a foreign subsidiary’s assets at the exchange
rate at the balance sheet date.

This risk has no impact on our cash flow and so may not be hedged provided the market is efficient. Where
the market is inefficient, there may be need to hedge the risk from having adverse effect on the share
value.

3. ECONOMIC RISK refers to the effect of exchange rate movements on the international
competitiveness of a company and present value of future cash flows. It is the long term movement in
exchange rates caused by changes in the competitiveness of a country. It is the degree to which the
present value of a firm’s future cash flow is affected by adverse exchange rate. This risk can be hedged
by matching assets and liabilities, diversifying the supplier and customer base, diversifying operations
worldwide and changing of prices.

HEDGING OF TRANSACTION RISK

This is divided into Internal techniques and External techniques.

INTERNAL HEDGING TECHNIQUES are those techniques that exploit characteristics of the
company’s trading relationship without recourse to the external currency or money markets.

1. LEADING AND LAGGING: Leading involves accelerating payments (advanced payments) to

avoid potential additional costs due to currency rate movements and LAGGING is the practice of
delaying payments if currency rate movements are expected to make the later payment cheaper.
Leading is used to avoid over payment when the company paying expects the currency of payment

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to appreciate while Lagging is used to pay less when the paying company expects the currency of
payment to depreciate.
2. INVOICING IN HOME CURRENCY: the importer ensures that the invoices are in its local
currency while the exporter invoices all customers in its local currency. This method is dependent
on the bargaining strength or the exporter’s competitive position. An alternative method of
achieving the same result is to negotiate contracts expressed in the foreign currency but at a pre-
determined fixed rate of exchange
3. MATCHING RECEIPTS AND PAYMENTS: a company can reduce its transaction risk
exposure by offsetting its payments against receipts in that currency. This can be achieved by
having foreign accounts with a bank with receipts occurring before payments and time difference
not been too long.
4. NETTING is a process in which credit balances are netted off against debit balances so that
only the reduced net amounts remain due to be paid by actual currency flows. It could be bilateral
netting where only two companies are involved or multilateral netting which involves more
than two group companies.
Multilateral netting involves minimising the number of transactions taking place through the
country’s banks. This limit the fees that the banks receive for undertaking the transactions and so
some government do not allow multilateral netting to maximize fees their banks can receive.
Some other governments allow multilateral netting in the belief that this will make companies
more willing to operate from those countries and any fees lost is compensated by the extra
business these companies and their subsidiaries bring into the country.

STEPS TO SOLVE MULTILATERAL NETTING

a. Construct a table with companies receiving money (money is owed to) down the left side
(vertical column) and companies making payments (money is owed by) across the top
(horizontal row)
b. Enter all the amounts the company owes or is been owed and convert to the agreed
settlement currency.
c. Add across (horizontally) to get total receipts expected and down the table (vertically) to
determine total payments for each company
d. Determine the net receivable or payable for each company based on the settlement currency
(note that the net column should sum up to zero)
e. Interpret your final solution

ILLUSTRATION ON MULTILATERAL NETTING

Riskfree Group is made up of 3 companies- one in Germany, Hongkong and one in US. The following inter-
company transactions took place during the first quarter of 2015.

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OWED TO OWED BY AMOUNT

GERMANY HONGKONG €10m
HONGKONG GERMANY HK$5m
US GERMANY $12m
GERMANY US €6m
HONGKONG US HK$20m
US HONGKONG $16m

The Group has introduced a system of multilateral netting to minimize the number of inter-group
payments. The US dollar will be used as a settlement currency. Exchange rates are as follows: HK$11.2475
= €1, €0.6919 = $1 and HK$7.7821 = $1.

Illustrate the effect of multilateral netting on inter group receipts and payments.

5. DO NOTHING: is a method when the company uses the exchange rates available on the date
of payment or receipt. This is on the belief that you win some and you lose some.

EXTERNAL HEDGING TECHNIQUES

1. Forward Exchange Contract is an immediate firm and binding agreement to exchange
(purchase or sell) a specified quantity of a stated foreign currency at a rate of exchange rate fixed
at the time the contract is made for performance (delivery of the currency and payment for it) at
a future time which is agreed when making the contract.

Forward contract hedge against transaction exposure by allowing the importer or exporter to
arrange for a bank to sell or buy a quantity of a stated foreign currency at an agreed future date,
at a rate of exchange determined when the forward contract is made. The trader will know in
advance how much local currency they will receive or how much the local currency they must pay.
ADVANTAGES OF FORWARD CONTRACT
1. The contract can be tailored to the user’s exact requirements with quantity to be delivered,
date and price all flexible
2. The trader will know in advance how much money will be received or paid
3. Payment is not required until the contract is settled

DISADVANTAGES OF FORWARD CONTRACTS

1. The user may not be able to negotiate good terms as the price is dependent on the size of the
deal and how the user is rated
2. Users have to bear the spread of the contract between the buying and selling price
3. Deals can only be reversed by going back to the original party and offsetting the original trade
4. The credit worthiness of the other party may be a problem (it is exposed to default risk)

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FAILURE TO SATISFY A FORWARD CONTRACT

A customer might be unable to satisfy a forward contract for one of the following reasons
a. The supplier fails to deliver the specified goods and the importer rejects the goods and refuses
to pay
b. Supplier sends fewer goods than expected resulting in less payment
c. Supplier is late with delivery and so payment has to be delayed

CLOSE OUT OF FORWARD CONTRACTS

If a customer cannot satisfy a forward exchange contract, the bank will make the customer fulfil
the contract

a. If the customer has arranged for the bank to buy currency but then cannot deliver the
currency: the bank will sell the currency to the customer at the spot rate or buy the currency
back under the terms of the forward exchange contract.
b. If the customer has contacted the bank to sell them currency, the bank will sell the specified
currency at the forward exchange rate or buy back the unwanted currency at the spot rate.

The bank forces the customer to fulfil its own part of the contract by either selling or buying the
missing currency at the spot rate in an arrangement known as closing out a forward exchange
contract.

SYNTHETIC FOREIGN EXCHANGE AGREEMENTS (SAFEs)

In order to reduce the volatility of their exchange rates , some governments have banned foreign
currency trading. In such markets SAFEs are used; SAFEs are just like forward contracts but no
currency is actually delivered, instead the two counter parties settle the profit or loss (calculated
as the difference between the agreed SAFE rate and the prevailing spot rate) on a notional
amount of currency. SAFE can be used to create a foreign currency loan in a currency that is of no
interest to the lender.

STEPS IN FORWARD CONTRACT

▪ All transactions in the same currency within the same period should be matched together to get
the net exposure
▪ Determine if the company has or needs the net exposure
▪ Determine if the Bank is buying or selling
▪ Calculate the net outcome based on the bank’s position

ILLUSTRATION
Copyright plc a company based in Abuja has the following transactions with a US company
DUE IN 1 MONTH

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Payments to suppliers $600,000

Receipts from customers $400,000

DUE IN 3 MONTHS
Payments to suppliers $800,000
Receipts from customers $1,200,000

Exchange rates $/₦

Spot 1.6186 – 1.6202
1 month forward $ 1.6180 – $1.6200--------N
3 months forward 1.6173 – 1.6194
Required
a. Calculate the net naira receipts or payments for both its one month and three month
transactions if it hedges risk using the forward markets
b. Determine how much the company actually gains or loses as a result of the hedging
transaction if the $/₦ exchange rate in one and three month’s time are 1.6192 – 1.6208
and 1.6200 – 1.6220 respectively.
c. Itemize the key advantages and disadvantages of forward market.

2. MONEY MARKET HEDGING involves creating a foreign asset (deposit) to offset a foreign
payment risk (liability) or creating a foreign liability (loan) to offset a foreign receipt risk (asset).
It is the manufacture of a forward rate using the spot exchange rate and interest rates of the home and
overseas countries. It requires preferential access to the short term markets and can be a substitute for
forward contracts.
Money Market Hedging involves borrowing in one currency, converting the money borrowed into
another currency and putting the money on deposit until the time at which the transaction is
completed, hoping to take advantage of favourable interest rate movements.

Money Market hedging is a method that exploits short term interest rates to fix an appropriate
forward rate.

The main challenges with a money market hedge are that it is difficult to reverse and it can be
relatively expensive. It is not always possible to construct a money market hedging depending on
the currencies with which you are dealing, as you may not be able to get access to short term
money market in the overseas.

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STEPS FOR MONEY MARKET HEDGING FOREIGN RECEIPTS (ASSET) : BCD

▪ Create a liability: Borrow the appropriate amount from a foreign bank in the foreign currency
today. Appropriate Amount = Receipt / 1 + borrowing rate of the foreign currency
▪ Convert it immediately to home currency ; company has the money, the bank is buying. All
conversions are done immediately which means using the spot rate.
▪ Place it on deposit in the home currency
▪ In the future, the debtor pays the bank, while the company collects its money from the local bank.
(converted amount (1 + deposit rate)

Note all rates are assumed to be per annum and so should be converted to the number of months
in the transaction when calculating. All conversions under Money market hedging are done
immediately at the spot rate.

STEPS FOR MONEY MARKET HEDGING PAYMENTS (LIABILITY) : DCB

▪ Create an Asset: Deposit an appropriate amount in a foreign bank in the foreign currency today.
Appropriate amount = Payments / 1 + deposit rate
▪ Convert the deposit amount: Determine the amount of home currency required to get the
deposit now. The company needs the money so the bank is selling at the spot rate.
▪ Borrow from a local bank: Collect a loan from the local bank in the home currency.
▪ In the future, the bank pays the creditor while the company pays the local bank. (converted
amount (1 + borrowing rate)

ARBITRAGE PROFITS

It is the simultaneous purchase and sale of a security in different markets with the aim of making a
risk-free profit through the exploitation of any price differences between the markets.

ILLUSTRATION ON MONEY MARKET HEDGING

Calculate using money market hedge the net naira payment or receipt from the transactions
below:
I. A Nigerian importer has to pay a supplier €4 million in 3 months’ time
II. A Nigerian company expects to receive €9 million in 7 months’ time.

The relevant exchange rates are:

₦/€
Spot rate ₦0.3205 --- ₦0.3210 = 1€
3 months FR 0.3215 --- 0.3222
Interest rates are as follows:

Borrowing Deposit
€ 5.5% = 7/12 x 5.5% = 3.208% 3.5% = 3/12 x 3.5% = 0.875%
Naira 10% = 3/12 x 10% = 0.025 8% = 7/12 x 8% = 4.67%

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3. CURRENCY FUTURES : is a standardized contract to buy or sell a fixed amount of currency

at a fixed rate at a fixed future date. Futures are standardized contracts that are traded on an
organized exchange such as the Chicago mercantile exchange or London International Financial
Futures and Options Exchange (LIFFE). Future contracts are assumed to mature at the end of
March, June, September or December. Buying the Futures Contract means receiving the contract
currency and Selling the futures contract means supplying the contract currency.

Futures are a derivative which derives their value from movement in the spot rate. A currency
futures contract is an agreement between two parties to buy/sell a particular currency at a
particular rate on a particular future date. Currency futures deals are in the form of standardized
contracts of a fixed amount of money and are available only in a limited range of currencies and
limited range of forward periods. The exchange rates are quoted in terms of the foreign currency
as measured in US dollars and premiums are quoted in US cents per euro, pound.

Futures price is the futures market best estimate of the currency rate in the future
The price of currency futures moves in ticks. A Tick is the smallest movement in the futures
exchange rate and is normally four decimal places (0.0001 = 1 tick).
TICK VALUE = size of futures contract X tick size
Basis is the difference between the spot exchange rate and the futures price. Basis covers the
contract from todays date to the end of the futures contract.(it is assumed that all contracts
mature at the end of the month)
At maturity the futures price and the actual price are expected to be the same and so no basis.
Basis is the difference between the spot exchange rate and the futures price. There is no basis
risk when the contract is held to maturity.

Basis risk is a risk that the price of a currency future will vary from the price of the underlying
asset (spot rate) as expiry of the contract approaches. Basis risk is the probability that the basis
may not reduce uniformly (in a linear manner) as expected. There is no basis risk when the
contract is held to maturity.
It is assumed that the Basis falls uniformly over time but the basis may not fall in that
predictable way creating an imperfect hedge.

Unexpired Basis = refers to unutilised basis as at the transaction date.the difference between
the transaction date and the end of the futures contract

Perfect hedge is a hedge that has no basis risk and covers the whole transaction (number of
contracts will be a whole number).

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IMPERFECT HEDGE is a hedge where the basis is different from the expected basis over time and
the contracts are not whole number contracts. Hedge Efficiency compares the profit made on the
futures market with the loss made on the cash or commodity market and vice versa.

MARK TO MARKET PROCESS OR OPERATIONS OF CURRENCY FUTURES:

Both parties in a futures contract deposit some cash (initial margin) with the futures exchange in
a margin account as a security against the trader defaulting on their trading obligations. The
Futures exchange monitors the margin account on a daily basis. If the trader is making losses, the
futures exchange may require additional margin payments known as variation margins. The call
for extra payment is called a margin call.

An initial margin is similar to a deposit. The profit or loss is received into or paid from the margin
account on a daily process in a process called marking to the market. The company will be
required to maintain a minimum balance in its margin account known as the maintenance
margin. This practice creates uncertainty as the company will not know in advance the extent of
such margin payments.

A company is an open position whenever it has an undertaking to buy futures (Long position) or
sell futures (short position). A company is in a closing position when the futures contract matures
or when the trader closes it out by selling or buying an equal number of futures for the same
settlement date.
In order to manage Basis risk, it is important to choose a currency future with the closest maturity
date to the actual transaction. This reduces the unexpired basis when the transaction is closed
out.

PRINCIPLES IN CHOOSING FUTURES CONTRACTS

GENERALLY FOR PAYMENTS : CHOOSE A CONTRACT TO BUY foreign currency
FUTURES EXCEPT IF THE CURRENCY IS NOT AVAILABLE. Where the currency is not
available in the futures market, you will do the corresponding “that is
sell local currency futures.

GENERALLY FOR RECEIPTS: CHOOSE A CONTRACT TO SELL FUTURES EXCEPT IF THE

CURRENCY IS NOT AVAILABLE. Where the currency is not available in the
futures market, you will do the corresponding “that is buy local currency
futures.
➢ When making a foreign currency payment in future: buy the foreign currency futures now and
sell the same number of foreign currency futures contracts on the date that you buy the actual
currency. (closing out)

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➢ When receiving a foreign currency in future: sell the foreign currency futures now and buy the
same number of foreign currency futures on the date you sell the actual currency.

STEPS IN CALCULATING FUTURES HEDGE

▪ Identify the exposure : payment or receipt

▪ Choose the contract type :
PAYMENT --- YOU NEED THE CURRENCY : ENTER A FUTURES CONTRACT TO BUY THAT
CURRENCY IN FUTURES CONTRACT. CHECK IF THE CURRENCY IS AVAILABLE BY LOOKING
AT THE CURRENCY OF THE CONTRACT SIZE, DO THE OPPOSITE.

RECEIPT------ YOU HAVE THE CURRENCY: ENTER A FUTURES CONTRACT TO SELL THAT
CURRENCY. CHECK IF THE CURRENCY IS AVAILABLE BY LOOKING AT THE CURRENCY OF
THE CONTRACT SIZE, DO THE OPPOSITE.
contract to buy or sell futures. For simplicity you enter a contract to sell now if you are
hedging a future decrease in value (receipt) and you enter a contract to buy now if you
are hedging a future increase in value (payment). So I can say enter a contract to sell
futures, if you are hedging a Receipt and enter a contract to buy futures, if you are
hedging a payment provided the currency is available in the market. (currency is
available in the market, if the exposure to be hedged is in same currency with the contract
size of the futures contract).
Where the currency is not available, then the opposite corresponding transaction would
be chosen. For example, if I want to hedge a $ receipt exposure against depreciating
over the £, I am supposed to enter a contract to sell $ futures now but if the contract
size is in £, we cannot sell $ futures, so we rather choose a contract to buy £ futures (in
buying the £ futures, we end up selling the $)
▪ Contract Expiry date: the contract to be chosen is the first contract after the transaction
date. (the contract must be after the exposure transaction date)
▪ Opening Futures price: this is the price given for any futures contract chosen. Where the
opening price and settlement price are given. The settlement price should be chosen.
▪ Number of contracts = exposure / contract size. To calculate number of contracts both
the exposure and contract size should be in same currency. Where the currencies differ,
the currency of the exposure should be converted using the opening futures price of the
contract chosen.
▪ Identify the closing futures price which may be given or calculate using the knowledge
of unexpired basis.
Where the closing futures price is not given, we can use a lock up exchange rate to
determine the hedged amount based on our knowledge of basis.
Basis is the difference between the spot rate now and the opening futures price while
unexpired basis is the basis that has not been utilised by the transaction date
▪ LOCK UP EXCHANGE RATE = opening futures price ± unexpired basis

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Calculate the basis = spot rate – opening futures price (covers from today to the contract
end)
Calculate unexpired basis = months remaining after transaction period / months covered
under the basis x basis calculated above
Calculate the lock up exchange rate = opening futures price ± unexpired basis
Use the lock up exchange rate to determine the final hedged outcome

The Lock up rate is advisable for exam purposes.

You can also use the approach below

▪ Determine the Futures profit or loss considering the buying price and the selling price =
(closing futures price – opening futures price) x contract size X number of contracts or
(closing futures price – opening futures price) x tick value x number of contracts
▪ Determine the net outcome =( receipts + profit) or (receipt – loss) or (payments – profit)
or (payments plus loss). The currency used for this calculation will be opposite to the
currency of the receipt or payment being hedged. The value of the futures profit or loss
will also have to be converted using the closing spot rate.

ADVANTAGES OF CURRENCY FUTURES

1. The transaction costs are usually lower than the forward contracts
2. The exact date of receipt or payment of the currency does not have to be known because the
futures contract does not have to be closed out until the actual cash receipt or payment is made
3. Counterparty risk should be reduced and buying & selling contracts easier since it is done on
exchange regulated markets.
4. There is a single specified price determined by the market and not the negotiating strength of the
customer
5. Reversal can easily take place in the market

DISADVANTAGES OF CURRENCY FUTURES

1. The contracts cannot be tailored to the users exact requirements

2. Hedge inefficiencies are caused by having to deal in a whole number of contracts and by basis risk
3. Only a limited number of currencies are the subject of futures contract
4. The procedure of converting between two currencies neither of which is the US dollar is twice as
complex for futures as for a forward contract
5. Using the market will involve various costs including brokers fees
6. Volatile trading conditions on the futures markets mean that the potential loss can be high.

4. CURRENCY OPTIONS

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This is a contract that gives the holder the right but not the obligation to take a particular course of
action at some time in the future (buy or sell a quantity of a particular item on or before a specified
date in the future, at a fixed price that is fixed in the contract). The option could either be a

▪ Financial Option is an option on financial items like currencies, interest rates, share prices
and stock index value
▪ Commodity option is an option on commodities such as wheat, metal , gold or copper
▪ Real options are real choices facing a company when it is considering whether to invest
in a new capital project. It could be to make a further investment if the project is
successful, abandon the investment after it has been started if it appears it will not be
successful or wait before investing instead of investing immediately.

Currency Option protects against adverse exchange rate movements while allowing the investor to take
advantage of favourable exchange rate movements. This is very useful in situations where the cash flow
is not certain to occur.

CALL OPTIONS is an option that gives the Holder the right to purchase the underlying item in option
agreement while PUT OPTIONS gives the Holder the right to sell the underlying item in the option
agreement.

TYPES OF OPTIONS

▪ AMERICAN OPTION is one that can be exercised at any time on or before the expiry date
▪ EUROPEAN OPTION is one that can only be exercised at the expiry date and not before.
▪ BERMUDAN OPTION is one that can be exercised on specific restricted dates only.

TYPES OF OPTION MARKETS

Options can be traded on regulated exchanges (exchange traded options) or over the counter (OTC
options). In an OTC option, buyers and sellers fixes the rate such as caps, floors, collars and so on while
the exchange fixes the strike price. An OTC option is one tailor made to fit a company’s precise
requirements.

The exercise or strike price is the price at which the holder can buy or sell the underlying item.

The seller of the option is the option writer while the buyer is the option holder. Exercise price is the price
with which the future transaction will take place. It is the price with which the prevailing spot rate should
be compared in order to determine whether the option should be exercised or not. The exercise price for
the option may be the same as the current spot rate, or it may be favourable or less favourable to the
option holder than the current spot rate. A long position is a position to buy while a position to sell is
called a short position.

OPTION PREMIUM is the price paid by the holder to the writer for the option whether it is exercised or
not. The premium should be paid in advance and is non-refundable.

The level of the option premiums depend on the following factors:

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▪ The exercise price

▪ The maturity of the option
▪ The volatility of the exchange and interest rate
▪ Interest rate differentials, affecting how much banks charge

EXERCISING OPTIONS

▪ IN THE MONEY (ITM) occurs when the option strike price is more favourable than the market
price
▪ AT THE MONEY (ATM) occurs when the option strike price is equal to the market price.
▪ OUT OF THE MONEY (OTM) occurs when the option strike price is less favourable than the market
price.

VALUE OF OPTION is the difference between the strike price and current market price. A call option will
be exercised if the market price of the underlying item is more favourable than the exercise price of the
option while a put option will only be exercised if the market price is greater than the exercise price of
the option.

Option does not have to be exercised if it is not favourable as long as the premium is paid. Options can be
used to hedge the company against an adverse movement in exchange rates while also allowing them to
take advantage of a favourable movement in exchange rates (an advantage it has over future and forward
contracts)

STEPS IN CALCULATING OPTIONS HEDGE

▪ Identify the exposure : payment or receipt

▪ Choose the contract type :
▪ PAYMENT --- YOU NEED THE CURRENCY : ENTER AN OPTIONS CONTRACT TO BUY (CALL
OPTION) THAT CURRENCY IN OPTIONS CONTRACT. CHECK IF THE CURRENCY IS
AVAILABLE BY LOOKING AT THE CURRENCY OF THE CONTRACT SIZE, DO THE OPPOSITE.

▪ RECEIPT------ YOU HAVE THE CURRENCY: ENTER AN OPTIONS CONTRACT TO SELL (PUT
OPTION) THAT CURRENCY. CHECK IF THE CURRENCY IS AVAILABLE BY LOOKING AT THE
CURRENCY OF THE CONTRACT SIZE, DO THE OPPOSITE.

contract to buy (Call ) or sell (put) Options. For simplicity you enter a contract to sell now
(Put Option), if you are hedging a decrease in value (receipt) and you enter a contract to
buy now (call option), if you are hedging an increase in value (payment). So I can say enter
a contract to sell (Put) options, if you are hedging a Receipt, and you should enter a
contract to buy (call) options, if you are hedging a payment provided the currency is
available in the market. (currency is available in the market, if the exposure to be hedged
is in same currency with the contract size of the options contract).

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Where the currency is not available, then the opposite corresponding transaction would
be chosen. For example, if I want to hedge a $ receipt exposure against depreciating
over the £, I am supposed to enter a contract to sell $ options now but if the contract
size is in £, we cannot sell $ options, so we rather choose a contract to buy £ options (in
buying the £ options, we end up selling the $)
▪ Contract Expiry date: the contract to be chosen is the first contract after the transaction
date. (the contract must be after the exposure transaction date)
▪ Number of contracts = exposure / contract size. To calculate number of contracts both
the exposure and contract size should be in same currency. Where the currencies differ,
the currency of the exposure should be converted using the exercise or strike price of the
contract chosen.
▪ Calculate the premium associated with the contract and strike price chosen
Total premium = premium x contract size x number of contracts
• Appropriate Strike price or exercise price : it is expected that the exercise price would be
given but where it is not given
CALL OPTION: Choose the price that gives the lowest cost after adding strike price to
premium. STRIKE PRICE + PREMIUM = XX (LOWEST COST SHOULD BE CHOSEN)
PUT OPTION: Choose the price that gives the highest return after deducting the
premium from the strike price. (STRIKE PRICE – PREMIUM = XX ( HIGHEST INCOME
SHOULD BE CHOSEN)

▪ Determine the Options profit: an option can only be exercised if it is favourable. So

where it is not favourable, it would not be exercised. The profit is the difference between
the exercise price and the actual price. (loss cannot be made in options).
▪ Determine the net outcome =( receipts + profit) or (payments – profit) . The currency
used for this calculation will be opposite to the currency of the receipt or payment being
hedged. The value of the Options profit will also have to be converted using the closing
spot rate.

5. CURRENCY SWAPS : is an arrangement whereby two organizations or parties contractually

agree to swap interest rate commitments on borrowings in different countries. There are 2
elements in a currency swap
➢ Exchange of Principals in different currencies which are swapped back at the original spot
rate (just like a Forex swap)
➢ Exchange interest rate – timings are dependent on individual contracts

BENEFITS OF SWAP
▪ Flexibility: swaps are easy to arrange and are flexible since they can be arranged in any size and
are reversible
▪ Cost : transaction costs are low since there is no commission or premium to be paid

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▪ Market avoidance: both parties can get the currency they require without subjecting themselves
to the uncertainties of the foreign exchange market
▪ Access to finance: the company can obtain debt finance in another country and currency where
it is little known and may have poorer credit rating.
▪ Financial restructuring: it may be used to restructure the currency base of the company’s
liabilities thereby reducing the exchange rate exposure
▪ Conversion of debt type: it enables the company also convert its interest rate from a fixed rate to
a floating rate and vice versa.
▪ Liquidity improvement; it could be used to absorb excess liquidity in one currency which is not
needed immediately, to create funds in another when there is a need.

DISADVANTAGES OF SWAP
▪ Risk of default by the other party to the swap (counterparty risk); if one party defaults, the other
party faces the risk of making the payment.
▪ Position or market risk: it may increase the financial risk of the company in a bid to make
speculative gains
▪ Sovereign risk; there may be a risk of political disturbances or exchange controls in the country
whose currency is being used for a swap
▪ Arrangement fees: there are fees that would be paid to the intermediary even though he accepts
no liability for the swap.

6. FOREX SWAP is an agreement where parties agree to swap equivalent amount of currency for a
period and then swap them at the end of the period at an agreed spot rate. Swap rate and amount
of currency is agreed between the parties in advance. It is called a fixed rate/fixed rate swap.
OBJECTIVES OF FOREX SWAP
▪ To hedge against Forex risk for a longer period
▪ Allows access to capital markets
▪ It is useful in countries with exchange controls or volatile exchange rates.

ILLUSTRATIONS ON CURRENCY RISK MANAGEMENT

QUESTION 1 {ICAN NOVEMBER 2019 QUESTION 5}
You have worked with a major oil servicing company in Nigeria, with headquarters in the USA,
for the past six years. Recently you completed your ICAN examinations, and have been asked
to join the international treasury department in New York for a two-year attachment.
The company is due to pay a UK supplier the sum of £5 million in three months’ time.
Your team is considering alternative methods of hedging the expected payments against
adverse movements in exchange rate.
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CURRENCY RISK MANAGEMENT

Exchange rate information:

US$ per £1
Spot rate 1.9410 - 1.9531
One –month forward rate 1.9339 - 1.9452
Three – month forward rate 1.9223 - 1.9339

FUTURES MARKET (Contract size of £62,500, Quotation: US$ per £1)

2 month expiry 1.9305
5-month expiry 1.9170

OPTIONS MARKET (£31,250 contract size, premiums are quoted in cents per £1)
CALL OPTION PUT OPTION
Exercise price 2-month expiry 5-month expiry 2-month expiry 5-month expiry
1.9000 2.88 3.55 0.15 0.28
1.9200 1.59 2.32 1.00 1.85
1.9400 0.96 1.15 2.05 2.95
Required
You are required to advise the company which of the following hedging strategies should be
adopted for the payment due in three months. Show all workings.
a. Forward contracts
b. Currency futures
c. Currency options (15 marks)
d. In your personal investment portfolio, you have gone short (i.e you have sold) 110,000
units of Big Bank plc. Call and put options exist on the bank’s shares.
You decide to hedge your position using put options on the bank shares. For the
relevant option, you know that; N(d1) = 0.45
You are required to calculate how many put options you will need to buy or sell in order
to delta-hedge. Be specific (5 marks).

MAR/JUNE 2016
It is expected that Lirio Co will receive Euro (€) 20 million in three months’ time from the sale of its investment. The
€ has continued to remain weak, while the $ has continued to remain strong through 2015 and the start of 2016.

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The financial press has also reported that there may be a permanent shift in the €/$ exchange rate, with firms facing
economic exposure. Lirio Co has decided to hedge the € receipt using one of currency forward contracts, currency
futures contracts or currency options contracts.
The following exchange contracts and rates are available to Lirio Co.
Per €1
Spot rates $1·1585 – $1·1618
Three-month forward rates $1·1559 – $1·1601

Currency futures (contract size $125,000, quotation: € per $1)

March futures €0·8638
June futures €0·8656

Currency options (contract size $125,000, exercise price quotation € per $1, premium € per $1)
Calls Puts
Exercise price March June March June
0·8600 0·0255 0·0290 0·0267 0·0319
It can be assumed that futures and options contracts expire at the end of their respective months. Assume that today
is 1 Mach 2016.
Required
Advise Lirio Co on, and recommends, an appropriate hedging strategy for the Euro (€) receipt it is due
to receive in three months’ time from the sale of the equity investment; (14 marks)

CMC CO: MOCK EXAM 2 BPP

CMC is a large listed company based in Switzerland and uses Swiss Francs as its currency. It imports tea, coffee and
cocoa from different countries and sells its blended products to supermarkets and large retailers worldwide. They intend
setting up a treasury function to manage their foreign currency exposures using derivative products.
They want you to assist with how a payment of US$5,060,000 which is due in 4 months’ time will be hedged using the
following additional information:
Current Spot rate US$1.0635 per CHF1
There is a forward rate between the US$ and the CHF of US$1.0677 per CHF1.
Current annual inflation rate in the US is three times higher than Switzerland.
EXCHANGE TRADED CURRENCY FUTURES
Contract size CHF125,000 price quotation : US$ per CHF1
3-month expiry 1.0647
6 month expiry 1.0659
EXCHANGE TRADED CURRENCY OPTIONS
Contract size CHF 125,000, exercise price quotation: US$ per CHF1, premium: cents per CHF1

CALL OPTIONS PUT OPTIONS

Exercise price 3-month expiry 6-month expiry 3-month expiry 6-month expiry
1.06 1.87 2.75 1.41 2.16
1.07 1.34 2.22 1.88 2.63

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CURRENCY RISK MANAGEMENT

It can be assumed that futures and options contracts expire at the end of the month and transaction costs related to
these can be ignored.
Required
Advise CMC Co on an appropriate hedging strategy to manage the foreign exchange exposure of the US$ payment
in 4 months’ time. Show all relevant calculations, including the number of contracts bought or sold in the exchange
traded derivative markets. (15 marks)

JUNE 2004 EXAMS

Assume that it is now 1 July, Polytot plc, a UK based multinational company, has received an export order valued at
675 million pesos from a company in Grobbia, a country that has recently been accepted into the World Trade
Organization, but which does not yet have a freely convertible currency.
The Grobbian company only has sufficient US$ to pay for 60% of the goods, at the official US$ exchange rate.
The balance would be payable in the local currency, the Grobbian peso, for which there is no official foreign exchange
market. Polytot is due to receive payment for four months’ time and has been informed that an unofficial market in
Grobbian peso exists in which the peso can be converted into pounds. The exchange rate in this market is 15% worse
for Polytot than the ‘official’ rate of exchange between the peso and the pound.
Exchange rates

$/£
Spot 1.5475 – 1.5510
3 months forward 1.5362 - 1.5398
1 year forward 1.5140 – 1.5178

Official Spot rate; Grobbian peso/£ 156.30

Official Spot rate Grobbian peso/ $ 98.20

PHILADELPHIA SE $/£ OPTIONS £31,250 (premium : Cents per pound)

CALLS PUTS
SEPT DEC MARCH SEPT DEC MARCH
1.5250 2.95 3.35 3.65 2.00 3.25 4.35
1.5500 1.80 2.25 2.65 3.30 4.60 5.75
1.5750 0.90 1.40 1.80 4.90 6.25 7.35
1.6000 0.25 0.75 1.10 6.75 8.05 9.15

$/£ CURRENCY FUTURES (CME, £62,500)

September 1.5350
December 1.5275

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Assume that options and futures contracts mature at the relevant month end.
Required
Calculate the expected revenues in £ sterling from the sale of the company in Grobbia as a result of each of these
hedges. Provide a reasonable recommendation as to which hedge should be selected.

INTEREST RATE SWAPS is an agreement whereby the parties to the agreement exchange interest
rate commitments over an agreed period. A swap between floating rate interest and fixed rate interest is
known as a “plain vanilla” or generic swap”. The variable rate included in a swap is LIBOR (London inter-
bank offered rate). This benchmark of interest is the rate paid between banks.

ILLUSTRATION ON INTEREST RATE SWAPS

Gemma wants to borrow £20 million for five years, with interest payable at six monthly intervals. It can borrow
this money from a bank at a floating rate for LIBOR plus 1%, but wants to obtain a fixed rate for the full five
year period. A swaps bank indicates that it will be willing to receive a fixed rate of 9.7% in exchange for
payments of six month LIBOR. Evaluate the hedge if the LIBOR is 11% or 8.8%.
ILLUSTRATION (ICAN PAST QUESTION NOVEMBER 2020)
a. What risks might an industrial company face as a result of interests movements {8 marks}
b. A plc wants to borrow N200 million for five years with interest payable at six-monthly intervals. It can
borrow from a bank at a floating rate of NIBOR plus 1% but wants to obtain a fixed rate for the full
five-year period. A swap bank has indicated that it will be willing to receive a fixed rate of 8.5% in
exchange for payments of six-month NIBOR.
Required :
Calculate the fixed interest six-monthly payment with the swap in place {4 marks}
c. Calculate
I. The interest payments if NIBOR is 10% {4 marks}
II. The interest payments if NIBOR is 7.5% {4 marks}

{Total 20 Marks}
ILLUSTRATION ON SWAP [ June 2012 amended]
Whyte Group Limited, a listed company, recently issued debt finance to acquire assets in order to increase
its activity levels. This debt finance is in the form of a floating rate bond, with a face value of $320 million,
redeemable in 4 years. The bond interest, payable annually, is based on the spot yield curve plus 60 basis
points. The next annual payment is due at the end of year one.
Whyte Group Limited[WGL] is concerned that the expected rise in interest rates over the coming few years
would make it increasingly difficult to pay the interest due. It is therefore proposing to either swap the floating
rate interest payment to a fixed rate payment, or to raise new equity capital and use that to pay off the floating
rate bond. The new equity capital would either be issued as rights to the existing shareholders or as shares
to new shareholders.

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Sky Bank has offered Whyte Group Limited an interest rate swap, whereby WGL would pay Sky Bank interest
based on an equivalent fixed annual rate of 3.761/4% in exchange for receiving a variable amount based on
the current yield curve rate. Payments and receipts will be made at the end of each year, for the next four
years. Sky Bank will charge an annual fee of 20 basis points if the swap is agreed and will also guarantee
the swap. The current annual spot yield curve rates are as follows:
YEAR 1 2 3 4
RATE 2.5% 3.1% 3.5% 3.8%
The current annual forward rates for two, three and four are as follows:
YEAR 2 3 4
RATE 3.7% 4.3% 4,7%
Required:
a. Based on the above information, calculate the amounts WGL expects to pay or receive every year
on the swap excluding the bank fee of 20 basis points
b. Explain why the fixed annual rate of interest of 3.761/4% is less than the 4 year yield curve rate of
3.8%
c. Demonstrate that WGL’s interest payment liability does not change , after it has undertaken the
swap, whether the interest rates increase to 5% or reduce to 3%.
d. Discuss the advantages and disadvantages of the swap for Whyte Group Limited.

ILLUSTRATION ON SWAP BETWEEN TWO COMPANIES

Hankali plc and Bakomi plc want to raise ₦100m five year loans. Bakomi wants to borrow at a fixed rate of
interest, wanting to have a certainty about its future interest liabilities. Hankali wishes to borrow at a floating
rate because its treasurer believes that interest rates are likely to fall in the future.
The current borrowing rates applicable to the two companies in the cash market are as follows:
Floating Fixed
HANKALI NIBOR + 1% 14%
BAKOMI NIBOR + 2% 15.75%
Sharp Bank has agreed to arrange an interest swap for three years between the two companies at a one off
fee of ₦50,000 each.
Required
a. Advise the organization if an interest rate swap would be beneficial showing how it would work and
any benefit for each of the three years, if it is agreed that any benefit would be shared equally by
both companies (10 marks)

ILLUSTRATION ON SWAP BETWEEN TWO COMPANIES [DEC 2014 AMENDED]

Keshi can borrow the funds at a variable rate of LIBOR plus 40 basis points or a fixed rate of 5.5%. LIBOR
is currently 3.8% but Keshi feels that this could increase or decrease by 0.5% over the coming months.

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CURRENCY RISK MANAGEMENT

Razu bank has offered Keshi Co a swap on a counter party variable rate of LIBOR plus 30 basis points or a
fixed rate of 4.6%, where Keshi Co receives 70% of any benefits accruing from undertaking the swap, prior
to any bank charges. Razu bank will charge Keshi 10 basis points for the swap.
Based on the interest rate swap, recommend what the effective rate of hedging the $18,000,000 loan.
ILLUSTRATION (MAY 2017 ICAN PAST QUESTION)
Large plc(LP) wishes to borrow N200 million for five years to finance the purchase of new non-current assets.
The preference of the company’s directors is that these funds are borrowed at a fixed rate of interest. The
company’s long term debt is currently rated BBB, meaning LP would have to pay 6.5% per annum for fixed
rate borrowing. Alternatively, LP could borrow at a floating rate i.e, the prime lending rate (PLR) + 2.25% at
the present time.
The directors of LP have recently been informed by its bank that TK plc, is also currently looking to borrow
N200 million for five years at a floating rate of interest and its AA rating gives it access to floating rate
borrowing at PLR + 1.50% per annum. TK plc would pay 5.5% per annum for fixed rate borrowing at the
present time.
Required :
a. State five reasons that a company might have for entering into an interest rate swap (5 marks)
b. Show how an interest rate swap could be used to the equal benefit of both companies, assuming
that the terms of the swap agreement are such that LP’s swap payment to TK plc is to be 5.5% fixed
per annum (7 marks)
c. Identify, with a supporting brief explanation, which of the two companies would be disadvantaged, if
PLR were to fall consistently within the five year terms of the interest rate swap (1 mark)
d. Identify two risks that both companies will face, should they decide to enter into the interest rate
swap agreement (2 marks)

GRACE MAKES THE DIFFERENCE 23

RELEVANT APPROACH TO BOND VALUATION

BOND VALUATION
Bonds and their variants such as loan notes, debentures and loan stocks are IOUs issued by
Government and Corporations as a means of raising debt finance. A bond is an instrument
requiring the issuer (debtor or borrower) to repay to the lender (investor/holder) the amount
borrowed plus interest over some specified period of time.
Bonds are usually called fixed income or fixed interest securities to distinguish them from
equities as they give fixed returns to investors. Plain vanilla bonds are bonds which make
regular interest rates and redemption value on maturity.
The main features of a bond or debenture are discussed below.
▪ Par value of a bond is the face value, nominal value or stated amount of the bond. It
is the price at which the bond was initially registered and issued. It is usually N100 or
N1,000.
▪ Interest rate is fixed and paid on the face value. The interest rate is also known as
the coupon rate. The interest payment is the amount payable as returns to the debt
holder {Interest payment = interest rate x face value}. It is tax-deductible. It is usually
stated per annum and assumed to be paid in same manner. {care should be taken
where interest is paid otherwise}
▪ Maturity is the period for which the bond needs to be repaid. It is also called the
redemption period of the bond.
▪ Redemption value is the value that a bond-holder will get on maturity. The redemption
value may be at par, or at a premium (more than par value} or at a discount {less than
the par value}.
▪ Market value is the price at which the bond is currently sold or bought in the market.
It may be different from the par value or redemption value.

TYPES OF BONDS
A discount bond is one in which the market value of the bond is less than the par value but
the yield is higher than the coupon rate.
Any bond issued at a price lower than the face value is known as a Discount Bond.
PURE DISCOUNT BONDS are also called deep-discount bonds or zero-coupon bonds.
Zero coupon bonds are bonds that does not pay any interest during their life but are issued
at a deep discount to their face value. Investors are attracted by the capital gain on maturity.

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A deep discount bond is a bond issued at a deep discount with low interest paid annually
Premium bonds are bonds having a market value greater than its par value.
OPTION BASED BONDS
A Callable bond is a bond that gives the issuer {Government or Company} the right but not
the obligation to repurchase the bond at a pre-determined price (call price) at a certain time
(call date). This bond is risky to the investor, it attracts a higher interest rate.
A Putable bond is one in which the bond holder {investor} has the right but not the obligation,
to sell the bond to the issuer at a pre-determined price. This bond is less risky to the investor,
it attracts a lower interest rate.
Perpetual Bonds refer to bonds with indefinite life and therefore no maturity value. They are
also called consols or irredeemable bonds.
A floating rate bond is a bond whose interest rate fluctuates with shifts in the general level
of interest rates.
Convertible bonds are bonds that gives the holder the right but not the obligation to convert
to ordinary shares at an agreed rate in the future.
Straight bonds / redeemable bonds/ traditional bonds are bonds that have a clearly
specified date of maturity and redemption value. {it is also called a non-convertible bond}
VALUATION OF BONDS
MARKET PRICE OF BOND / ISSUE PRICE/ MARKET VALUE/ THEORETICAL PRICE
Market price of a bond is the present value of all future cashflows (interest and
redemption value) discounted at the cost of debt.
The price of any asset is equal to the present value of the expected cash-flows from the
asset{Fundamental theory of valuation} (the expected cash flows are annual coupons
from year 1 to maturity date and the redemption value at maturity) discounted at a
suitable discount rate. The redemption value could be at par, premium or discount.
The market value of a bond is the present value of the future cash flows that must be paid to
service the debt, discounted at the lender’s required rate of return {pre-tax cost of debt/IRR}.
The appropriate discount or capitalization rate would depend upon the risk of the bond, the
Yield to maturity/IRR is usually used. (calculation of YTM would be seen later}. The discount
rate is the interest rate that investors could earn on bonds with similar characteristics.

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The yield is expected to be given but where it is not given but the credit rating is given,
the yield would-be Risk-free rate + credit spread {note that tax would not be deducted
because the required yield is the pre-tax yield}
By comparing the present value of a bond with the current market value, it can be
determined whether the bond is overvalued or undervalued. The value of the bond
depends upon the bond’s interest rate. Bond values declines with rising interest rate (discount
rate) because the bond’s cash flows {interest and principal repayment} are discounted at a
higher interest rate. The market interest rate is also called the market yield and is usually
used as the discount rate.
The market value of a zero-coupon bond is the present value of the bond’s redemption
value since it only has one cash flow. {does not pay interest}
BOND VALUES AND SEMI-ANNUAL INTEREST PAYMENTS
It is usually assumed that interest is paid annually but where this is not the case {interest paid
in a manner that is not annually such as semi- annually, quarterly or monthly}, The period
would need to be adjusted as well as the interest rates and discount rates to refer the
payment nature of the bond.
For instance, if payment is semi-annually that is twice a year, the period would be current
period x 2, the discount and interest rate would be divided by 2.
If it is monthly, the multiplier and divisor would be 12, and if it is quarterly 4.
SCENARIO 1
a. What is the current market value of a bond with a face value of N1,000 and 8% annual
coupon, if the bond has yield to maturity of 10%, redemption value of 5% premium to
the par value and a maturity of 5 years. Comment on your result.
b. Would your answer be different if the coupon on the bond in “a” was paid semi-
annually?
c. What is the market value of a N1,000 par value zero coupon bond with an 8% yield
to maturity due to mature 15 years from today. The average interest rate in the country
is 7.5% (assuming semi-annual compounding) and the redemption value is at par.
▪ If the interest rate (YTM) remains constant for the next 4 years, what would the
price be in 4 years time? (assuming semi-annual compounding)
▪ If the interest rate (YTM) rises to 10%, what will be the price of the zero- coupon
bond in 4 years time? (assuming semi-annual compounding)

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SOLUTION
YEAR CASHFLOW N DCF @10% PV N
1-5 Interest 80 3.791 303.28
5 Redemption value 1,000 x 1.05 = 1,050 0.621 652.05

Market price 955.33

This is a discount bond as the market price is lower than the par value
B PART OF THE QUESTION
Period = 5 x 2 = 10, interest = 8/2 = 4% x 1,000 = N40, DCF = 10/2 = 5%
YEAR CASHFLOW N DCF @5% PV N
1 - 10 Interest 40 7.722 308.88
10 Redemption value 1,050 0.614 644.70

Market price 953.58

C PART OF THE QUESTION

Zero coupon bond does not pay interest, that does not exempt it from the effect of semi-
annual compounding. Period = 15 x 2 = 30 years and DCF will be 8/2 = 4%
YEAR CASHFLOW N DCF @4% PV N
1 - 30 Interest 0 …….. 0
30 Redemption value 1,000 0.308 308

Market price 308

D PART OF THE QUESTION

YEAR CASHFLOW N DCF @4% PV N
1-8 Interest 0 6.733 0
8 Redemption value 1,000 0.731 731

Market price 731

E PART OF THE QUESTION

YTM IS 10% = 10/2 = 5% and 4 x 2 = 8 years because of semi-annual compounding
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YEAR CASHFLOW N DCF @5% PV N

1-8 Interest 0 6.463 0
8 Redemption value 1,000 0.677 677

Market price 677

BOND YIELDS AND PRICING

There is an inverse relationship between the yield of a bond and its price or value. The
higher the rate of return (or yield) required, the lower the price of the bond and vice versa. As
the yield on a bond increases, the less attractive the price of the bond (what people are willing
to pay). The above relationship is based on the fact that interest is fixed and investors would
prefer to pay lower price so as to get higher yield. The relationship is not linear but convex to
the origin.
In the bond market, investment decisions are made on the basis of bond’s yield rather
than its price because the bond yield affects the price at which it trades and serves as
an important measure of potential or expected return.
For instance if a company’s current Yield is = interest / mkt price = 7/100 = 7%, in order to be
competitive, the company may have to reduce the price of the bond to 90 = 7/80 = 8.8% so
as to give a yield higher than other alternative bonds. {Bond prices have an inverse or
indirect relationship with the yield}
Another bond = 8/100 = 8% yield
Nominal yield is the coupon rate of the bond while Current yield relates the coupon interest
to the market value (current yield = annual coupon / price). Yield To Maturity (YTM)
considers both the interest income, capital gains/losses and also the timing of cash flows
received over the life of an issue (it can be called the IRR of a bond).
GROSS REDEMPTION YIELD (GRY) or YIELD TO MATURITY (YTM) is the rate of return
at which the sum of the present values of all future income streams of the bond (interest and
redemption amount) is equal to the current price {Outflows} of the bond. It is the measure of
a bond’s rate of return that considers both the interest income and any capital gain or loss.
YTM is the bond’s internal rate of return.
YTM has the following assumptions
1. All coupons can be reinvested at the YTM
2. The bond is held to maturity
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RELEVANT APPROACH TO BOND VALUATION

3. All coupons are received at a prompt and timely fashion

4. The returns are gross returns (no tax or cost deduction}

YTM can be calculated when the current price, interest payments and redemption values are
known.
NOMINAL YIELD
This is the annual interest on the bond’s par value. It is same as the coupon rate. {interest /
par value}
CURRENT YIELD
This is the annual interest divided by the bond’s current value. It considers only the annual
interest and not capital gain or loss. {interest / market value}
YIELD-TO-CALL & YIELD -TO- PUT
This refers to the return on a bond that has provision to be redeemed or called or bought back
before maturity {Callable & Putable}. The basis for calculating YTM is same as yield-to -call
just that the call period is different from the maturity period & the call value may be different
from the redemption value.
YIELD TO PUT arises when a bond can be sold back to the issuer at the option of the holder.
It is calculated in same way as the YTM but using the putable date and value.
QUESTION ON YIELD TO CALL
A bond is expected to mature in 10 years. The bond has a face value of N1,000 and an 8%
coupon rate paid annually. The price of the bond is N1,100. The bond is callable in 5 years
time at a call price of N1,050.
a. Calculate the yield to call
b. Calculate the yield to call if the interest was paid semi-annually

SOLUTION
YIELD TO CALL = IRR
Market price = N1,100; callable period = 5 years, callable value = N1,050, Interest = 8% x
N1,000 = N80
year N Dcf @ 8% PV N Dcf @ 5% PV
0 Mkt price (1,100) 1.000 (1,100) 1.000 (1,100)
1-5 Interest 80 3.993 319.44 4.329 346.32
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5 RV 1,050 0.681 715.05 0.784 823.2

(65.51) 69.52
IRR = LR + {NPV LR / NPV LR – NPV HR} X [HR – LR]
= 5 + {69.52/ 69.52 + 65.51} X {8 – 5} = 6.54%
QUESTION ON YIELD TO PUT
A bond with a par value of N1,000 was issued 18 years ago. It has a current maturity of 10
years and a current market value of N895. The bond pays annual coupon of 7% and it is
putable at par in 4 years. What is the yield to put?
SOLUTION
year N Dcf @ 7%
PV N Dcf @ 10% PV
0 Mkt price (895) 1.000 (895) 1.000 (1,100)
1–4 Interest 70 3.387 237.09 3.170 221.90
4 RV 1,000 0.763 763 0.683 683
105.09 (195.10)
IRR = LR + {NPV LR / NPV LR – NPV HR} X [HR – LR]
= 7 + {105.09/ 105.09 + 195.10} X {10 – 7} = 8.05%
QUESTION ON YIELD TO MATURITY
A bond matures in 5 years and pays a 12% annual coupon. If the current market value of the
bond is N1,120. Calculate the YTM and explain to the Board the implication of the coupon
paid semi-annually.
SOLUTION
year N Dcf @ 12%PV N Dcf @ 10% PV
0 Mkt price (1,120) 1.000 (1,120) 1.000 (1,120)
1–5 Interest 120 3.605 432.6 3.791 454.92
5 RV 1,000 0.567 567 0.621 621
(120.4) (44.08)
IRR = LR + {NPV LR / NPV LR – NPV HR} X [HR – LR]
= 10 + {- 44.08 / -44.08 + 120.4} X {12 – 10} = 8.84%

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BOND VALUE AND AMORTIZATION OF PRINCIPAL

A bond may be amortized every year, that is, repayment of principal every year rather than at
maturity. In this case, the principal will decline with annual payments and interest will be
calculated on the outstanding amount. The cash flows of the bonds will be uneven.
YIELD CURVE
This is simply a graph which shows the “term structure of interest rate” {the relationship
between the yield and the maturity} for gross yields and risk free debt securities.
USING THE YIELD CURVE TO DERIVE A FORWARD RATE
If an investor could invest N10,000 for one year or two years with the following annual spot
yields.
Maturity Yield
1 year 3%
2 years 3.2%
Determine the forward rate for the second year
Invest for one year = N10,000 {1.03} = N10,300
Invest for two years = N10,000(1.032)2 = N10,650.24
The extra return for investing for two years is 10,650.24 – 10, 300 / 10,300 = 3.4%
That 3.4% is known as the forward rate.
Forward rate can also be calculated as {1 + rateyear after}n / {1 + rateyear before}n - 1 ;
where n represents the year
In this scenario it will be Forward rate = {1 + rate2}2 / {1 + rate1}1 - 1 = {1.032}2 / 1.03} – 1 =
3.4%
SCENARIO ON BOND VALUATIONS USING THE YIELD CURVE
A company wants to issue a bond that is redeemable at par in four years and pays interest at
6% of nominal value.
The annual spot yield curve for a bond of this class of risk is as follows:
MATURITY YIELD
ONE YEAR 3%

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TWO YEARS 3.5%

THREE YEARS 4.2%
FOUR YEARS 5%
Calculate the
a. forward rates for each of the years
b. price that the bond could be sold for (amount company could raise)
c. and then calculate the gross redemption yield (yield to maturity, cost of debt)

SOLUTION
YEAR FR = {1 + RATE2)2/ {1 + RATE 1)1 – 1 FORWARD RATE
1 3%
2 [(1 + 0.035)2 / {1 + 0.03)1 } – 1 4%
3 (1.042)3 / 1.035)2 - 1 6%
4 (1.05)4 / (1.042)3 - 1 7%

MARKET PRICE
Maturity = 4 years, interest = 6% x N100 = N6, Redemption value = N100, yield = different
yields annually
YEAR N DCF PV
1 Interest 6 @3% YR 1 = 0.971 5.83
2 Interest 6 @3.5% YR 2 = 0.934 5.60
3 Interest 6 @4.2% YR 3 = 0.884 5.30
4 Interest + redemption value 106 @5% YR 4 =0.823 87.24
Market price 103.97

YTM CALCULATION
YEAR N DCF @6% PV DCF @4% PV N
0 Mkt price (103.97) 1.000 (103.97) 1.000 (103.97)
1-4 Interest 6 3.465 20.79 3.630 21.78
4 RV 100 0.792 79.2 0.855 85.5
(3.98) 3.31
IRR = 4 + { 3.31 / 3.31 + 3.98} X {6 – 4} = 4.91%

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SCENARIO ON YIELD CURVE

Where the risk free rate is not given {that is no yield curve}, it can be calculated from the
information on similar bonds in the scenario. The fact that a Government issues more than
one bond implies that the risk-free rate is not given.
The major factor to note here is that market price is the Present value of all cash flows
associated with the bond and the bonds are in same risk.
ILLUSTRATION ON CONSTRUCTION OF YIELD CURVE
There are three bonds in issue for a given risk class by the Government. All three bonds pay
interest annually in arrears and are to be redeemed at par at maturity. Relevant information
about the three bonds is as follows
BOND MATURITY COUPON RATE MARKET VALUE
A 1 YEAR 6.0% N102
B 2 YEARS 5.0% N101
C 3 YEARS 4.0% N97
Required
Construct the yield curve that is implied by the data above
SOLUTION
The yield curve of each year can be calculated independently using Bonds with that maturity
YIELD CURVE FOR YEAR 1 USING BOND A
YEAR N DCF PV
1 Interest + RV = 6 + 100 106 1/1+R 102
Market price 102
106 x 1 / 1 + R = 102
106 = 102 {1 + R}
1 + R = 106/102
1 + R = 1.0392
R = 1.0392 – 1 = 3.92%
YIELD CURVE FOR YEAR 2 USING BOND B

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YEAR N DCF PV
1 Interest 5 @3.92% YR 1 = 0.962 4.81
2 Interest + RV = 5 + 100 105 1 / [1 + R]2 96.19
Market price 101
PV in year 2 = mkt price – PV in year 1 = 101 – 4.81 = N96.19 {balancing Figure}
105 x [1/ 1 + R]2 = 96.19
105 = 96.19[1 + R]2
[1 + R}2 = 105 / 96.19
[1 + R}2 = 1.092
1 + R = Ꝩ1.092
1 + R = 1.045
R = 1.045 – 1 = 4.5%
YIELD CURVE FOR YEAR 3 USING BOND C
YEAR N DCF PV
1 Interest 4 @3.92% YR 1 = 0.962 3.85
2 Interest 4 @4.5% YR 2 = 0.916 3.66
3 Interest + RV = 4 + 100 104 1 / (1 + R)3 89.49
Market price 97
PV in year 3 = mkt price – PV in year 1 & 2 = 97 – { 3.85 + 3.66)= N89.49{balancing Figure}
104 x [1/ 1 + R]3 = 89.49
104 = 89.49[1 + R]3
[1 + R}3 = 104 / 89.49
[1 + R}3 = 1.16
1 + R = 3Ꝩ1.16
1 + R = 1.05
R = 1.05 – 1 = 5%

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WHERE THE INTEREST RATE IS NOT GIVEN

The company has just issued a bond at a market price of ₦125 per nominal. The bond is
expected to be redeemed in 4 years time at par and the YTM is 8%. Calculate the interest
rate on this bond.
SOLUTION
YEAR DCF @ 8% PV N
1 Interest X 0.926 0.926X
2 Interest X 0.857 0.857X
3 Interest X 0.794 0.794X
4 Interest X 0.735 0.735X
4 Redemption value 100 0.735 73.5
73.5 + 3.312X
73.5 + 3.312X = 125
3.312X = 125 – 73.5
X = 51.5 / 3.312 = 15.56
X = 15.56%

TERM STRUCTURE OF INTEREST RATE/ YIELD CURVE

The yield curve is an analysis of the relationship between the yields on debt with different
periods to maturity. It is simply a graph that shows the relationship between the yield and
maturity of a government bond.
A plot of required rates of return (yields) against maturity is called a yield curve. The normal
expectation is that the yield curve will slope upwards because interest yields are normally
higher for longer dated debt instruments. The opposite may happen when interest rates are
expected to rise in the future. When the yield curve is inverse (sloping downwards), this is an
indication that the markets expect short term interest rates to fall at some time in the future.
When the yield curve has a steep upward slope indicates that the markets expect short term
interest rates to rise at some time in the future.
The following points are important about the yield curve
1. Yields are gross yields, ignoring taxation (pre-tax yields)
2. A yield curve is constructed for risk free debt securities such as government bonds.

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RELEVANT APPROACH TO BOND VALUATION

3. Risk free debt is the debt where the investor has no credit risk whatsoever, because it
is certain that the borrower will repay the debt at maturity.

The shape of the yield curve at any point in time is the result of the three following theories
acting together.

WHY AN UPWARD SLOPING YIELD CURVE?

a. EXPECTATIONS THEORY: the normal upward sloping curve reflects the expectation
that inflation levels and therefore interest rates will increase in the future. It implies that
the long-term interest rates will be higher than short term rates.
Downward sloping yield curve or inverted yield curve reflects expectation that
interest rates will fall in the future.
b. LIQUIDITY PREFERENCE THEORY: investors have a natural preference for more
liquid (shorter maturity) investments. They will need to be compensated if they are
deprived of cash for a longer period. Therefore, the longer, the maturity period, the
higher the yield required leading to an upward sloping curve, assuming that the interest
rates were not expected to fall in the future.

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Holding a bond for a longer period exposes you to price risk/ liquidity risk and
so more yield. Rates go up when liquidity is tight and vice versa

c. MARKET SEGMENTATION THEORY; suggests that there are different players in the
short term end of the market and the long term end of the market. Investors are
assumed to be risk averse and invest in segments of the market that match their
liability commitments. For example banks tend to be active in the short term end of the
market and pension funds would tend to invest in long term maturities to match the
long term nature of their liabilities. The supply and demand forces in various segments
of the market in part influence the shape of the yield curve. If there is an increased
supply in the long-term end of the market because the government needs to borrow
more, this may cause the price to fall and the yield to rise and may result in an upward
sloping yield curve.
This theory is based on the demand and supply dynamics of different maturity
segment of the bonds. The supply and demand of bonds of particular maturity
segments is what drives their yield. Higher supply & lower demand implies
higher yield while lower supply & higher demand implies lower yield. Demand
and supply is based on yields and so yields alter the demand and supply of the
bonds.

FLAT YIELD CURVE: A yield curve may be flat if short and long term yields are almost
identical. It is a sign of economic transition either from recession to expansion
BOND DURATION
Duration is the weighted average length of time to the receipt of the bond’s benefits (coupon
and redemption value), the weights being the present value of the benefits involved. Duration
gives each bond an overall risk weighting that allows two bonds to be compared.
Duration is a measure of the average life of a bond, defined as the weighted average of the
times until each payment is made. It is the sensitivity of the price of a bond to changes in in
interest rate, The higher the sensitivity, the higher the duration of a bond. Duration can be
defined as the time to recover one half of the project value. It is a concept widely used by
analysts in the bond markets to measure how long an investor in bonds must wait before his
investment in the bond is recovered.

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PROPERTIES OF DURATION
▪ Longer dated bonds that is bonds with longer maturities will have longer durations
▪ Lower coupon bonds will have longer durations. This is because a higher coupon bond
results in the investor receiving income sooner than a bond with lower coupon with
same redemption.
▪ Bond with lower yields will give longer durations (present value of flows in the future
will rise if yield falls thereby lengthening the duration
▪ The duration of a bond is an indication of the price sensitivity of the bond to a change
in market yields on bonds. A rise in interest rate will lead to a greater fall in the price
of a bond with longer duration.
▪ Duration of a zero coupon bond is same as the maturity of the bond.
▪ It assumes that there is a linear relationship between the Bond’s price and the yield.

MACAULAY DURATION is a concept of duration that looks into the present value of the bond
considering the time value of money. Macaulay Duration shows the weighted average time it
takes to receive the bond’s benefits. Duration is an indication of the pre-sensitivity of the bond
to a change in the market yield. Duration is calculated using the cash flows from the year that
cash flows start to become positive. There is an inverse relationship between lenders required
rate of return and market value. When there is a rise in interest rate, the fall in the price of the
bond is greater for bonds with a higher/longer duration.
Macaulay Duration = weighted present value of cash inflows / present value of the cash
inflows
MODIFIED DURATION is a measure of the sensitivity of the price of a bond to a change in
the interest rate. It is a measure of interest rate risk associated with a bond.
Modified Duration = Macaulay duration/ 1 + Gross redemption yield.
The change in bond price = modified duration x change in yield x current market price
of the bond.
There is an inverse relationship between yield and bond price and so the modified duration
figure is expressed as a negative number.
Modified durations share same properties with Macaulay duration. The higher the modified
duration, the greater the sensitivity of the bond to a change in the yield.

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BENEFITS OF DURATION
▪ Duration allows bonds of different maturities and coupon rates to be directly compared.
This makes decision making regarding bond finance easier and more effective
▪ If a bond portfolio is constructed based on weighted average duration, it is possible to
determine portfolio value changes based on estimated changes in interest rates
▪ Managers may be able to modify interest rate risk by changing the duration of the bond
portfolio

ASSUMPTIONS OF DURATION
▪ There is a small change in yield
▪ There is a parallel change in yield
▪ There is an instantaneous change in yield
▪ The relationship between price and maturity is a flat yield curve.
▪ There is a linear relationship between price and yield on a bond.

LIMITATIONS
The main limitation of duration is that it assumes a linear relationship between interest rates
and price but this is not so as there is a convex relationship between price and yield. Duration
should be treated with care as the more convex the relationship, the more inaccurate the
duration.
The actual relationship between interest rates and bond price is a curve which is convex in
nature. Bonds with greater convexity will have a higher price than bonds with lower convexity.
The lower the coupon rate, the higher a bond’s convexity. Zero coupon bonds have the
highest convexity.
Another limitation is that duration is further distorted by changes in the shape of the yield
curve. Changes in interest rates caused by a change in the shape of the yield curve will result
in duration being a less indicator of the price change.
The assumptions of duration above could also be a limitation where the yield changes are
large, not parallel or non-instantaneous.

SCENARIO ON BOND DURATION

a. Calculate the Macaulay duration of the bonds in the table below if cost of capital is
10%.

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BOND YEAR 1 N YEAR 2 N YEAR 3 N YEAR 4 N Total return

N
BOND 1 10 10 10 110 140
BOND 2 20 20 20 120 180
b. Calculate the Modified duration of the bonds above if the YTM is 12%
c. Compute the change in price of the above bonds based on the modified duration of
the bonds in “b” above if there is an expectation of 1.25% change in interest rate and
the current price of Bond A and B are N135 and N155 respectively. Comment on your
answer.

SOLUTION
YEAR N DCF @ 10% PV W WPV
1 10 0.909 9.09 1 9.09
2 10 0.826 8.26 2 16.52
3 10 0.751 7.51 3 22.53
4 110 0.683 75.13 4 300.52
99.99 348.66
DURATION = WPV / PV = 348.66 / 99.99 = 3.49 years
B PART OF THE ILLUSTRATION
Modified Duration = Macaulay duration / 1 + YTM = 3.49 / 1 + 0.12 = 3.12%
C PART OF THE ILLUSTRATION
% CHANGE IN PRICE = modified duration x % change in yield x current price of bond
% change in price = -3.12% x 1.25% x N135
% change in price = -0.05%
SCENARIO ON DURATION AND CAPITAL INVESTMENT
Calculate the NPV and Duration of the project with the information in the table below with a
cost of capital of 10%.
Year 0 1 2 3 4 5 6
Annual cash flow -200,000 -40,000 30,000 120,000 150,000 100,000 50,000

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DURATION OF A PORTFOLIO
Duration of a portfolio is the weighted average of the durations of the different bonds in the
portfolio.
Duration of a portfolio = W1D1 + W2D2 + W3D3 + W4D4
Weight of each bond = Mv of bond / total market value of the bond
D1, D2, D3 & D4 = duration of each bond in the portfolio
CREDIT RISK
Credit risk also referred to as default risk, is the risk undertaken by the lender that the
borrower will default either on interest payments or on the repayment of principal on the due
date, or on both. Credit risk arises from the inability of a party to fulfill its obligation under the
terms of a contract. The credit risk of an individual or bond is determined by the
following two factors;
PROBABILITY OF DEFAULT is the probability that the borrower or counter party will default
on its contractual obligations to repay its debt.
THE RECOVERY RATE is the fraction of the face value of an obligation that can be recovered
once the borrower has defaulted. When a company defaults, bond holders do not necessarily
lose their entire investment. Part of the investment may be recovered depending on the
recovery rate.
LOSS GIVEN DEFAULT (LGD) is the difference between the amounts of money owed by
the borrower less the amount of money recovered. It is the amount that could be lost if a
borrower defaults. It can also be stated in percentage or calculated absolutely.
The EXPECTED LOSS (EL) from credit risk shows the amount of money the lender should
expect to lose from the investment in a bond or loan with credit risk. The expected loss is
the product of the loss given default and the probability of default.
ILLUSTRATION ON EXPECTED LOSS
A bank has loaned N20,000,000 to Topnotch plc. The bank holds collateral worth
N15,000,000. The probability of default is estimated at 2%. Calculate the expected loss.
Total amount = N20,000,000
Recovery rate = N15,000,000
Loss given default = total amount – recovery rate = 20m – 15m = N5m

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Expected loss = loss given default x probability of default = N5m x 2% = N100,000

CREDIT RISK MEASUREMENT
The most common approach is to assess the probability of default using financial and other
information on borrowers and assign a rating that reflects the expected loss from investing in
the particular bond. This assignment of credit ratings is done by credit rating companies such
as Standard and poor’s, Moody’s investor services or Fitch. These ratings are widely
accepted as indicators of the credit risk of a bond. The table below shows the credit rating
used by Moody’s and Standard and Moody.
STANDARD & MOODY DESCRIPTION OF CATEGORY
POOR
AAA Aaa Prime, highest quality, lowest default risk, highest
safety
AA Aa High grade quality, high safety
A A Upper medium grade quality, adequate safety
BBB Baa Medium grade quality, moderate safety
BB Ba Lower medium grade quality, inadequate safety
B B Speculative, high risk
CCC Caa Poor quality, high default risk and highly speculative
CC Ca Highly speculative, substantial risk
C C Lowest grade quality, in default
For standard and poor’s ratings, those ratings from AA to CCC may be modified by the
addition of a plus or minus sign to show relative standing within the major rating categories.
With Moody’s , numerical modifiers 1,2 and 3 are added to each ratings category from Aa to
Caa. Both credit ratings estimate default probabilities from the empirical performance of
issued corporate bonds of each category.
Sub investment grade bonds or junk bonds is a speculative investment for the lender or
holder.
CREDIT RISK is the risk that a party to whom cash is loaned will not be able to service the
debt. It is also called default risk. The credit risk premium is called a spread and is the
difference between a debt under consideration and the risk free rate of return.
The size of the spread allows for additional risk in the debt that is not risk free. The spread is
higher for debt with higher risk for investors or lenders.

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CRITERIA FOR ESTABLISHING CREDIT RATINGS

1 FIRM SIZE
2 FINANCIAL GEARING
Long term debt/total debt in relation to capital, gearing,
working capital mgt, off balance sheet commitments
3 INDUSTRY RISK Strength of the industry within the country, measured by
the impact of economic forces, demand factors
4 COUNTRY RISK No issuer’s debt will be rated higher than the country of
the origin (sovereign ceiling concept)
5 INDUSTRY POSITION Issuer’s position in the relevant industry compared with
competitors in terms of operating efficiency
6 MANAGEMENT Company’s planning, controls, financial policies and
EVALUATION strategies, overall quality of management and
succession, merger & acquisition performance, financial
result achievement
7 ASSET BACKING Asset management
8 CASH FLOW ADEQUACY Relationship of cash flow to gearing and ability to finance
all business cash needs
9 ACCOUNTING QUALITY Auditor’s qualification of the accounts, accounting
policies for inventory, goodwill, depreciation
10 FINANCIAL FLEXIBILITY Evaluation of financing needs, plans and alternatives
under stress, banking relationship, debt covenant
11 EARNINGS Earnings power including return on capital, pre tax and
PROTECTION net profit margins, source of finance

FACTORS CONSIDERED IN CREDIT RATING

1. Country risk
2. Industry risk
3. Financial flexibility
4. Earnings adequacy
5. Management evaluation

CREDIT MIGRATION
CREDIT MIGRATION is the probability that the credit rating of a borrower may change after
a bond is issued. It tries to explain the fact that a bond issuer may be assigned a different
credit rating by the credit agency after the bond is issued due to economic conditions or
management actions that have made the borrower more or less risky.

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The significance of credit migration lies in the fact that the assignment of a lower credit rating
will decrease the market value of the corporate bond.
CREDIT ENHANCEMENT
This is the process of reducing credit risk by requiring collateral, insurance or other
agreements to provide the lender with reassurance that it will be compensated if the borrower
defaulted. Credit enhancement is a key part of the securitization transaction in structured
finance and is important for credit rating agencies when raising a securitization.
CREDIT SPREADS
This is the premium required by an investor in a corporate bond to compensate for the credit
risk of the bond. The yield to a government bond holder is the compensation for forgoing
consumption today and saving while corporate bond holders require the compensation for
credit risk in addition to the compensation for deferred consumption.
Yield on corporate bond = risk free rate + credit spread
Credit spreads reflect credit risk of a bond and so is inversely related to the credit quality of
the bond
The cost of debt capital is determined by credit rating, maturity of the debt, risk free rate at
appropriate maturity and the corporate tax rate.
The deterioration in the credit quality of a bond, referred to as credit migration, will affect the
market value of the bond.
CREDIT RATINGS
Credit rating companies use financial ratios and other information in order to arrive at the
credit score of a company. One of the models that are employed by credit rating agencies to
link the observed credit rating to financial characteristics of a company is Kaplan-Urwitz
model.
An unsubordinated debt is a debt that has priority claim while subordinated debt has no priority
claim. For quoted companies, it is usually;
Y = 5.67 + 0.011F + 5.13π – 2.36S – 2.85L + 0.007C – 0.87β – 2.90σ
Where Y is the score model
F is the size of a firm measured in total assets in $million
π is the net income/total assets
S is debt status (subordinated debt = 1, other wise 0)

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L is gearing (measured as long-term debt/total assets)

C is interest cover (profit before interest and tax/interest payment)
β is beta of the company using CAPM
σ is the standard deviation of the residual error from the CAPM

ILLUSTRATION 1 ON CREDIT RATING

The following information is available for Topnotch a quoted company.
Total assets = $650m
Net income = $250m
Type of debt = unsubordinated
Long term debt = $200m
Profit before interest and tax = $500m
Interest payments = $40m
Standard deviation = 0.151
In addition, the following CAPM was estimated: RTOPNOTCH = 0.045 + 0.800 x market risk
premium
Topnotch’s volatility and the standard deviation is volatility of the market are 22% and 20%
respectively.
Required
What is the predicted credit rating for Topnotch using the Kaplan-Urwitz model which is
expressed as Y = 5.67 + 0.011F + 5.13π – 2.36S – 2.85L + 0.007C – 0.87β – 2.90σ?
The classification of companies into credit rating categories is done in the following way
Score Rating category
Y ≥ 6.76 AAA
Y ≥ 5.19 AA
Y ≥ 3.28 A
Y ≥ 1.57 BBB
Y≥0 BB

SOLUTION
F= $650m
Π = income / TA = 250/650 = 0.385
S = unsubordinated = 0
L = long term debt / total assets = 200/650 = 0.308
C = EBIT / I = 500/40 = 12.5
B = 0.8
σ =0.151

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Y = 5.67 + [0.011 x 650] + [5.13 x 0.385] –[2.36 x 0] –[2.85 x 0.308] + [0.007 x 12.5] – [0.87
x 0.8] – [2.90 x 0.151] = 12.87

ILLUSTRATION 2 (MAY 2016 ICAN PAST QUESTION)

Skylet Limited is a major player in the aviation industry with a credit rating of AA. The company
plans to raise ₦5 billion from the bond market. The features of the bond are:
Maturity is 4 years, coupon payment: annual, coupon rate is 5% and the redemption value is
at par.
The current annual spot yield curve for government bonds is as follows:
One year 3.3%
Two year 3.8%
Three year 4.5%
Four year 5.3%
The following table of spreads (in basis points) is given for the aviation industry.
RATING 1 YEAR 2 YEAR 3 YEAR 4 YEAR
AAA 12 23 36 50
AA 27 40 51 60
A 43 55 67 80
You are required to calculate
a. Calculate
▪ The issue price of the bond (6 marks)
▪ The yield to maturity (3 marks)
▪ The duration (6 marks)
b. Discuss why conflicts of interest might exist between shareholders and bond holders
(5 marks) (total 20 marks)

ILLUSTRATION 3 (MAY 2018 ICAN PAST QUESTION)

Kazaure Limited has a cash surplus of ₦20m which the financial manager is keen to invest
in corporate bonds. He has identified two potential investment opportunities in two different
companies which are both rated by A by the major credit rating agencies.
BOND A
The issuer plans to raise ₦500m 2-year bond with a coupon rate of 10%. The bond is
redeemable at premium of 8% to nominal value.
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BOND B
The issuer plans to raise ₦800m 3-year bond with a coupon rate of 12% and redeemable
at par.
The annual spot yield curve for government bonds is:
1 year 2 year 3 year
9.50% 10.40% 10.50%

Extract from a major credit rating agency’s website: Table of Spreads (in basis points)
RATING 1 YEAR 2 YEAR 3 YEAR
AAA 6 16 28
AA 15 25 40
A 20 30 50
Required :
a. For a nominal value of ₦1,000, calculate the theoretical issue prices of the two
bonds and indicate how many of each of the bonds Kazaure Limited can buy
assuming it invests in only one of them. Note: calculate Issue prices to the nearest ₦
b. Irrespective of your answer in (a), assume Bond A is issued at ₦1,054 and Bond B is
issued at ₦1,026. Calculate the yield to maturity of each bond at the time of issue.
(5 marks)
c. Calculate the duration of each bond. What does duration measure? (6 marks)
d. If you expect interest rates to increase in the market, which of the two bonds, A or B,
would you like to buy and why? No calculation is required (4 marks) (Total 20
marks)

SOLUTION
CALCULATE THE YIELD ON THE BOND
YEAR 1 2 3
Riskfree rate % 9.5 10.4 10.5
A% 0.20 0.30 0.50
Yield 9.70 10.7 11.0

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MARKET PRICE FOR BOND A

Coupon = 10% x N1,000 = N100
Redemption value = N1,000 x 1.08 = N1,080
Final year = N100 + N1,080 = N1,180
YEAR N DCF PV N
1 Interest 100 @9.7% YR 1 = 0.912 91.2
2 Interest + redemption value 1,180 @10.7% YR 2 = 0.816 962.88
Market price 1,054.08

Number of Bonds = Amount available / market price = N20,000,000 / N1,054.08 = 18,974

bonds
YTM FOR BOND A
YEAR N DCF@ 10% PV DCF@15% PV
0 MKT price (1,054) 1.000 (1,054) 1.000 (1,054)
1-2 interest 100 1.736 173.60 1.626 162.60
2 RV 1080 0.826 892.08 0.756 816.48
11.68 -74.2
YTM = 10 + {11.68 / 11.68 + 74.2} X [15 – 10] = 10.68%
DURATION FOR BOND A
YEAR N DCF @10.68% PV WEIGHT WPV
1 Interest 100 0.904 90.4 1 90.4
2 Interest + RV 1,180 0.816 962.88 2 1,925.76

1,053.28 2,016.16
Duration = WPV / PV = 2016.16 / 1,053.28 = 1.91 Years

MARKET PRICE FOR BOND B

Coupon = 12% x N1,000 = N120
Redemption value = N1,000
Final year = N120 + N1,000 = N1,120

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YEAR N DCF PV N
1 Interest 120 @9.7% YR 1 = 0.912 109.44
2 Interest 120 @10.7% YR 2 = 0.816 97.92
2 Interest + redemption value 1,120 @11% YR 3 = 0.731 818.72
Market price 1026.08

Number of Bonds = Amount available / market price = N20,000,000 / N1,026.08 = 19,492

bonds
YTM FOR BOND B
YEAR N DCF@ 12% PV DCF@ 6% PV
0 MKT price (1,026) 1.000 (1,026) 1.000 (1,026)
1-3 interest 120 2.402 288.24 2.673 320.76
3 RV 1000 0.712 712 0.840 840
-25.76 134.76
YTM = 6 + {134.76 / 134.76 + 25.76} X [12 – 6] = 11.04%
DURATION FOR BOND B
YEAR N DCF @11.04% PV WEIGHT WPV
1 Interest 120 0.900 108 1 108
2 interest 120 0.811 97.32 2 194.64
3 Interest + RV 1,120 0.730 817.6 3 2,452.8

1,022.92 2,755.44
Duration = WPV / PV = 2755.44 / 1,022.92 = 2.69 Years

Duration measures the average period in years it would take a bond to recover its present
value. It also measures the sensitivity of a bond’s price to changes in the interest rates
measured in percentage.
The higher the duration, the more sensitive the bond to changes in interest rate and vice
versa. Bond A in this scenario will be preferred as it has a lower duration of 1.91 years and
so less sensitive to increase in interest rate.
ILLUSTRATION 4 ON BOND VALUATION (MARCH/JUNE ACCA 2017 Q4)
Toltuck Co is a listed company in the building industry which specialises in the construction
of large commercial and residential developments. Toltuck Co had been profitable for many

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RELEVANT APPROACH TO BOND VALUATION

years, but has just incurred major losses on the last two developments which it has completed
in its home country of Arumland. These developments were an out-of-town retail centre and
a major residential development. Toltuck Co’s directors have blamed the poor results primarily
on the recent recession in Arumland, although demand for the residential development also
appears to have been adversely affected by it being located in an area which has suffered
serious flooding over the last two years.
As a result of returns from these two major developments being much lower than expected,
Toltuck Co has had to finance current work-in-progress by a significantly greater amount of
debt finance, giving it higher gearing than most other construction companies operating in
Arumland. Toltuck Co’s directors have recently been alarmed by a major credit agency’s
decision to downgrade Toltuck Co’s credit rating from AA to BBB. The directors are very
concerned about the impact this will have on the valuation of Toltuck Co’s bonds and the
future cost of debt.
The following information can be used to assess the consequences of the change in Toltuck
Co’s credit rating.
Toltuck Co has issued an 8% bond, which has a face or nominal value of $100 and a premium
of 2% on redemption in three years’ time. The coupon on the bond is payable on an annual
basis.
The government of Arumland has three bonds in issue. They all have a face or nominal
value of $100 and are all redeemable at par. Taxation can be ignored on government bonds.
They are of the same risk class and the coupon on each is payable on an annual basis.
Details of the bonds are as follows:
Bond Redeemable Coupon Current market value
$
1 1 year 9% 104
2 2 years 7% 102
3 3 years 6% 98
Credit spreads, published by the credit agency, are as follows (shown in basis points):
Rating 1 year 2 years 3 years
AA 18 31 45
BBB 54 69 86
Toltuck Co’s shareholder base can be divided broadly into two groups. The majority of
shareholders are comfortable with investing in a company where dividends in some years will
be high, but there will be low or no dividends in other years because of the cash demands
facing the business. However, a minority of shareholders would like Toltuck Co to achieve at
least a minimum dividend each year and are concerned about the company undertaking
investments which they regard as very speculative. Shareholders from both groups have
expressed some concerns to the board about the impact of the fall in credit rating on their
investment.
Required:
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RELEVANT APPROACH TO BOND VALUATION

(a) Calculate the valuation and yield to maturity of Toltuck Co’s $100 bond under its
old and new credit ratings. (10
marks)
(b) Discuss the factors which may have affected the credit rating of Toltuck Co
published by the credit agency. (8
marks)
(c) Discuss the impact of the fall in Toltuck Co’s credit rating on its ability to raise
financial capital and on its shareholders’ return. (7
marks)
(25 marks)

CONVERTIBLE BOND
The minimum value of a convertible bond is its value as a straight debt or its
conversion value. Holders will either convert if conversion value exceeds the straight
value debt or let the option lapse and keep the security as a straight debt if it has a
higher value.
The minimum growth in the share price of a company for conversion to be justified is
the growth rate that equates the present value of conversion to the market value of the
convertible debt {if given} or the market value of the straight debt from the conversion
period.
Convertible Debts carry a rate of interest like other bonds but gives the holder the right but
not the obligation to exchange the debentures at an agreed period in the future at an agreed
ratio.
Conversion price [CP] is the nominal value of the convertible debenture that can be
converted into one ordinary share. It represents the effective price paid for the ordinary shares
if conversion occurs. {CP = face value of bond / number of shares into which bond may be
converted}.
Conversion ratio [CR] is the number of ordinary shares into which a convertible bond may
be converted. {CR = face value of bond / conversion price}
ILLUSTRATION
A PLC issues a debenture at par carrying a 9% coupon. The debenture is redeemable in 5
years and each unit of N100 is convertible into 20 ordinary shares at any time prior to

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RELEVANT APPROACH TO BOND VALUATION

redemption. At the date of issue, the yield on comparable non-convertible debenture is 12%
and the company’s shares are quoted at 400k.
Required
a. Calculate the conversion premium on the debenture at the date of the issue and
explain the relationship between the conversion premium and the coupon rate on the
convertible debenture.
b. Assuming a 10% annual growth rate in the share price, calculate the conversion value
of the debenture three years after issue and explain why the debentures market value
is likely to exceed this figure.
c. Explain why the market value of a convertible debenture is likely to be affected by the
dividend policy of the issuing company.
d. Explain what strategy a company might be pursuing when raising capital in the form
of a convertible as distinct from raising straight debt or straight equity.

SOLUTION
PART A
Conversion premium = conversion price – market price / market price]%
Conversion price = Nominal value / conversion ratio = N100 / 20 shares = N5
Conversion premium = N5 – N4 / N4 = 25%
The existence of conversion premium makes it possible for an organization to issue
convertible debt with a lower interest (coupon rate) compared to straight debt. This premium
reflects expectations of increase in share price between the date of issue and the date of
conversion.
Conversion premium makes it possible for the investor to purchase the shares at a discount
to the prevailing market price.

PART B
Conversion value = share price now{1 + g}n x conversion ratio = N4(1.10)3 x 20 = N106.48
The market value of the convertible debt would usually exceed the conversion value because
investors expect continuous growth in share prices above the cost of capital (opportunity cost

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RELEVANT APPROACH TO BOND VALUATION

of funds tied up in the debenture). Market values should trade higher than the conversion
value as an incentive to justify conversion.
PART C
The dividend policy refers to rules and regulations guiding how an organization distributes its
profit between dividend payment and retained earnings. A growth oriented organization will
retain more earnings so as to increase the share price and vice-versa.
The higher the retention, the higher the benefit to convertible debt through increased share
price.
The market value of a convertible debenture is likely to be affected by the dividend policy
because the dividend policy has a significant impact on the share price which is required in
determining market value.
PART D
The strategy is simply one of delayed equity on the assumption that all holders will exercise
their option. They are usually attractive when share prices are low.
It acts as a medium to raise debt that would be redeemed by conversion with little or no impact
on the liquidity. It is a strategy that can help manipulate the gearing ratio of the company and
EPS.

VALUATION OF A CONVERTIBLE BOND

The debt and equity characteristics of the convertible debt produce two methods of valuation
1. Straight debt value: this is the value of the security ignoring the option to convert. This
is the present value of the interest payments and the redemption value discounted at
the required return on an ordinary debenture of same risk.
2. Conversion value is the value of the ordinary shares into which the security could be
converted. CV = share price now {1 + growth rate}number of years to conversion x conversion
ratio { note that P0{1 + g)n is share price in the year of conversion}.
3. The higher of the two is chosen as holders will convert if conversion value exceeds
the straight debt value or keep it as a debt if the straight value is higher.

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ILLUSTRATION
An investor holds a 7% convertible bond. Its conversion option expires in 1 year. The
conversion ratio is 50 shares and the current share price is N1.40. if the security is not
converted, it will be redeemed in 8 years time at par. The current yield on similar ordinary
debentures is 10%.
Required
a. Determine the current straight debt value and conversion value of the security.
b. By how much must the share price increase to induce holders to convert?

SOLUTION
PART A
Current conversion value = share price now x conversion ratio = N1.40 x 50 = N70
Current market value of straight debt is about N84 as computed below
year N DCF@10% PV
1 -8 INTEREST 7 5.335 37,35
8 Redemption value 100 0.467 46.70
84.05
B PART
For holders to convert the conversion value in one year time {conversion period} should be
greater or equal to the value of a straight debt or the current market price of the convertible
debt.
Calculate the value of a straight debt in one year time
year N DCF@10% PV
1 -7 INTEREST 7 4.868 34.08
7 Redemption value 100 0.513 51.30
85.38
PV OF conversion = market value of debt in 1 year time
PV of conversion = share price at conversion x conversion ratio = P0 {1 + g}n x R
N1.40(1 + g) x 50 = 85.38
70(1 + g) = 85.38
1 + g = 85.38/70

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G = 1.22 – 1 = 22%
ADVANTAGES OF CONVERTIBLE BONDS TO THE COMPANY
1. Lower interest rate than a similar debenture
2. The interest is tax deductible
3. It is self liquidating
4. It has fewer covenants.
5. It could be used where shares are under-priced

TO INVESTORS
1. They are able to wait and see how the share price moves before investing in equity
2. There is greater security for their principal compared with equity in the short term
3. Investors receive a minimum income up to the conversion period
4. They will be able to benefit from a rise in the company’s share price
ILLUSTRATION

Topnotch plc has issued 10% convertible loan stock which is due for redemption in 10 years
time {that is year 10}. The option to convert is open only for another two years. If conversion
has not taken place by the end of year 2, the option will lapse. The issue was sold to the
public at a price of N92 for N100 of convertible loan stock. The conversion rate is at present
(beginning of year 1} 25 equity shares for N100 stock.
Non-convertible loan stock in a similar class is presently yielding 12%. The market price of
Topnotch plc equity shares is N3 per share. The market price of the convertible loan stock is
at present N96. The price of the equity shares has been increasing steady over time, reflecting
the performance of the company. The shares currently pay a dividend of N0.25 per share.
Required
a. What is the value of the security as a simple unconvertible loan stock?
b. What is the current minimum value of the convertible, explain why the convertible is
currently trading above the minimum price?
c. What is the expected minimum annual rate of growth in the equity share price that is
required to justify the holder of the convertible loan stock holding unto his security with
the intention of converting into equity before the option expires?
d. What factors determine the market price of the convertible?

SOLUTION

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RELEVANT APPROACH TO BOND VALUATION

YEAR NCF N DCF @12% PV N

1 - 10 INTEREST 10 5.650 56.5
10 Redemption value 100 0.322 32.2

Market price 88.70

B PART OF THE QUESTION

The current minimum value of the convertible is the higher of the conversion value now and
the redemption value as a straight debt.
Value as a straight debt = N88.70
Conversion value = share price x conversion ratio = N3 x 25 shares = N75

C PART OF THE QUESTION

Minimum growth rate that will motivate the investor to convert should be the rate where the
PV of conversion is equal to the market price of the convertible debt.
YEAR N Dcf @12% PV N
1 Interest 10 0.893 8.93
2 interest 10 0.797 7.97
2 Conversion value X 0.797 0.797X
Market price 16.9 + 0.797X
16.9 + 0.797X = N96
0.797X = 96 – 16.9
Conversion value ;X = 79.1 / 0.797 = N99.23
P0[1 + g]n x R = conversion value
3[1 + g]2 x 25 = 99.23
75[1 + g]2 = 99.23
[1 + g]2 = 99.23 / 75
[1 + g]2 = 1.32
1 + g = Ꝩ1.32

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G = 1.15 -1 = 15%
D PART OF THE QUESTION
▪ The share price ; as the share price increases, the value of the convertible increases
▪ The time to expiry of the option to convert: the longer the period of conversion will
mean a higher value for the convertible debt.
▪ The conversion price – The lower the conversion price, the higher the value of the
convertible
▪ Risk associated with the company’s shares : the higher the risk, the higher the value
▪ The dividend paid on the shares: the higher the dividend paid, the lower the value of
the convertible debt.
▪ The expected return on the shares – the higher the return, the higher the value of the
convertible debt

ILLUSTRATION 5 (NOVEMBER 2016 ICAN PAST QUESTIONS)

Honey Comb Plc, has issued 10% convertible loan stock which is due for redemption in 10
years’ time i.e December 31, 2025. The option to convert is open only for another two years.
If conversion does not take place by December 31, 2017, the option will lapse. The issue was
sold to the public at a price of ₦920 for ₦1,000 of convertible loan stock. The conversion rate
at January 1, 2016 was 250 equity shares for ₦1,000 of stock. Non –convertible loan stock
in a similar risk class is presently yielding 12%. The market price of Honey Comb Plc equity
shares has been increasingly steadily over time reflecting the performance of the company.
The shares currently pay a dividend of ₦0.30 per share. The current price of the convertible
security is ₦960 and each share is currently valued at ₦3.00. A holder of the convertible loan
stock is considering whether to sell his holdings or continue to hold the stock. Ignore taxation,
while answering the questions.
Required :
a. What is the value of the security as simple unconvertible loan stock? (5 marks)
b. What is the expected minimum annual rate of growth in the equity share price that is
required to justify the holder of convertible loan stock holding on to the security before
the option expires? (12 marks)
c. What recommendation would you make to the holder of the security and why? (3
marks) {total 20 marks)

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ILLUSTRATION 6 (MAY 2017 ICAN PAST QUESTION)

You are a financial consultant to a major company based in Kano. The company plans to
build a major warehouse in Abuja. You plan to convince the company’s manager to raise the
needed funds through a convertible bond issue. Based on the company’s current bond rating
of BBB, you have projected the following offer terms:
Maturity 6 years
Annual coupon 1%
Conversion ratio 50 shares
Par value per bond ₦1,000
Issue price 98% of par value
Current stock price ₦16
Risk free rate 0.5%
Coupon on straight bonds 2% (Trading at par)
The proposal suggests raising up to ₦20,000,000. However with key financial ratios close to
the boundaries of the rating category, offering the full amount could threathen the BBB rating.
Given an average business risk profile, the following rating guidelines apply:
Rating category Minimum interest cover Default spread
BBB 2.39 0.5%
BBB- 2.04 1.0%

Selected financial data about the company:

Estimated EBIT ₦2,200,000
Current Interest Expenses ₦800,000

Required :
a. i. Determine the value of the convertible bond offer (5 marks)
ii. Discuss why the convertible bond cannot generally be considered as cheap debt
despite its low coupon, given its financing advantage quantified in economic terms (3
marks)
b. i. Compute the company’s current interest coverage ratio (1 mark)
ii. How much money should be raised with the convertible bond issue (in thousands of
naira in order to avoid the threat of a rating downgrade, based on the quoted rating
guidelines? (4 marks)

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RELEVANT APPROACH TO BOND VALUATION

c. Advise the company on the advantages of convertible bond for companies on one
hand and for investors on the other hand. (7 marks) (Total 20
marks)

SOLUTION
Note, that the conversion value is assumed to be at par and the yield which is discount rate
is 2% because the debt is trading at par {coupon on a straight debt]
YEAR DCF @ 2% PV
1 -6 Interest 1% x 1,000 = 10 5.601 56.01
6 Redemption value 1,000 0.888 888
944.01

The convertible debt should not be called a cheap debt because it involves both debt and
equity option.
B PART
Interest cover = EBIT / I = 2,200,000 / 800,000 = 2.75
MAXIMUM VALUE THAT CAN BE RAISED =EBIT/I = 2.39
2,200,000 / X = 2.39
2,200,000 = 2.39 X
X = 2,200,000/2.39
X = 920,502
Additional interest = 920,502 – 800,000 = N120,502
Maximum debt = 1% x debt = 120,502
120,502/0.01 = N12,050,200

ILLUSTRATION 7 ( December 2012 ACCA Exams (Q24 BPP kit)}

Coeden co is a listed company operating in the hospitality and leisure industry. Its board of
directors met recently to discuss a new strategy for the business. The proposal put forward
was to sell all the hotel properties that Coeden co owns and rent them back on a long term
rental agreement. Coeden co would then focus solely on the provision of hotel services at

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RELEVANT APPROACH TO BOND VALUATION

these properties under its popular brand name. The proposal stated that the funds raised from
the sale of the hotel properties would be used to pay off 70% of the outstanding non-current
liabilities and the remaining funds would be retained for future investments.
The board of directors is of the opinion that reducing the level of debt in Coeden co will reduce
the company’s risk and therefore its cost of capital. If the proposal is undertaken and Coeden
co focuses exclusively on the provision of hotel services, It can be assumed that the current
market value of equity will remain unchanged after implementing the proposal.
COEDEN CO FINANCIAL INFORMATION
EXTRACT FROM THE MOST RECENT STATEMENT OF FINANCIAL POSITION
$’000
Non-current assets (revalued recently) 42,560
Current assets 26,840
Total assets 69,400

Share capital (25c per share par value) 3,250

Reserves 21,780
Non-current liabilities (5.2% redeemable 42,000
bonds)
Current liabilities 2,370
Total capital and liabilities 69,400
Coeden co’s latest free cash flow to equity of $2,600,000 was estimated after taking into
account taxation, interest and reinvestment in assets to continue with the current level of
business. It can be assumed that the annual reinvestment in assets required to continue with
the current level of business is equivalent to the annual amount of depreciation. Over the past
few years, Coeden co has consistently used 40% of its free cash flow to equity on new
investments while distributing the remaining 60%. The market value of equity calculated on
the basis of the free cash flow to equity model provides a reasonable estimate of the current
market value of Coeden co.
The bonds are redeemable at par in three years and pay the coupon on an annual basis.
Although the bonds are not traded, it is estimated that Coeden co’s current debt credit rating
is BBB but would improve to A+ if the non-current liabilities are reduced by 70%
OTHER INFORMATION
Coeden Co’s current equity beta is 1.1 and it can be assumed that debt beta is 0. The risk
free rate is estimated to be 4% and the market risk premium is estimated to be 6%.

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RELEVANT APPROACH TO BOND VALUATION

There is no beta available for companies offering just hotel services, since most companies
own their own buildings. The average asset beta for property companies has been
estimated at 0.4. it has been estimated that the hotel services business accounts for
approximately 60% of the current value of Coeden co and the property company business
accounts for the remaining 40%.
Coeden Co’s corporation tax rate is 20%. The three year borrowing credit spread on A+
rated bonds is 60 basis points and 90 basis points on BBB rated bonds, over the risk-
free rate of interest.
Required
a. Calculate, and comment on, Coeden Co’s cost of equity and weighted average cost
of capital before and after implementing the proposal. Briefly explain any assumptions
made (20 marks)
b. Discuss the validity of the assumption that the market value of equity will remain
unchanged after the implementation of the proposal (5 marks)
SOLUTION
BEFORE THE PROPOSAL
Ke = Rf + B {Rm – Rf} = 4 + 1.1{6} = 10.6%
Ve = D0 {1 + g} / ke – g = 2,600,000 { 1 + 0.042} / 0.106 – 0.042} = N42,331,250
ROI = Ke where it is given or can be calculated.
G = ROI x retention ratio = 10.6% x 40% = 0.042
Kd = Rf + credit spread = 4 + 0.9% = 4.9%
VD = mkt price of debt x number of debt = N100.79 x N42,000,000/100 = N42,331,800
The market price of debt is equal to pv of interest and redemption value for the maturity
YEAR N DCF @ 4.9% PV
1-3 interest 5.2 2.728 14.19
3 Redemption value 100 0.866 86.60

100.79

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WACC
SOURCE MV COST AV.COST
EQUITY N42,331,250 10.6% 4,487,113
DEBT N42,331,800 4.9%[1 – 0.20]= 1,659,407
84,663,050 6,146,520
WACC = Average cost / mkt value = 6,146,520 / 84,663,050 = 7.3%

AFTER PROPOSAL
Debt is reduced by 70%, credit rating changed to A+ and Properties disposed leaving only
the Hospitality business
Kd = Rf + Credit spread = 4 + 0.6 = 4.6%
Vd = mkt price x number of debt = N101.67 x 12,600,000 / 100 = N12,810,420
The market price of debt is equal to pv of interest and redemption value for the maturity
YEAR N DCF @ 4.6% PV
1-3 interest 5.2 2.744 14.27
3 Redemption value 100 0.874 87.40

Market price 101.67

Book value of debt remaining = 30% x N42,000,000 = N12,600,000
Ve = D0 {1 + g} / ke – g = 2,600,000 { 1 + 0.042} / 0.106 – 0.042} = N42,331,250
ADJUSTED COST OF EQUITY
▪ Identify Beta Equity before the proposal = 1.1 {business risk of 2 biz & financial risk}
▪ Remove the old financial risk = Ba = Be x Ve / Ve + Vd[1 – T] =
1.1 x 42,331,250 /42,331,250 + 42,331.800[1 – 0.20] = 0.61
▪ Beta Asset of coy = [% invested in property x Ba property] + [% invested in Hospitality
x Ba Hospitality]
0.61 = [0.40 x 40%] + [60% x X]
0.61 = 0.16 + 0.60X
X = 0.61 – 0.16 / 0.60 = 0.75
▪ Add the new financial risk
▪ Be = Ba + [Ba – Bd] Vd[1 – T] / Ve
▪ Be = 0.75 + [0.75 – 0] 12,600,000[1 – 0.20] / 42,331,250 = 0.93
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RELEVANT APPROACH TO BOND VALUATION

▪ Ke = Rf + B[Rm – Rf] = 4 + [0.93 x 6] = 9.58%

WACC
SOURCE MV COST AV.COST
EQUITY N42,331,250 9.58% 4,055,334
DEBT N12,600,000 4.6%[1 – 0.20]= 463,680
54,931,250 4,519,014
WACC = Average cost / mkt value = 4,519,014 / 54,931,250 = 8.2%
Interpret
Before Proposal After Proposal Comment
Cost of equity 10.6% 9.58% Debt is reduced, financial risk
reduces which implies a lower
cost of equity
Gross Cost of debt 4.9% 4.6% Cost of debt reduces when
there is lower financial risk.
Beta Asset 0.61 0.75 Beta asset represents
business risk, which in this
scenario is increasing because
the sale of hotels means the
company is no longer
diversified and so fully
exposed to both systematic
and unsystematic risk
WACC 7.3% 8.2% WACC is increasing likely
because the increase in
business risk exceeds the
reduction in financial risk
ASSUMPTIONS
▪ The market value of equity remains constant
▪ The estimates in the computation are reliable and accurate
▪ The tax rate, growth rate and risk free rate are constant and reliable
▪ The beta asset represents the business risk of the respective industries
▪ The risk associated with the computations and the scenario have been fully accounted
for or a sensitivity analysis may be conducted to assess further risk.
▪ The credit spread would remain constant within the appraisal period

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RELEVANT APPROACH TO BOND VALUATION

B PART OF THE QUESTION

▪ The assumption that the market value of equity remaining constant after implementing
the proposal may not be realistic because
1. Market is influenced by the WACC of the organization and so a change in the WACC
should be reflected by change in market value.
2. The company has had a lot of restructural changes like reduction in debt, disposal of
a business unit and a change in credit rating which all are expected to have an impact
on the value of equity.
3. The cost of equity is a major determinant of value of equity which is ignored by the
assumption.
4. The assumption implies there is no change in risk which is unrealistic.

This assumption can only be justified on the basis that the market is inefficient and has not
incorporated all the changes associated with the proposal.

ILLUSTRATION 8
QUESTION 1 COMPULSORY; SEPTEMBER/DECEMBER 2016 SAMPLE QUESTION
(Q66 BPP KIT)
Morada Co is involved in offering bespoke travel services and maintenance services. In
addition to owning a few hotels, it has built strong relationships with companies in the
hospitality industry all over the world. It has a good reputation of offering unique, high quality
holiday packages at reasonable costs for its clients. The strong relationships have also
enabled it to offer repair and maintenance services to a number of hotel chains and cruise
ship companies.
Following a long discussion at a meeting of the board of directors (BoD) about the future
strategic direction which Morada Co should follow, three directors continued to discuss one
particular issue over dinner. In the meeting, the BoD had expressed concern that Morada Co
was exposed to excessive risk and therefore its cost of capital was too high. The BoD feared
that several good projects had been rejected over the previous two years, because they did
not meet Morada Co’s high cost of capital threshold. Each director put forward a proposal,
which they then discussed in turn. At the conclusion of the dinner, the directors decided to
ask for a written report on the proposals put forward by the first director and the second
director, before taking all three proposals to the BoD for further discussion.
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RELEVANT APPROACH TO BOND VALUATION

First director’s proposal

The first director is of the opinion that Morada Co should reduce its debt in order to mitigate
its risk and therefore reduce its cost of capital. He proposes that the company should sell its
repair and maintenance services business unit and focus just on offering bespoke travel
services and hotel accommodation. In the sale, the book value of non-current assets will
reduce by 30% and the book value of current liabilities will reduce by 10%. It is thought that
the non-current assets can be sold for an after-tax profit of 15%.
The first director suggests that the funds arising from the sale of the repair and maintenance
services business unit and cash resources should be used to pay off 80% of the long-term
debt. It is estimated that as a result of this, Morada Co’s credit rating will improve from Baa2
to A2.

Second director’s proposal

The second director is of the opinion that risk diversification is the best way to reduce Morada
Co’s risk and therefore reduce its cost of capital. He proposes that the company raise
additional funds using debt finance and then create a new strategic business unit. This
business unit will focus on construction of new commercial properties.
The second director suggests that $70 million should be borrowed and used to invest in
purchasing non-current assets for the construction business unit. The new debt will be issued
in the form of four-year redeemable bonds paying an annual coupon of 6·2%. It is estimated
that if this amount of debt is raised, then Morada Co’s credit rating will worsen to Ca3 from
Baa2. Current liabilities are estimated to increase to $28 million.

Third director’s proposal

The third director is of the opinion that Morada Co does not need to undertake the proposals
suggested by the first director and the second director just to reduce the company’s risk
profile. She feels that the above proposals require a fundamental change in corporate strategy
and should be considered in terms of more than just tools to manage risk. Instead, she
proposes that a risk management system should be set up to appraise Morada Co’s current
risk profile, considering each type of business risk and financial risk within the company, and
taking appropriate action to manage the risk where it is deemed necessary.

Morada Co, extracts from the forecast financial position for the coming year
$000
Non-current assets 280,000
Current assets 48,000
––––––––
Total assets 328,000
––––––––
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RELEVANT APPROACH TO BOND VALUATION

Equity and liabilities

Share capital (40c/share) 50,000
Retained earnings 137,000
––––––––
Total equity 187,000
––––––––
Non-current liabilities (6·2% redeemable bonds) 120,000
Current liabilities 21,000
––––––––
Total liabilities 141,000
––––––––
Total liabilities and equity capital 328,000
––––––––

Other financial information

Morada Co’s forecast after-tax earnings for the coming year are expected to be $28 million.
It is estimated that the company will make a 9% return after-tax on any new investment in
non-current assets, and will suffer a 9% decrease in after-tax earnings on any reduction in
investment in non-current assets.
Morada Co’s current share price is $2·88 per share. According to the company’s finance
division, it is very difficult to predict how the share price will react to either the proposal made
by the first director or the proposal made by the second director. Therefore it has been
assumed that the share price will not change following either proposal.
The finance division has further assumed that the proportion of the book value of non-current
assets invested in each business unit gives a fair representation of the size of each business
unit within Morada Co.
Morada Co’s equity beta is estimated at 1·2, while the asset beta of the repairs and
maintenance services business unit is estimated to be 0·65. The relevant equity beta for the
new, larger company including the construction unit relevant to the second director’s
proposals has been estimated as 1·21.
The bonds are redeemable in four years’ time at face value. For the purposes of estimating
the cost of capital, it can be assumed that debt beta is zero. However, the four-year credit
spread over the risk free rate of return is 60 basis points for A2 rated bonds, 90 basis points
for Baa2 rated bonds and 240 basis points for Ca3 rated bonds.
A tax rate of 20% is applicable to all companies. The current risk free rate of return is
estimated to be 3·8% and the market risk premium is estimated to be 7%.
Required:
(a) Explain how business risk and financial risk are related; and how risk mitigation
and risk diversification can form part of a company’s risk management strategy. (6
marks)
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RELEVANT APPROACH TO BOND VALUATION

(b) Prepare a report for the board of directors of Morada Co which:

(i) Estimates Morada Co’s cost of equity and cost of capital, based on market value of
equity and debt, before any changes and then after implementing the proposals put
forward by the first and by the second directors; (17 marks)
(ii) Estimates the impact of the first and second directors’ proposals on Morada Co’s
forecast after-tax earnings and forecast financial position for the coming year; and (7
marks)
(iii) Discusses the impact on Morada Co of the changes proposed by the first and
second directors and recommends whether or not either proposal should be accepted.
The discussion should include an explanation of any assumptions made in the
estimates in (b)(i) and (b)(ii) above. (9 marks)
Professional marks will be awarded in part (b) for the format, structure and presentation of
the report.
(4 marks)
(c) Discuss the possible reasons for the third director’s proposal that a risk
management system should consider each risk, before taking appropriate action. (7
marks)
(50 marks)
ILLUSTRATION 9
SECTION A: QUESTION 1 SEPTEMBER/DECEMBER 2017 SAMPLE QUESTION
Conejo Co is a listed company based in Ardillia and uses $ as its currency. The currency was
formed around 20 years ago and was initially involved in cybernetics, robotics and artificial
intelligence within the information technology industry. At that time due to the risky ventures
Conejo Co undertook, its cash flows and profits were very varied and unstable. Around 10
years ago, it started an information systems consultancy business and a business developing
cyber security systems. Both these businesses have been successful and have been growing
consistently. This in turn has resulted in a stable growth in revenues, profits and cash flows.
The company continues its research and product development in artificial intelligence and
robotics, but this business unit has shrunk proportionally to the other two units.
Just under eight years ago, Conejo Co was successfully listed on Ardilla’s national stock
exchange offering 60% of its share capital to external equity holders, whilst the original
founding members retained the remaining 40% of the equity capital. The company retains
financed largely by equity capital and reserves, with only a small amount of debt capital. Due
to this, and its steadily growing sales revenue, profits and cash flows, it has attracted a credit
rating of A from the credit rating agencies.

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RELEVANT APPROACH TO BOND VALUATION

At a recent board of directors (BOD) meeting, the company’s chief financial officer (CFO)
argued that it was time for Conejo Co to change its capital structure by undertaking a financial
reconstruction, and be financed by higher levels of debt. As part of her explanation, the CFO
said that Conejo Co is now better able to bear the increased risk resulting from higher levels
of debt finance, would be better protected from predatory acquisition bids if it was financed
by higher levels of debt; and could take advantage of the tax benefits offered by increased
debt finance. She also suggested that the expected credit migration from a credit rating of A
to a credit rating of BBB, if the financial reconstruction detailed below took place, would not
weaken Conejo Co financially.
Financial Reconstruction
The BOD decided to consider the financial reconstruction plan further before making a final
decision. The financial reconstruction plan would involve raising $1,320 million ($1.32 billion)
new debt finance consisting of bonds issued at their face value of $100. The bonds would be
redeemed in five years’ time at their face value of $100 each. The funds raised from the issue
of the new bonds would be used to implement one of the following two proposals:
1) Proposal 1: either buy back equity shares at their current share price, which would be
cancelled after they have been repurchased; or
2) Proposal 2: invest in additional assets in new business ventures
Conejo Co, Financial Information
Extract from the forecast financial position for next year
$m
Non-current assets 1,735
Current assets 530
Total assets 2,265

Equity and Liabilities

Share capital ($1 per share par value) 400
Reserves 1,700
Total equity 2,100

Non- current liabilities 120

Current liabilities 45
Total liabilities 165
Total Liabilities and capital 2,265

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RELEVANT APPROACH TO BOND VALUATION

Conejo Co’s forecast after-tax profit for next year is $350 million and its current share price is
$11 per share.
The non-current liabilities consist solely of 5.2% coupon bonds with a face value of $100 each,
which are redeemable at their face value in three years’ time. These bonds are currently
trading at $107.80 per $100. The bond’s covenant stipulates that should Conejo Co’s
borrowing increase, the coupon payable on these bonds will increase by 37 basis points.
Conejo Co pays tax at a rate of 15% per year and its after tax return on the new investment
is estimated at 12%
Other financial Information
Current government bond yield curve
YEAR 1 2 3 4 5
1.5% 1.7% 1.9% 2.2% 2.5%

Yield spreads (in basis points)

1 year 2 years 3 years 4 years 5 years
A 40 49 59 68 75
BBB 70 81 94 105 112
B 148 167 185 202 218
The finance director wants to determine the percentage change in the value of Conejo Co’s
current bonds, if the credit rating changes from A to BBB. Further more, she wants to
determine the coupon rate at which new bonds would need to be issued, based on the current
yield curve and appropriate yield spreads given above.
Conejo Co’s chief executive officer (CEO) suggested that if Conejo Co paid back the capital
and interest of the new bond in fixed annual repayments of capital and interest through the
five-year life of the bond, then the risk associated with the extra debt finance would be largely
mitigated. In this case, it was possible that credit migration, by credit rating companies, from
A rating to BBB rating may not happen. He suggested that comparing the duration of the new
bond based on the interest payable annually and the face value in five years’ time with the
duration of the new bond where the borrowing is paid in fixed annual repayments of interest
and capital could be used to demonstrate this risk mitigation.
Required :
a. Discuss the possible reasons for the finance Director’s suggestions that Conejo Co
could benefit from higher levels of debt with respect to risk, from protection against
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RELEVANT APPROACH TO BOND VALUATION

acquisition bids, and from tax benefits

(7 marks)
b. Prepare a report for the board of directors of Conejo Co which:
i. Estimates, and briefly comments on, the change in the value of the current
bond and the coupon rate required for the new bond, as requested by the CFO;
(6 marks)
ii. Estimates the Macaulay Duration of the new bond based on the interest
payable annually and face value repayment, and the Macaulay Duration based
on the fixed annual repayment of the interest and capital as suggested by the
CEO; (6 marks)
iii. Estimates the impact of the two proposals on how the funds may be used on
next year’s forecast earnings, forecast financial position, forecast earnings per
share and on forecast gearing (11
marks)
iv. Using the estimates from “b” , discuss the impact of the proposed financial
reconstruction and the proposals on the use of funds on:
▪ Conejo Co
▪ Possible reactions of credit rating companies and on the expected credit
migration, including the suggestions made by the CEO;
▪ Conejo Co’s equity holders
▪ Conejo Co’s current and new debt holders. (16 marks)
Professional marks will be awarded in part (b) for the format, structure and presentation of
the report. (50 marks)
ILLUSTRATION 10 ON BOND EVALUATION
Kenand co has a cash surplus of $1m, which the financial manager is keen to invest in
corporate bonds. He has identified two potential investment opportunities, in two different
companies which are both rated A by the major credit rating agencies:
OPTION 1:
AB co has $100m of bonds already in issue. The bonds carry a coupon rate of 5% per annum,
and the financial press is reporting that the bonds have a bid yield of 6.2% per annum. The
bonds are redeemable at a 10% premium to nominal value in 4 years.
OPTION 2:

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XY Co is about to issue $50m of 3 year bonds with a coupon rate of 4% per annum. The
bonds will be redeemable at par in 3 years. The annual spot yield curve for government bonds
is
1 year 3.54%
2 year 4.01%
3 year 4.70%
4 year 5.60%

EXTRACTS FROM A MAJOR CREDIT RATING AGENCY’S WEBSITE:

TABLE OF SPREADS (IN BASIS POINTS)
RATING 1 YEAR 2 YEAR 3 YEAR 4 YEAR
AAA 5 18 29 40
AA 16 30 42 50
A 26 39 50 60
Required:
a. Calculate the theoretical market value of a $100 bond in AB Co, and the theoretical
issue price of the $100 bond in XY co. calculate how many bonds Kenand co will be
able to buy with its $1m. (6 marks)
b. Estimate the Macaulay duration of the AB co bonds and the XY Co bonds , and
interpret your results (8 marks)
c. Among the criteria used by credit agencies for establishing a credit rating are the
following: industry risk, earnings protection, financial flexibility and evaluation of the
company’s management. Briefly explain each criterion and suggest factors that could
be used to assess it. (8 marks)
ILLUSTRATION 11
Julius Berger plc is a major player in the road construction industry with a credit rating of AA.
The company plans to raise N750 million from the bond market. Two different bonds are being
considered.
OPTION 1: a 4 year bond with an annual coupon rate of 5%. The bonds will be redeemable
at par
Option 2: this is a three year bond, with an annual coupon rate of 4% redeemable at a
premium of 5% to nominal value.
The current annual spot yield curve for Government bonds is as follows:
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RELEVANT APPROACH TO BOND VALUATION

1 year 3.3%, 2 year 3.8%, 3 year 4.5% and 4 year 5.3%.

The following table of spreads (in basis points) is given for the construction industry
Rating 1 year 2 year 3 year 4 year
AAA 12 23 36 50
AA 27 40 51 60
A 43 55 67 80
Required
Calculate the theoretical issue prices of the bond and the duration of the bonds.
ILLUSTRATION 12
GNT co is considering an investment in one of two corporate bonds. Both bonds have a par
value of N1,000 and pay coupon interest on an annual basis. The market price of the first
bond is N1,079.68. its coupon rate is 6% and it is due to be redeemed at par in five years.
The second bond is about to be issued with a coupon rate of 4% and will also be redeemable
at par in five years. Both bonds are expected to have the same gross redemption yields (yields
to maturity). The yield to maturity of a company bond is determined by its credit rating.
a. Estimate the Macaulay duration of the two bonds GNT Co is considering for investment
(9 marks)
b. Discuss how useful duration is as a measure of the sensitivity of a bond price to
changes in interest rates (8
marks)
c. Among the criteria used by credit agencies for establishing a company’s credit rating
are the following; industry risk, earnings protection, financial flexibility and evaluation
of the company’s management. Briefly explain each criterion and suggest factors that
could be used to assess it. (8
marks)

ILLUSTRATION 13 ON BOND PRICING

A small unquoted company wants to issue 10- year bonds and its finance director is trying to
work out the cost of debt in order to assess the profitability of the company.
The following information is available for the company
Total assets N120 million

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Net income N6 million

Type of proposed debt Subordinated
Long term debt N14 million
Income before interest and tax N8 million
Interest payments N1 million
The earnings of the company for the last 5 years are as follows;
Year Earnings
2016 N5 M
2015 N4.2 M
2014 N3.2 M
2013 N3.8 M
2012 N2.2 M
The finance director has decided to use the Kaplan Urwitz model for unquoted companies to
assess the cost of debt. The model is given by:
Y = 4.41 + 0.001Size + 6.40profitability – 2.56debt – 2.72Leverage + 0.006Interest – 0.53Cov
The classification of companies into credit rating categories is done in the following way
Score Rating category
Y ≥ 6.76 AAA
Y ≥ 5.19 AA
Y ≥ 3.28 A
Y ≥ 1.57 BBB
Y≥0 BB
The following table gives the yield to maturity for 10 year corporate bonds by credit category
RATING COST OF DEBT (YIELD TO MATURITY)
AAA 6.6%
AA 7.3%
A 7.8%
BBB 8.4%
BB 9.4%
B 10.5%
Calculate the cost of debt.
ILLUSTRATION 14
ABC Transport company is considering raising new capital of N40 million in the bond market
for the acquisition of two new luxury buses. The debt would have a term of maturity of four
years. The market capitalization of the company’s equity is N1.5 billion and it has a 25%

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RELEVANT APPROACH TO BOND VALUATION

market gearing ratio (debt to total market value). This new issue would be ranked for payment,
in the event of default, equally with the company’s other long term debt and the latest credit
assessment places the company at AA. Interest would be paid to holders annually. The
company’s current debt carries an average coupon of 4% and has three years to maturity.
The company’s effective tax rate is 30%.
The current yield curve suggests that , at three years, government treasuries yield 3.5% and
four years they yield 5.1%. the current credit risk spread is estimated to be 50 basis points at
AA. If the issue proceeds, the company’s investment bankers suggest that a 90 basis point
spread will need to be offered to guarantee take up by its institutional clients
Required
a. Advise on the coupon rate that should be applied to the new debt issue to ensure that
it is fully subscribed
b. Estimate the current and revised market valuation of the company’s debt and the
increase in the company’s effective cost of debt capital.
c. Briefly consider company-specific factors that will be used in credit rating assessment
to classify the company as AA. (20 marks)

ILLUSTRATION 15
Your company, which is in the Aviation business, is considering raising new capital of ₦40m
in the bond market for the acquisition of two new 737 Boeing planes. The debt would have a
term to maturity of four years. The market capitalization of the company’s equity is ₦1.5 billion
and it has a 25% market gearing ratio (market value of debt to total market value of the
company). This new issue would be ranked for payment, in the event for default, equally with
the company’s other long-term debt and the latest credit risk assessment places the company
at AA. Interest would be paid to holders annually. The company’s current debt carries an
average coupon of 4% and has three years to maturity. The company’s effective tax rate is
30%.
The current yield curve suggests that , at three years, government treasuries yield 3.5% and
four years they yield 5.1%. The current credit risk spread is estimated to be 50 basis points
at AA. If the issue proceeds, the company’s investment bankers suggest that a 90 basis point
spread will need to be offered to guarantee take up by its institutional clients.
Required
a. Advise on the coupon rate that should be applied to the new debt issue to ensure that
it is fully subscribed. (4 marks)
b. Estimate the current and revised market valuation of the company’s debt and the
increase in the company’s effective cost of debt capital (10 marks)
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RELEVANT APPROACH TO BOND VALUATION

c. Briefly consider company-specific factors that will be used in the credit rating
assessment to classify the company as AA. (6 marks)
(20 marks)

ILLUSTRATION 16
A. Briefly discuss possible reasons for an upward sloping yield curve
B. The financial manager of KK funds plc’s pension fund is reviewing strategy regarding
the fund. Over 60% of the fund is invested in fixed rate long term bonds. Interest rates
are expected to be quite volatile for the next few years.
Among the pension funds current investments are two AAA rated bonds:
1. Zero coupon December 2020
2. 12% December 2020 (interest is payable semi-annually)

The current annual redemption yield (yield to maturity) on both bonds is 6%. The semi-
annual yield may be assumed to be 3%. Both bonds have a par value and redemption
value of ₦100. Assume it is now January 1,2006.
Required
I. Estimate the market price of each of the bonds if interest rates (yields)
a) Increase by 1%
b) Decrease by 1%

The changes in interest rates may be assumed to be parallel shifts in the yield curve (yield
changes by an equal amount at all points of the yield curve).
II. Comment upon and briefly explain the size of the expected price movements from
the current prices, and how such changes in interest rates might affect the strategy
of the financial manager with respect to investing in the two bonds.
III. How might the bond investment strategy of the financial manager be affected if the
yield curve was expected to steepen (the gap between short term and long term
interest rates to widen)

ILLUSTRATION 17
APT limited is a large unlisted company which has identified a new project for which it will
need to increase its long term borrowings from ₦250m to ₦400m. This amount will cover a

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RELEVANT APPROACH TO BOND VALUATION

significant proportion of the total cost of the project and the rest of the funds will come from
cash held by the company.
The current ₦250m unsubordinated borrowing is in the form of a 4% bond which is trading at
₦98.71 per ₦100 and is due to be redeemed at par in three years. The issued bond has a
credit rating of AA. The new borrowing will also be raised in the form of a traded bond with a
par value of ₦100 per unit. It is anticipated that the new project will generate sufficient cash
flows to be able to redeem the new bond at ₦100 par value per unit in five years. It can be
assumed that coupons on both bonds are paid annually.
Both bonds would be ranked equally for payment in the event of default and the directors
expect that as a result of the new issue, the credit rating for both bonds will fall to A. The
directors are considering the following two alternative options when issuing the new bond.
OPTION 1:
Issue the new bond at a fixed coupon of 5% but at a premium or discount, whichever is
appropriate to ensure full take up of the bond; or
OPTION 2:
Issue the new bond at a fixed coupon rate of 6% and at par value. The bond will be
redeemable at par.
The following extracts are provided on current government bond yield curve and yield spreads
for the sector in which APT limited operates.
CURRENT GOVERNMENT BOND YIELD CURVE
1 year 3.2%
2 year 3.7%
3 year 4.2%
4 year 4.8%
5 year 5.0%

EXTRACTS FROM A MAJOR CREDIT RATING AGENCY’S WEBSITE:

TABLE OF SPREADS (IN BASIS POINTS)
RATING 1 YEAR 2 YEAR 3 YEAR 4 YEAR 5 YEAR
AAA 5 9 14 19 25
AA 16 22 30 40 47
A 65 76 87 100 112

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BBB 102 121 142 167 193

Required:
a. Calculate the expected percentage fall in the market value of the existing bond if APT’s
limited credit rating falls from AA to A.
b. Advise the directors on the financial implications of choosing each of the two options
when issuing the new bond. Support the advice with appropriate calculations.
c. Among the criteria used by credit agencies for establishing a credit rating are the
following: industry risk, earnings protection, financial flexibility and evaluation of the
company’s management. Briefly explain each criterion and suggest factors that could
be used to assess it. (8 marks)
ILLUSTRATION 18
Calculate and explain the yield to maturity, the yield to put and the yield to call
on a bond maturing in 3 years with an 8% coupon quoted at 104. The bond is
putable at 100 and callable at 102. Both options can be exercised in 1 year.
Ignore transaction cost. (5 marks)

REALISED YIELD OR EXPECTED HORIZON YIELD OR TOTAL RETURN

This is the expected rate of return on a bond that you anticipate selling prior to its maturity. It
requires estimate of the holding period, expected future selling price of the bond at the
end of the holding period and the reinvestment rate for the coupon flows prior to selling
the bond.
ILLUSTRATION
An investor with a 3 year investment horizon is considering purchasing a 10 year , 8% coupon
bond for N428.40. The YTM of this bond is 10%. The investor expects to be able to reinvest
the coupon interest payments at an annual interest rate of 6% and that at the end of the
planned investment horizon, the then 7 year old bond would be selling to offer 6%. Assume
semi-annual coupon payments.
Calculate the expected horizon yield?
SOLUTION
▪ Calculate the future value of annuity = FV = A{1 + r}n - 1 / r

Note Annual coupon of 8% will now be 4% due to semi-annual coupon payments = 4% x

N100 = N40
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RELEVANT APPROACH TO BOND VALUATION

R is the coupon rate of 6% which is now 3% {6/2} due to semi annual compounding and
number of years is now 6 periods {3 x 2} due to semi compounding.
40{ 1 .03}6 – 1 / 0.03 = N258.74
▪ Determine the projected selling price of the bond at the end of the holding period

Remaining years is 7 years that is 14 periods and YTM of 6% now 3%

Price
Year Cash flow DCF @ 3% PV N
1 – 14 40 11.296 451.84
14 100 0.661 66.10

517.94

▪ Determine the total amount that will be available to the investor at the end of the
holding period = future value of coupon + selling price = N258.74 + N517.94 =
776.68
▪ Determine the expected holding period yield = growth rate required for the original
price {N428.40} to equate the total amount {N776.68}
▪ EV / BV}1/N - 1 = 776.68 / 428.40}1/6 – 1 = 10.42%
▪ The expected return on semi-annual basis is 10.42% or 20.84% on an annual basis.

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Interest rate risk is the potential for investment losses that result from a change in the interest
rate.
Methods to manage the interest rate risk are

▪ Netting
▪ Smoothing
▪ Matching
▪ Pooling of Assets and Liabilities
▪ Forward rate agreements [FRA]
▪ Interest rate futures
▪ Interest rate options guarantee [option on FRA]
▪ Interest rate options on futures
▪ Interest rate Collar
▪ Interest rate Swaps

Interest rate risk is the potential for investment losses that result from a change in the interest
rate. It is the probability of a decline in the value of an asset resulting from unexpected
fluctuation in interest rates.
Risk arises for businesses due to uncertainty in the future. Interest rate risk arises when
businesses do not know
▪ How much interest they might have to pay on borrowings either already made or
planned to
▪ How much interest they might earn on deposits either already made or planned to

The primary aim of interest rate risk management is to limit the uncertainty for the
business, so that it can plan with greater confidence and not to guarantee the business the
best possible outcome.
HEDGING is a means of reducing risk. It involves coming to an agreement with another party
who is prepared to take on the risk that you would otherwise bear.
REDUCING INTEREST RATE RISK
Methods of reducing interest rate risk include:

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▪ Diversification: refers to adding securities into the portfolio whose value is less prone
to interest rate fluctuation.
▪ Netting involves aggregating all positions, assets and liabilities, and hedging the
net exposure
▪ Smoothing involves maintaining a balance between fixed and floating rate
borrowing. In this method, the management of loans or deposits are simply
divided so that some [loans and deposits] are on a fixed rate and some are on a
variable rate.
▪ Matching involves matching assets and liabilities to have a common interest rate.
This method requires a business to have both assets and liabilities with the same kind
of interest rate. The closer the two amounts, the better.
This is also related to the assets and liabilities management that relates to matching
the periods over which the loans and deposits cover.

ILLUSTRATION
Relevant Haven plc [RHP] has a deposit of $500,000 on which it expects an interest of
LIBOR plus 1%. RHP also has a loan of $550,000 on which it is expected to pay an interest
of LIBOR plus 2%. Show how the matching concept can be used to hedge the interest
rate risk if LIBOR IS CURRENTLY 5% AND EXPECTED to increase by 2% over the period
SOLUTION
DEPOSIT = $500,000 = 6% x 500,000 = $30,000 ; 8% x 500,000 = $40,000
LOAN = $550,000 = 7% x 550,000 = $38,500; 9% x 550,000 = $49,500
Difference $8,500 $9,500
With the matching the exposure is reduced to barely $1,000 but without the matching, the
interest rate payment exposure would be $11,000
POOLING OF ASSETS AND LIABILITIES :
Pooling means asking the bank to pool the amount of all its subsidiaries when considering
interest levels and overdraft limits. It should reduce the interest payable, stop overdraft limits
being breached and allow greater control by the treasury department. It also gives the
potential to take advantage of better rates of interest on larger cash deposits.

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FORWARD RATE AGREEMENTS (FRA):

FRA is an agreement between a company and a bank, about the interest rate on future
borrowings or bank deposits. It does not involve the actual transfer of capital from one party
to the other. It is based on the idea of a forward contract, where the interest rate to be used
in future is agreed on and the actual interest rate at maturity determines if there is a gain or
loss.
It allows borrowers or lenders to fix their future rate of interest. The FRA runs for a given
period in the future. ‘3 - 9’ FRA shows that the FRA starts in 3 months time and last for 6
months.
In a borrowing contract, where the company agrees a maximum rate that it is willing to pay,
If the actual interest rate proves to be higher than the rate agreed, the FRA intermediary pays
the company the difference as a compensation but If the actual interest rate is lower than the
rate agreed, the company pays the bank the difference and vice versa.
When you are borrowing, you are hedging an increase in interest rate (you are fixing a
maximum that you will pay) but if you are investing, you are hedging a decrease in interest
rate (you are a fixing the minimum that you can receive).
The loans or deposits can be with one financial institution and the FRA can be with an entirely
different one, but the net outcome should provide the business with a fixed rate of interest.
This is achieved by the compensating amounts either being paid to or received from the
supplier of the FRA depending on how the interest rate has moved.
First step in solving FRA questions is determining the appropriate FRA . you need the
following
1. Today’s date as per the scenario
2. The commencement date of the transaction
3. Number of months of the transaction

How many months from today do I need the loan + number of months of the loan
The lower rate in the FRA agreement is for investment while the higher rate is for
borrowing except otherwise stated.
TEST QUESTION
Today is 30 June, I need a loan on 1 September and I intend to pay back on 30 December.
Determine the Appropriate FRA

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Start date is the number of moths from today = 30 June – 1 September = 2 months
Number of months required = 1 September – 30 December = 4 months
FRA should terminate in 2 + 4 = 6 months.
FRA 2 ------ 6
TEST QUESTION
J Plc intends to invest an amount in 4 months time which will be required for a project 8 months from
today. He intends to hedge using the FRA. Advise on the appropriate FRA.
Start date from today = 4 months
Number of months FRA required = 8months – 4 months = 4 months
FRA Should terminate in 4 + 4 = 8 months
FRA 4 - 8
ILLUSTRATION 1 ON FRA
It is 30 June. Your company will need $20 million 3 month fixed loan from 1 October. You want to hedge
using FRA. The relevant FRA rate is 11.25 – 12 on 30 June.
a. What is the required FRA and at what rate?
b. What is the result of the FRA and the effective loan rate in three months time if the market rate is
14% or 9%?

SOLUTION
Start date = 30 june – 1 Oct = 3 months
Number of months = 3 months
FRA should terminate in 3 + 3 = 6 months
Suitable FRA = 3 – 6 and the FRA rate is 12% as the higher rate is quoted for loan transactions.
B PART OF THE QUESTION
FRA ; FIXED TARGET = 12% X $20m x 3/12 = $600,000
14% 9%
Actual payment 14% x 20m x 3/12 [$700,000] 9% x 20m x 3/12 [$450,000]
Refund [14 – 12]% x 20m x 3/12 $100,000 [12% - 9%] x 20m x 3/12 [150,000]
Net payment [$600,000] [600,000]
Effective rate Net / exposure x 12/N 600,000/ 20,000,000 x 12 /3 12%

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QUESTION 2 { ICAN PAST QUESTION MAY 2018 ON INTEREST RATE RISK}

Katangwa Limited will need to borrow ₦50 million in three months‟ time for a period of six months. The
company is concerned that interest rates are expected to rise over the next few months.
Interest rates and forward rate agreements (FRAs) are currently quoted as follows:
● Spot 5.75 – 5.50
● 3 – 6 FRA 5.82 – 5.59
● 3 – 9 FRA 5.94 – 5.64
Required:
a. Explain how a forward rate agreement (FRA) may be useful to the company. Illustrate this on the basis
that interest rates
i. Rise to 6.50%
ii. Fall to 4.50% (8 Marks)
b. Compare the use of interest rate futures with FRA in this instance (4 Marks)
c. Explain how interest rate guarantees or short-term interest rate cap could be used. (3 Marks)
(Total 15 Marks)
SOLUTION
Start date = 3 months
Number of months = 6 months
FRA should terminate in 3 + 6 = 9 months
Suitable FRA = 3 – 9 and the FRA rate is 5.94% as the higher rate is quoted for loan transactions.
FRA ; FIXED TARGET = 5.94% X N50m x 6/12 = N1,485,000
6.5% 4.5%
Actual payment 6.5% x 50m x 6/12 [N1,625,000] 4.5% x 50m x 6/12 [N1,125,000]
Refund [6.5 – 5.94]% x 50m x N140,000 [5.94 – 4.5]% x 50m x 6/12 [N360,000]
6/12
Net payment [N1,485,000] [1,485,000]
Effective rate Net / exposure x 12/N 1,485,000/ 50,000,000 x 12 5.94%
/6

QUESTION 3 {ICAN PAST QUESTION MAY 2015 ON HEDGING AND INTEREST RATE }
Finance Managers of Multinational Firms manage foreign exchange risks. In the light of the above statement,
you are required to:
a. Explain what is meant by ‘hedging’. (3 Marks)
b. Identify and explain THREE Internal Hedging techniques. (6 Marks)
c. On 31 December 2014, Famak Plc realised that it needs a N100million fixed rate loan on 1 April 2015,
Famak Plc would want to hedge using Forward Rate Agreement (FRA).
The relevant FRA rate will be 6% on 31 December, 2014. Determine the result of the FRA and the effective
loan rate if the 6 month FRA benchmark moves to: (i) 5%; (ii) 9%. (6 Marks)
(Total 15 Marks)

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QUESTION 4
Relevant Haven’s Cashflow forecast shows that it will have to invest $20m with GTB in 4 months’ time for a
period of 3 months. The company fears that by the time this investment commences, interest rates may have
fallen or risen by 50 basis points. The current LIBOR is 5% and the current interest rates on their deposit is
LIBOR less 80 basis points.
RAND Merchant Bank has provided the following FRA rates
FRA PERIOD FRA RATES %
3V7 5 .05 – 4.95
4V7 5.35 --- 5.15
4V3 4.95 --- 4.85
Required
a. What are the net cash flows if the interest rate increases or decreases as expected by the company?
b. Comment on your results

SOLUTION
Determine the appropriate FRA
Start date = 4 months
Number of months required = 3 months
FRA should terminate in 4 + 3 = 7 months
FRA 4 – 7 and the appropriate rate is 5.15%
IMPLICATION OF ACTUAL RATE
Interest rate may increase = 5% + 0.5% = 5.5%
Interest may decreases = 5% - 0.5% = 4.5%
Specific rate = LIBOR – 0.80%
FRA
Target = [5.15% - 0.80%} x $20,000,000 x 3/12 = 4.35% x 20,000,000 x 3/12 = $217,500
5.5% 4.5%
Actual Receipt [5.5 – 0.8]% = 4.7% x 235,000 4.5 – 0.8]% =3.7% x 20m x 185,000
20m x 3/12 3/12
Refund [5.5 – 5.15]% x 20m x [17,500] [5.15 – 4.5] x 20m x 3/12 32,500
3/12
Net Receipt 217,500 217,500
Effective rate Net / exposure x 12/N 217,500/ 20,000,000 x 12 /3 4.35%

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INTEREST RATE FUTURES

Tick is the smallest movement in a futures price . 1 tick is equivalent to 0.01% or 0.0001.
Futures price = 100% - interest rate %
Equivalent interest rate = 100 – futures price
Basis period is the period covered by the Futures contract from today to the end of the futures
contract. Basis is the difference between the spot rate [current LIBOR] and the opening futures price.
Unexpired basis is the basis left when the transaction matures before the end of the contract.
Lock in rate = opening futures price + unexpired basis + margin over specific rate
Opening futures price is the price associated with the chosen futures contract [usually given] while
closing futures price is the futures price on maturity and is calculated as 100 – unexpired basis –
actual rate at maturity. Futures price = 100 – interest rate

They are similar in effect to FRAs, except that the terms, amounts and periods are standardized having fixed
sizes and gives the owners the right to earn interest or pay interest at a given rate. Interest rate futures can
be bought and sold on exchanges such as intercontinental exchange futures Europe.
The price of the futures contracts depends on the prevailing interest rate and it is crucial to understand that
as interest rates rise, the market price of the futures contracts falls. The price of the futures is 100%
- interest rate. The basis risk is the risk that in practice, the futures price movements do not move perfectly
with interest rates.
Selling a futures creates the obligation to borrow money and the obligation to pay interest while
Buying a futures creates the obligation to deposit money and the right to receive interest.
Borrowers fear that the interest rates may increase [higher interest payments] and if this happens,
the Futures price will fall in the future. To hedge this, the borrower would need to Sell futures now [at
the high rate] and buy when it has fallen in the future to make a profit.
Lenders fear the interest rates may fall [reduced income] and if this happens, the Futures price will
increase in the future. To hedge this, the lender would need to buy now [at the lower rate] and sell in
the future when the Futures price has increased in the future to make a profit.
Short term interest rate futures contracts (STIRs) normally represent interest receivable or payable on
notional lending or borrowing for a three month period beginning on a standard future date. The contract size
depends on the currency in which the lending or borrowing takes place. Whole number of contracts should
be used and maturity dates are March, June, September and December.
Profits and losses on futures are measured in ticks (one tick equals 0.0001 or 1% = 100 ticks). Tick =
contract size x 3/12 x 0.0001
The pricing on an interest rate futures contract is determined by the interest rate (r) and is calculated
as 100 – r. interest futures are usually quoted in the form of index and so a price at 82 means 18%
(100-82).

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STEPS IN SETTING UP AN INTEREST RATE FUTURES

▪ Identify the exposure : it is either borrowing or investment
▪ Choose the contract type : if it is borrowing [fear of interest rate increasing], we choose a contract
to pay interest {sell futures] now; but if it is investing [fear of interest rate falling], we choose a
contract to receive interest { buy futures] at the start.
▪ Pick the contract expiry: it should be a contract that aligns with the start of the transaction (unlike
currency futures that looks at the end of the contract)
▪ Determine number of contracts required = (exposure / contract size) x (transaction period /
futures contract period). Note futures contract period is assumed to be 3 months except otherwise
stated. All contracts required should be in whole numbers.
▪ You could use the Lock-In-Rate approach where the Effective Rate is Opening Futures Rate
+ unexpired Basis + margin over the specific rate. This is actually a short cut in the exam as
opposed to the profit/loss approach.

Determine profit or loss per contract: it is comparing the transaction at the start (at the opening
futures price) with the transaction at the end (at the closing futures price). Don’t forget that the
transaction at the end must be the opposite of the transaction at the start.
In determining the profit or loss, you may not be given the closing futures price. In that case you may
need to compute the price by adding the opening spot rate (100 – existing bank rate) to the unexpired
basis.
Determine total profit or loss = profit x number of contracts x contract size x 3/12

▪ Determine the net borrowing or investment.

▪ Determine the target interest amount based on the desired interest rate (principal x interest rate x
duration). This is simply determining what the actual interest payment will be in the future.

MARK TO MARKET PROCESS

▪ Meet a Broker : who explains to you the available contracts
▪ Contract type : contract to pay interest [sell futures] or receive interest [ buy futures]
▪ Exposure : Borrowing = pay interest; investment ‘ receive interest
▪ Futures contract are quarterly [Mar, June, Sept and Dec]
▪ Exposure ; Jan-Mar : March contract, Apr-June ; June Contract, July – Sept ; Sept contract and
Oct– Dec ; December contract.
▪ You would have to pay an initial deposit [initial margin]
▪ This deposit has a minimum balance that cannot be violated {maintenance margin]
▪ If you make a profit , you are credited, but if you make loss you are debited.
▪ If your deposit falls below the maintenance margin, the market will request Margin call] for more
deposit [variation margin]

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▪ Opens an account [open position]

▪ End, when you intend to leave the market; you do the opposite of your initial contract at the start.

ILLUSTRATION ON FUTURES
Lekki Gardens [LG] is expecting to receive $50,000,000 on 1 February 2021, which will be invested until it
is required for a large project on 1 August 2021. The company can invest funds at the inter-bank rate less
30 basis points. The current inter-bank rate is 7.25%. However, LG is of the opinion that interest rates could
increase or decrease by as much as 0.6% over the coming months.
The following information and quotes are provided from an appropriate exchange on $ futures. Margin
requirements can be ignored.
Three-month $ futures, $2,000,000 contract size; prices are quoted in basis points at 100 – annual %
yield
December 2020 94.55
March 2021 94.30
June 2021 94.15
It can be assumed that settlement for the futures is at the end of the month and that basis diminishes to zero
at contract maturity at a constant rate, based on monthly time intervals. Assume that it is 1 November, 2020
now and that there is no basis risk.
Required
Determine the net receipt or payment, if the above exposure is hedged using the Interest rate futures.

SOLUTION
Exposure ; investment ---- contract to receive interest [buy futures]
Which contract duration: pick March 2021 === 94.30 [ opening futures price] because the transaction date
is in Feb
Opening Futures price in % = 100 – 94.30 = 5.7%
Number of contracts = Exposure x Transaction period
Contract size futures period
= 50m / 2m x 6/3 = 50 contracts

EFFECTIVE RATE = Opening futures price + margin + unexpired basis

Effective rate = 5.7% + [- 0.3%] + 0.62% = 6.02%
Net receipt = 6.02% x 50m x 6/12 = N1,505,000

Basis is the difference between the Spot rate [ LIBOR now] and the Opening Futures price.
Basis should be zero at contract maturity. Basis covers the contract from today { today’s date to the end of
the futures contract]. It is assumed that the basis should reduce in a constant rate over the period.
Basis risk is the fact that the basis may not reduce as expected and so rendering our calculation inaccurate.

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Unexpired basis arises when an investor closes his position before the contract end. Unexpired basis can
simply be defined as the period between the transaction date and the end of the futures contract.

Basis = spot rate {Current LIBOR] – opening futures price = 7.25% - 5.7% = +1.55%
1 Nov 2020 – 30 march 2021 = 5 months basis period
1 feb 2021 – 30 March 2021 = 2 months unexpired period
Unexpired basis = 2/5 x +1.55% = +0.62%

PROFIT OR LOSS ON FUTURES IF INTEREST RATE INCREASES by 0.6% = 7.25% + 0.6% = 7.85%
START: INVESTMENT ; RECEIVE INTEREST @ Opening futures price 5.7%
END :PAY INTEREST @ closing futures price [closing interest rate – unexpired basis]7.85 – 0.62 = 7.23%
PROFIT/[LOSS] [ 1.53%]

SUMMARY = 7.25 + 0.60 = 7.85%

ACTUAL Specific rate LIBOR LESS 0.3% = 7.85 – 0.3]% = 7.55%
Futures loss [ 1.53%}
Effective rate 6.02%

PROFIT OR LOSS ON FUTURES IF INTEREST RATE DECREASES by 0.6% = 7.25% - 0.6% = 6.65%
START: INVESTMENT ; RECEIVE INTEREST @ Opening futures price 5.7%
END : PAY INTEREST @ closing futures price [6.65 – 0.62] 6.03%
PROFIT/LOSS [ 0.33%]

SUMMARY 7.25% - 0.60% = 6.65%

ACTUAL specific rate = LIBOR LESS 0.3% = 6.65 – 0.3]% = 6.35%
Futures loss [ 0.33%}
Effective rate 6.02%

ILLUSTRATION ON FUTURES
Black Co, a large listed company based in Europe, is expecting to borrow €12,000,000, in 3 months’ time
on 1 May 20X2. It expects to make a full repayment of the borrowed amount eight months from now. Currently
there is some uncertainty in the markets, with higher than normal rates of inflation, but an expectation that
the inflation level may soon come down. This has led some economists to predict a rise in interest rates and
others suggesting an unchanged outlook or maybe even a small fall in interest rates over the next six months.
Although Black Co is of the opinion that it is equally likely that interest rates could increase or fall by 0.8% in
3 months, it wishes to protect itself from interest rate fluctuations by using derivatives. The company can
borrow at LIBOR plus 80 basis points and LIBOR is currently 4.2%.
The following information and quotes from an appropriate exchange are provided on euro futures and options.
Margin requirements may be ignored.
Three-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25.
March 93.27

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June 94.16
September 95.02
It can be assumed that settlement for the futures contracts is at the end of the month. It can also be assumed
that basis diminishes to zero at contract maturity at a constant rate and that time intervals can be counted in
months.
Required
Determine the net interest payment if the exposure is hedged using interest rate futures

SOLUTION
Choose June contract : because transaction is in May ; OFP 94.16 = 100 – 94.16 = 5.84%
Effective rate = opening futures price + margin + unexpired basis
= 5.84% + 0.80 + (-0.66%) = 5.98%
No of contracts = 12,000,000 / 1,000,000 x 5 /3 = 20 contracts

Unexpired Basis calculation

Basis = Spot rate – opening futures price = 4.2% - 5.84% = -1.64% covers 5 months
Unused period = 1 May to June ending = 2 months
Unexpired basis = 2/5 x - 1.64% = -0.66%

ILLUSTRATION { MAY 2019 ICAN PAST QUESTION}

You are the head of the treasury group of Top Flight Aviation {TFA}, a Nigerian company. The company
operates chartered international flights for the elites in the country.
It is now December 31 and TFA needs to borrow £60m from a UK bank to finance a new air jet. The
borrowing and purchase will be in three months’ time and the borrowing will be for a period of six months.
You have decided to hedge the relevant interest rate risk using interest rate futures. Your expectation is that
interest rates will increase from 13% by 2% over the next three months.
In the month of March, the current price of sterling 3-month futures is 87.25. the standard contract size
is £500,000.
Required
a. Set out calculations of the effect of using the futures market to hedge against interest rate movements
I. If interest rate increases from 13% by 2% and the futures market price also moves by 2%
II. If interest rates increases from 13% by 2% and the futures market price moves by 1.75%
III. If interest rate falls from 13% by 1.5% and the futures market moves by 1.25%

In each case, show the Hedge Efficiency.

The time value of money, taxation and margin requirements should be ignored. [11 marks}
b. Show, for the situations in “a” above, whether the total cost of the loan after hedging would have
been lower with the futures hedge chosen by the treasurer or with an interest rate guarantee which

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the treasurer could have purchased at 13% for a premium of 0.25% of the size of the loan to be
guaranteed.
The time value of money, taxation and margin requirements should be ignored. [4 marks} {Total 15
Marks}

SOLUTION
Today’s date = Dec 31
Start date : 3 months time = March
Loan period = 6 months
Contract size = £500,000
Number of contracts = exposure / contract size x loan period / futures period
60,000,000 / 500,000 x 6 / 3 = 240 contracts.
Interest rate = 13%
Opening futures price = 87.25
I. If interest rate increases from 13% by 2% and the futures market price also moves by 2%
II. If interest rates increases from 13% by 2% and the futures market price moves by 1.75%
III. If interest rate falls from 13% by 1.5% and the futures market moves by 1.25%

Borrowing Scenario 1 Scenario 2 Scenario 3

Actual
Current 13% 13% 13%
New 15% 15% 13 – 1.5 = 11.5%
Loss [2%] [2%] 1.5%
Total loss = loss% x amount x 6/12 2% x 60,000,000 x 2% x 60,000,000 1.5% x 60,000,000
6/12= £600,000 loss x 6/12= x 6/12= £450,000
£600,000 loss profit

Futures
Opening @ pay interest 87.25 = 12.75% 87.25 = 12.75% 87.25 = 12.75%
Closing @ receive interest 87.25 – 2 = 85.25= 87.25 – 1.75 = 87.25 + 1.25 = 88.5
14.75% 85.5 = 14.5% = 11.5%
Gain / [loss] 2% 1.75% [1.25%]
Gain = loss% x no of contracts x 2% x 240 x 500,000 1.75% x 240 x 1.25% x 240 x
contract size x 3/12 x 3/12 = £600,000 500,000 x 3/12 = 500,000 x 3/12 =
profit £525,000 profit £375,000 loss

Hedge efficiency = profit / loss 600,000 / 600,000 = 525,000 / 450,000 / 375,000 =

100% 600,000 = 87.5% 120%

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Hedge efficiency shows how well the profit from one transaction {futures or actual} covers the expected loss
on another transaction {futures or actual].
B PART OF THE QUESTION
Compare the Futures market result to an interest rate Guarantee .
FUTURES MARKET NET RESULT
SCENARIO 1 2 3
Actual 15% x 60m x 6/12 = 15% x 60m x 6/12 = 11.5% x 60m x 6/12 =
payment [4,500,000] [4,500,000] [3,450,000]
Profit/loss 600,000 525,000 [375,000]
Net payment [3,900,000] [3,975,000] [3,825,000]

INTEREST RATE GUARANTEE

Interest rate guarantee is an option on FRA. It is simply a right not an obligation to pay or receive interest at
an agreed rate in the future. Premium must be paid in advance because it is an option. Recall that premium
is paid irrespective of whether you exercise or not. Premium is not prorated and is non-refundable.
purchased at 13% for a premium of 0.25% of the size of the loan to be guaranteed
Premium = 0.25% x 60,000,000 = £150,000
SCENARIO 1 2 3
Actual 15% 15% 11.5%
FRA 13% 13% 13%
YES/NO YES Yes NO
Payment 13% x 60m x 6/12 = [3,900,000] 13% x 60m x 6/12 = 11.5% x 60m x 6/12 =
[3,900,000] [3,450,000]
premium [150,000] [150,000] [150,000]
Net [4,050,000] [4,050,000] [3,600,000]
payment

ILLUSTRATION
Matrix Co is a large multinational company with a number of international subsidiary companies. Assume it
is 1 December 2020 today and Matrix Co is expecting to borrow $25,000,000 on 1 February 2021 for a
period of 7 months. The funds can be borrowed at LIBOR plus 40 basis points. LIBOR is currently 3.8%
but feels that this could increase or decrease by 0.5% over the coming months due to increasing uncertainty
in the markets.
Futures prices are quoted in basis points at 100 minus the annual percentage yield and settlement of
contracts is at the end of the March 2021.

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The current basis on the March futures price is 44 points and is expected to be 33 points on 1 January 2021,
22 points on 1 February 2021 and 11 points on 1 March 2021.[Basis is calculated as Spot rate less Opening
futures price, and the basis given is a negative basis.
Determine the effective annual interest rate and the net cash flow if this risk is hedged using Interest rate
futures considering the likelihood of increase or decrease in interest rate.
SOLUTION
Effective rate = Opening futures price + margin + unexpired basis
= 4.24% + 0.4% + (-0.22) = 4.38%

Basis = spot rate – opening futures price

-0.44 = 3.8% - X
X = 3.8% + 0.44% = 4.24%

INTEREST RATE OPTIONS

Options are named according to the underlying asset, commodity options where the underlying asset is a
commodity, currency option if the underlying asset is currency, interest rate option where underlying asset is
interest rate and real options where underlying asset is a real project or tangible asset. It could also be an
option on a FRA [Guarantee] or an option on futures.

This grants the buyer (holder) of the option the right but not the obligations, to deal at an agreed interest
rate (strike price) at a future maturity date. On the expiry date of the option, the buyer must decide whether
or not to exercise the rights. Clearly, a buyer of an option to borrow will not wish to exercise it if the market
interest rate is now below the option price, just as the lender will not exercise if the market rate of interest is
higher than that in the option agreement.
Borrowers can set a maximum on the interest they have to pay by buying put options known as Borrowers
option. The option will be exercised if the LIBOR is higher than the strike rate.
Lenders can set a minimum on the interest they receive by buying call options known as lenders option.
The option will be exercised if the LIBOR is lower than the strike rate.
SWAPTIONS is an option on a Swap which gives the holder the right but not the obligation to enter into a
swap agreement at a future date on terms that are fixed now.
INTEREST RATE CAP is an option which sets an interest rate ceiling. It is a series of borrowers option
setting a maximum interest rate on a variable rate borrowing protecting holders from adverse movements in
interest rates by setting a maximum borrowing cost for any roll over date on a variable rate loan. It is an
agreement where the seller (writer) agrees to compensate the buyer (holder) if interest rates rise above the
exercise rate at each reset date. [

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INTEREST RATE FLOOR is an option which sets a lower limit to interest rates. It is a series of successive
lender options that can be used to fix minimum interest rate for a series of interest rate periods. The writer
agrees to compensate the buyer if interest rates fall below the strike rate at each reset date.
STEPS IN SETTING UP AN INTEREST RATE Options
▪ Identify the exposure : it is either borrowing or investment
▪ Choose the contract type : if it is borrowing, we choose a contract to pay interest/ sell (put option)
but if it is investing, we choose a contract to receive interest buy (call option)
▪ Pick the contract expiry: it should be a contract that aligns with the start of the transaction (unlike
currency options that looks at the end of the contract)
▪ Determine number of contracts required = (exposure / contract size) x (transaction period /
options contract period). Note Options contract period is assumed to be 3 months except otherwise
stated. All contracts required should be in whole numbers.
▪ Determine the appropriate strike price: which is the lowest cost if you are paying (put option)
and the highest income if you are receiving (call option).
▪ Determine the premium and calculate the total premium (premium per contract x number of
contracts x contract size x 3/12)
▪ Determine whether to exercise or not by comparing the strike rate with the actual interest rate
or closing futures price (if the option is on futures)
▪ Calculate your profit per contract and the total profit (profit per contract x number of contracts
x contract size x 3/12
▪ Calculate the actual interest payment or receipt based on the current rate
▪ Determine your net outcome is Actual payment/receipt ± profit ± premium
▪ Determine the effective interest rate

INTEREST RATE GUARANTEE [IRG]

This is an option on a FRA. A premium is paid in advance and the downside risk is prevented. For a borrower,
if interest rates fall, the guarantee is not used and the firm borrows at the prevailing lower rate. If interest
rates are expected to rise, you will go for FRA but when you are unsure, you make use of the IRG.
ILLUSTRATION ON INTEREST RATE GUARANTEE
A company wishes to borrow $35 million in 3 months’ time for a period of 5 months. An IRG is available at
9% for a premium of 0.23% of the size of the loan.
Required
Calculate the interest payable if in three months’ time
▪ If the market interest rate is 10%
▪ If the market interest rate is 5%

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OPTIONS ON FUTURES
These are options to buy or sell futures on interest rates. All information about the futures remain valid.
Contracts are assumed to mature in March, June , September and December. Call option gives the right to
buy the futures contract while Put option gives the holder the right to sell the futures contract.
How to select an option price
For a call option {option to buy or receive interest] = choose the price that gives the highest receipt {strike
rate less premium}
For a put option {option to sell or pay interest} = choose the price that gives the lowest cost { strike rate
plus premium}
ILLUSTRATION
Options on three-month futures, $2,000,000 contract size, option premium are in annual %
Exercise price Premium on call option Premium on put option
93.75 0.175 0.118
94.00 0.155 0.225
94.50 0.150 0.310
95.00 0.140 0.420
Required
a. What is a tick and what is the tick value of the above contract table
b. If the exposure was a borrowing transaction of $18,000,000 for 4 months, show the contract type,
the number of contracts, the premium payable and the appropriate strike or exercise price. What will
be the net cost if the actual interest rate in the market is 7%.
c. If the exposure was an investment transaction of $23,500,000 for 6 months, show the contract type,
the premium payable, the number of contracts and the appropriate exercise price. What will be the
net receipt if the actual interest rate in the market is 9%

SOLUTION
Tick value = Tick x contract size x futures period = 0.0001 x $2,000,000 x 3/12 = $50
B PART OF THE QUESTION
Borrowing = contract to pay interest = [put option]
Number of contracts = {exposure / contract size} x { loan period / option period} = 18,000,000 / 2,000,000
x 4/3 = 12 contracts
Appropriate strike price : contract to pay interest: put option – Price that will give us the lowest net cost
Exercise price in ticks Exercise price in % Premium in % Net cost in %
93.75 6.25 0.118 6.37

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94.00 6.00 0.225 6.23

94.50 5.5 0.310 5.81
95.00 5.0 0.420 5.42
Appropriate exercise price is 95 = 5% as it gives the lowest cost
Yes/no : since you are paying, you only exercise if exercise rate is lower
Exercise price = 5%
Actual rate = 7%
Yes ; gain 2%
Total premium = premium% x number of contracts x contract size x options period = 0.42% x 12 x 2,000,000
x 3/12 = $252,000
PRESENTATION OF FINAL RESULT
Borrowing investment
Actual specific rate {xxx} xxx
Profit from option xxx xxx
Premium {xxx} {xxx}
Effective rate xxx xxx

C PART OF THE QUESTION

Contract type: contract to receive interest since it is an investment.
Number of contracts = {exposure / contract size} x { loan period / option period} = 23,500,000 / 2,000,000
x 6/3 = 23.5 contracts = 24 contracts
Appropriate exercise price is the rate that gives the highest receipt {call option] {exercise price – premium}
Exercise price in ticks Exercise price in % Premium in % Net receipt in %
93.75 6.25 0.175 6.08
94.00 6.00 0.155 5.85
94.50 5.5 0.150 5.35
95.00 5.0 0.140 4.86
Appropriate exercise price is 93.75 = 6.25% as it gives the highest receipt
YES / NO TO RECEIVE INTEREST {focus is on the higher interest receipt}
Exercise Price 6.25%
Actual rate 9%
NO 0

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Total premium = premium% x number of contracts x contract size x options period = 0.175% x 24 x 2,000,000
x 3/12 = $210,000
ILLUSTRATION ON OPTION ON FUTURES
Lekki Gardens [LG] is expecting to receive $50,000,000 on 1 February 2021, which will be invested until
it is required for a large project on 1 August 2021. The company can invest funds at the inter-bank rate less
30 basis points. The current inter-bank rate is 7.25%. However, LG is of the opinion that interest rates could
increase or decrease by as much as 0.6% over the coming months.
The following information and quotes are provided from an appropriate exchange on $ futures. Margin
requirements can be ignored.
Three-month $ futures, $2,000,000 contract size; prices are quoted in basis points at 100 – annual %
yield
December 2020 94.55
March 2021 94.30
June 2021 94.15

Option on Three-month $ futures, $2,000,000 contract size; option premiums are in annual %
CALLS PUTS
DECEMBER MARCH JUNE STRIKE DECEMBER MARCH JUNE
0.342 0.432 0.523 94.50 0.090 0.119 0.271
0.097 0.121 0.289 95.00 0.312 0.417 0.520

It can be assumed that settlement for the Options contract is at the end of the month and that basis diminishes
to zero at contract maturity at a constant rate, based on monthly time intervals. Assume that it is 1 November,
2020 now and that there is no basis risk.
Required
Determine the net receipt or payment and the effective rate, if the above exposure is hedged using the
Interest rate Options on futures.
SOLUTION
Exposure = investment ; contract type ; to receive interest [call option] ; contract; MARCH call option :
strike price = 95.00 ; premium = 0.121%
Number of contracts = $50,000,000 / $2,000,000 x 6/3 = 50 contracts
YES/NO ; RECEIVE INTEREST ; for call, you only exercise if your exercise price is higher
increases decreases
EXERCISE PRICE 95 = 100 - 95 5% 5%
CLOSING FUTURES PRICE 7.23% 6.03%

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Yes / no No 0 No 0

Summary
increases Decreases
Actual rate 7.85 6.65
Profit 0 0
Premium [0.121] [0.121]
Net 7.73% 6.53%

Closing futures price = closing interest rate – unexpired basis

Interest rate increases = 7.25% + 0.6%= 7.85% - [+0.62] = 7.23%
Interest rate reduces = 7.25% - 0.6% = 6.65% - [+0.62] = 6.03%

Unexpired basis
Basis = spot rate – opening futures price = 7.25% - [100 – 94.3) =
7.25% - 5.7% = +1.55% ; 1 Nov – 30 mar = 5 months
Unexpired basis = 1 Feb – 30 Mar = 2 months
Unexpired basis = 2/5 x +1.55% = 0.62
ILLUSTRATION ON OPTION ON FUTURES
Black Co, a large listed company based in Europe, is expecting to borrow €12,000,000, in 3 months’ time
on 1 May 20X2. It expects to make a full repayment of the borrowed amount eight months from now. Currently
there is some uncertainty in the markets, with higher than normal rates of inflation, but an expectation that
the inflation level may soon come down. This has led some economists to predict a rise in interest rates and
others suggesting an unchanged outlook or maybe even a small fall in interest rates over the next six months.
Although Black Co is of the opinion that it is equally likely that interest rates could increase or fall by 0.8% in
3 months, it wishes to protect itself from interest rate fluctuations by using derivatives. The company can
borrow at LIBOR plus 80 basis points and LIBOR is currently 4.2%.
The following information and quotes from an appropriate exchange are provided on euro futures and options.
Margin requirements may be ignored.
Three-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25.
March 93.27
June 94.16
September 95.02

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Option on Three-month € futures, €1,000,000 contract size; tick size 0.01%, option premiums are in annual
%
CALLS PUTS
March June September STRIKE March June September
0.279 0.391 0.446 96.00 0.006 0.163 0.276
0.012 0.090 0.263 96.50 0.196 0.581 0.754
It can be assumed that settlement for the futures contracts is at the end of the month. It can also be assumed
that basis diminishes to zero at contract maturity at a constant rate and that time intervals can be counted in
months.
Required
Determine the net interest payment if the exposure is hedged using interest rate Option on futures

SOLUTION
Exposure : Borrowing ………. Contract to pay interest [put option]
Contract duration: JUNE contract
Exercise price = 96.00 = 4% [lower] ; premium ; 0.163%
Number of contracts = 12,000,000 / 1,000,000 x 5/3 = 20 contracts
YES/NO ;;;;;;;;PUT OPTION;;;;PAY INTEREST
INCREASES 5% DECREASES 3.4%
STRIKE PRICE 4% 4%
CLOSING FUTURES PRICE 5.66% 4.06%
YES/NO Yes 1.66% Yes 0.06%

Closing futures price = closing rate – unexpired basis

Increases = closing rate = 4.2+ 0.8 = 5% - [-0.66] = 5.66%
Decreases = closing rate = 4.2 – 0.8 = 3.4% - [- 0.66] = 4.06%

Basis = 4.2% - 5.84% = -1.64% for 5 months

Unexpired basis period = 1 May to June 30 = 2 months
Unexpired basis = 2/5 x [-1.64%] = -0.66

SUMMARY; Borrowing
Increase Decrease
Actual specific rate 5 + 0.8 = [5.8%] 3.4 + 0.8 = [4.2%]
Profit 1.66% 0.06%
Premium [0.163%] [0.163%]
Net payment [4.303%] [4.303%]

ILLUSTRATION
Matrix Co is a large multinational company with a number of international subsidiary companies. Assume it
is 1 December 2020 today and Matrix Co is expecting to borrow $25,000,000 on 1 February 2021 for a period
of 7 months. The funds can be borrowed at LIBOR plus 40 basis points. LIBOR is currently 3.8% but feels

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that this could increase or decrease by 0.5% over the coming months due to increasing uncertainty in the
markets.
Option prices are quoted in basis points at 100 minus the annual percentage yield and settlement of contracts
is at the end of the March 2021. The following information are quotes for $ March options are provided from
an appropriate exchange. The options are based on 3-month $ futures and $1,000,000 contract size and
option premium are in annual %.
MARCH CALLS STRIKE PRICE MARCH PUTS
0.882 95.50 0.662
0.648 96.00 0.902
The current basis on the March futures price is 44 points and is expected to be 33 points on 1 January 2021,
22 points on 1 February 2021 and 11 points on 1 March 2021.[Basis is calculated as Spot rate less Opening
futures price, and the basis given is a negative basis.
Determine the effective annual interest rate and the net cash flow if this risk is hedged using Interest rate
Option on futures considering the likelihood of increase or decrease in interest rate.

ILLUSTRATION (ICAN PAST QUESTION MARCH/JULY 2020)

Mr. Big Heart is a Nigerian highly successful business man with interest in manufacturing, transportation,
telecommunication and aviation. He has recently shown interest in acquiring one of the La liga league football
clubs in Spain. Negotiation with the current owners of the club is now completed and price agreed.
Mr. Big Heart‟s group of companies have been able to raise a significant portion of the total amount needed
for the purchase consideration of the club but there is a shortfall of $150 million today September 16, 2020
and the total payment for the acquisition must be made by December 16, 2020. A two-month loan of $150
million, commencing from December 16, 2020 is therefore being considered.
The group finance director (GFD) has spoken to the bankers in Madrid who have agreed to provide the $150
million needed. Given Mr. Big Heart‟s credit rating, the short-term loan will be at a rate of 90 basis points
above LIBOR. Currently, LIBOR is at 6%. The bank has also suggested that, due to the current economic
uncertainty, LIBOR may rise by 1% or even fall by 0.5% over the coming months.
With this in mind, the group treasury department has been mandated to manage this risk in a manner it thinks
will best minimise the inherent interest risk. The department has obtained the following data from the money
and traded derivatives markets.
Derivative contracts may be assumed to mature at the end of the month.
Three months sterling future ($500,000 contract size, $12.50 tick size)
Sept. 93.870
Dec. 93.790
March 93.680
Options on three months sterling futures
($500,000 Contract size, premium cost in annual %)
Exercise price CALLS PUTS
SEPT DEC MAR SEPT DEC MAR
93.750 0.120 0.195 0.270 0.020 0.085 0.180
94.000 0.015 0.075 0.115 0.165 0.255 0.335
94.250 0 0.030 0.085 0.400 0.480 0.555

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FRA PRICES:
3V6 7.01 --- 6.91
3V5 7.08 --- 7.00
3V8 7.28 --- 7.20
Required:
Demonstrate and explain the possible ways in which the interest rate risk may be managed in relation to the
purchase of the club, using the information provided. Based on your analysis, advise on an appropriate
course of action.
Note: your analysis should be based on the three derivatives identified in the scenario that is:
▪ FRA
▪ Financial Futures
▪ Traded options (total 20 marks)

COLLAR ARRANGEMENT is a situation when the borrower can buy an interest rate cap and at the same
time sell an interest rate floor which reduces the cost for the company. The cost of a collar is lower than for
a cap alone. The aim is to receive compensation from the CAP when interest rate is higher and pay
compensation when interest rate is lower than the strike price. It is a combination of cap and floor.
ZERO COST COLLARS is a collar for which the premium is zero. It is a collar where the premium value to
and from a cap and floor are equal or close.
BORROWING CONTRACT to pay interest [put option] ; pay premium @ the price with the lower premium
Contract ; sell right to receive interest [call option] ; receive premium @ the other price
Net premium = [pay premium - receive premium]

Investment ; contract to receive interest [call option] ; pay premium @ the price with the lower premium
Contract ; sell right to pay interest [put option]; receive premium @ the other price
ILLUSTRATION ON COLLAR
A company wants to borrow $60,000,000 on the 1st of March for 3 months. The company can borrow at
LIBOR plus 2%. LIBOR is currently 8%.
A member of the treasury team has suggested the use of collar to reduce the premium cost of the purchased
option.
Market data: Interest rate options; option premium are in %
CALLS PUTS
March June September STRIKE March June September
0.80 0.77 0.74 92.00 0.20 0.22 0.24
0.15 0.12 0.10 93.00 0.60 0.70 0.80
Required
a. Calculate the effective interest rate the company will pay using a collar if
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▪ LIBOR rises to 9.5% and futures prices moves to 90.20

▪ LIBOR falls to 4.5% and futures prices moves to 96.10

SOLUTION TO A PART OF THE QUESTION

EXPOSURE BORROWING
CONTRACT TO pay interest [put option] March Put @92.00 ;; pay premium of 0.20%
sell To receive interest {call option] March Call @93.00;;receive premium of 0.15%
Net premium 0.20 – 0.15 = 0.05%

YES/NO Pay interest [PUT] Receive interest [CALL]

Strike price 100 – 92 = 8% 100 – 93 = 7%
Closing futures 100 – 90.20 = 9.8% 100 – 90.20 = 9.8%
Profit YES 1.8% NO 0

SUMMARY INTEREST RATE 9.5%

ACTUAL [9.5%]
Profit 1.8%
corresponding [0%]
premium [0.05%]
Effective rate [7.75%]

IF LIBOR FALLS TO 4.5%

EXPOSURE BORROWING
CONTRACT TO pay interest [put option] March Put @92.00 ;; pay premium of 0.20%
sell To receive interest {call option] March Call @93.00;;receive premium of 0.15%
Net premium [0.20] + 0.15 =- 0.05%

YES/NO Pay interest [PUT] Receive interest [CALL]

Strike price 100 – 92 = 8% 100 – 93 = 7%
Closing futures 100 – 96.10 = 3.9% 100 – 96.10 = 3.9%
Profit NO 0 YES 3.1%

SUMMARY INTEREST RATE 4.5%

ACTUAL [4.5%]
Profit 0%
corresponding [3.1%]
premium [0.05%]
Effective rate [7.65%]

b. If the transaction was an investment of $30,000,000 on 1st of August for 4 months. The company
invests at LIBOR less 1.5%. LIBOR is currently 8%.
▪ LIBOR rises to 9.5% and futures prices moves to 90.20

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▪ LIBOR falls to 4.5% and futures prices moves to 96.10

▪ EXPOSURE Investment
CONTRACT TO receive interest [call March call @93.00 ;; pay premium of
option] 0.15%
sell To pay interest {put option] March put @92.00;;receive premium of
0.20%
Net premium {0.15] +0.20 =+0.05%

YES/NO Receive interest [CALL] Pay interest [PUT]

Strike price 100 – 92 = 8% 100 – 93 = 7%
Closing futures 100 – 90.20 = 9.8% 100 – 90.20 = 9.8%
Profit NO 0 YES 2.8%

SUMMARY INTEREST RATE 9.5%

ACTUAL 9.5%
Profit 0%
corresponding [2.8%]
premium 0.05%
Effective rate 6.75%

IF LIBOR FALLS TO 4.5%

EXPOSURE INVESTMENT
CONTRACT TO receive interest [call option] March call @93.00 ;; pay premium of 0.15%
sell To pay interest {put option] March put @92.00;;receive premium of 0.20%
Net premium {0.15] +0.20 =+0.05%

YES/NO Receive interest [CALL] Pay interest [PUT]

Strike price 100 – 92 = 8% 100 – 93 = 7%
Closing futures 100 – 96.10 = 3.9% 100 – 96.10 = 3.9%
Profit YES 4.1% NO 0

SUMMARY INTEREST RATE 4.5%

ACTUAL 4.5%
Profit 4.1%
corresponding [0%]
premium 0.05%
Effective rate 8.65%

ILLUSTRATION ON COLLAR

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Black Co, a large listed company based in Europe, is expecting to borrow €12,000,000, in 3 months’ time
on 1 May 20X2. It expects to make a full repayment of the borrowed amount eight months from now. Currently
there is some uncertainty in the markets, with higher than normal rates of inflation, but an expectation that
the inflation level may soon come down. This has led some economists to predict a rise in interest rates and
others suggesting an unchanged outlook or maybe even a small fall in interest rates over the next six months.
Although Black Co is of the opinion that it is equally likely that interest rates could increase or fall by 0.8% in
3 months, it wishes to protect itself from interest rate fluctuations by using derivatives. The company can
borrow at LIBOR plus 80 basis points and LIBOR is currently 4.2%.
The following information and quotes from an appropriate exchange are provided on euro futures and options.
Margin requirements may be ignored.
Option on Three-month € futures, €1,000,000 contract size; tick size 0.01%, option premiums are in annual
%
CALLS PUTS
March June September STRIKE March June September
0.279 0.391 0.446 96.00 0.006 0.163 0.276
0.012 0.090 0.263 96.50 0.196 0.581 0.754
It can be assumed that settlement for the futures contracts is at the end of the month. It can also be assumed
that basis diminishes to zero at contract maturity at a constant rate and that time intervals can be counted in
months.
Required
Determine the net interest payment if the exposure is hedged using interest rate Collars

INTEREST RATE SWAPS is an agreement whereby the parties to the agreement exchange interest
rate commitments over an agreed period. A swap between floating rate interest and fixed rate interest is
known as a “plain vanilla” or generic swap”. The variable rate included in a swap is LIBOR (London inter-
bank offered rate). This benchmark of interest is the rate paid between banks.

ILLUSTRATION ON INTEREST RATE SWAPS

Gemma wants to borrow £20 million for five years, with interest payable at six monthly intervals. It can borrow
this money from a bank at a floating rate for LIBOR plus 1%, but wants to obtain a fixed rate for the full five
year period. A swaps bank indicates that it will be willing to receive a fixed rate of 9.7% in exchange for
payments of six month LIBOR. Evaluate the hedge if the LIBOR is 11% or 8.8%.
ILLUSTRATION (ICAN PAST QUESTION NOVEMBER 2020)
a. What risks might an industrial company face as a result of interests movements {8 marks}
b. A plc wants to borrow N200 million for five years with interest payable at six-monthly intervals. It can
borrow from a bank at a floating rate of NIBOR plus 1% but wants to obtain a fixed rate for the full
five-year period. A swap bank has indicated that it will be willing to receive a fixed rate of 8.5% in
exchange for payments of six-month NIBOR.
Required :

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Calculate the fixed interest six-monthly payment with the swap in place {4 marks}
c. Calculate
I. The interest payments if NIBOR is 10% {4 marks}
II. The interest payments if NIBOR is 7.5% {4 marks}

{Total 20 Marks}
ILLUSTRATION ON SWAP [ June 2012 amended]
Whyte Group Limited, a listed company, recently issued debt finance to acquire assets in order to increase
its activity levels. This debt finance is in the form of a floating rate bond, with a face value of $320 million,
redeemable in 4 years. The bond interest, payable annually, is based on the spot yield curve plus 60 basis
points. The next annual payment is due at the end of year one.
Whyte Group Limited[WGL] is concerned that the expected rise in interest rates over the coming few years
would make it increasingly difficult to pay the interest due. It is therefore proposing to either swap the floating
rate interest payment to a fixed rate payment, or to raise new equity capital and use that to pay off the floating
rate bond. The new equity capital would either be issued as rights to the existing shareholders or as shares
to new shareholders.
Sky Bank has offered Whyte Group Limited an interest rate swap, whereby WGL would pay Sky Bank interest
based on an equivalent fixed annual rate of 3.761/4% in exchange for receiving a variable amount based on
the current yield curve rate. Payments and receipts will be made at the end of each year, for the next four
years. Sky Bank will charge an annual fee of 20 basis points if the swap is agreed and will also guarantee
the swap. The current annual spot yield curve rates are as follows:
YEAR 1 2 3 4
RATE 2.5% 3.1% 3.5% 3.8%
The current annual forward rates for two, three and four are as follows:
YEAR 2 3 4
RATE 3.7% 4.3% 4,7%
Required:
a. Based on the above information, calculate the amounts WGL expects to pay or receive every year
on the swap excluding the bank fee of 20 basis points
b. Explain why the fixed annual rate of interest of 3.761/4% is less than the 4 year yield curve rate of
3.8%
c. Demonstrate that WGL’s interest payment liability does not change , after it has undertaken the
swap, whether the interest rates increase to 5% or reduce to 3%.
d. Discuss the advantages and disadvantages of the swap for Whyte Group Limited.

ILLUSTRATION ON SWAP BETWEEN TWO COMPANIES

Hankali plc and Bakomi plc want to raise ₦100m five year loans. Bakomi wants to borrow at a fixed rate of
interest, wanting to have a certainty about its future interest liabilities. Hankali wishes to borrow at a floating
rate because its treasurer believes that interest rates are likely to fall in the future.

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The current borrowing rates applicable to the two companies in the cash market are as follows:
Floating Fixed
HANKALI NIBOR + 1% 14%
BAKOMI NIBOR + 2% 15.75%
Sharp Bank has agreed to arrange an interest swap for three years between the two companies at a one off
fee of ₦50,000 each.
Required
a. Advise the organization if an interest rate swap would be beneficial showing how it would work and
any benefit for each of the three years, if it is agreed that any benefit would be shared equally by
both companies (10 marks)

ILLUSTRATION ON SWAP BETWEEN TWO COMPANIES [DEC 2014 AMENDED]

Keshi can borrow the funds at a variable rate of LIBOR plus 40 basis points or a fixed rate of 5.5%. LIBOR
is currently 3.8% but Keshi feels that this could increase or decrease by 0.5% over the coming months.
Razu bank has offered Keshi Co a swap on a counter party variable rate of LIBOR plus 30 basis points or a
fixed rate of 4.6%, where Keshi Co receives 70% of any benefits accruing from undertaking the swap, prior
to any bank charges. Razu bank will charge Keshi 10 basis points for the swap.
Based on the interest rate swap, recommend what the effective rate of hedging the $18,000,000 loan.
ILLUSTRATION (MAY 2017 ICAN PAST QUESTION)
Large plc(LP) wishes to borrow N200 million for five years to finance the purchase of new non-current assets.
The preference of the company’s directors is that these funds are borrowed at a fixed rate of interest. The
company’s long term debt is currently rated BBB, meaning LP would have to pay 6.5% per annum for fixed
rate borrowing. Alternatively, LP could borrow at a floating rate i.e, the prime lending rate (PLR) + 2.25% at
the present time.
The directors of LP have recently been informed by its bank that TK plc, is also currently looking to borrow
N200 million for five years at a floating rate of interest and its AA rating gives it access to floating rate
borrowing at PLR + 1.50% per annum. TK plc would pay 5.5% per annum for fixed rate borrowing at the
present time.
Required :
a. State five reasons that a company might have for entering into an interest rate swap (5 marks)
b. Show how an interest rate swap could be used to the equal benefit of both companies, assuming
that the terms of the swap agreement are such that LP’s swap payment to TK plc is to be 5.5% fixed
per annum (7 marks)
c. Identify, with a supporting brief explanation, which of the two companies would be disadvantaged, if
PLR were to fall consistently within the five year terms of the interest rate swap (1 mark)
d. Identify two risks that both companies will face, should they decide to enter into the interest rate
swap agreement (2 marks)

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ILLUSTRATION ON INTEREST RATE HEDGING

Awan co is expecting to receive $48,000,000 on 1 February 2014, which will be invested until it is required
for a large project on 1 June 2014. Due to uncertainty in the markets, the company is of the opinion that it is
likely that interest rates will fluctuate significantly over the coming months, although it is difficult to predict
whether they will increase or decrease.
Awan co’s treasury team want to hedge the company against adverse movements in interest rates using one
of the following derivative products;
Forward rate agreements, interest rate futures or options on interest rate futures
Awan co can invest funds at the relevant inter-bank rate less 20 basis points. The current interbank rate is
4.09%. However Awan co is of the opinion that interest rates could increase or decrease by as much as 0.9%
over the coming months.
The following information and quotes are provided from an appropriate exchange on $ futures and options.
Margin requirements can be ignored.
Three month $ futures, $2,000,000 contract size
Prices are quoted in basis points at 100 – annual % yield
December 2013 94.80
March 2014 94.76
June 2014 94.69

Options on three – month $ futures, $2,000,000 contract size, option premiums are in annual %
CALLS STRIKE PUTS
December March June December March June
0.342 0.432 0.523 94.50 0.090 0.119 0.271
0.097 0.121 0.289 95.00 0.312 0.417 0.520

Zanith bank has offered the following FRA rates to Awan co:
1=7 4.37%
3–4 4.78%
3–7 4.82%
4–7 4.87%
It can be assumed that settlement for the futures and options contracts is at the end of the month and that
basis diminishes to zero at contract maturity at a constant rate, based on monthly time intervals. Assume that
it is 1 November 2013 now and that there is no basis risk.
Required
I. Based on the three hedging choices Awan Co is considering, recommend a hedging strategy
for the $48,000,000 investment, if interest rates increase or decrease by 0.9%. support your
answer with appropriate calculations and discussion (19
marks)
II. A member of Awan Co’s treasury team has suggested that if option contracts are purchased
to hedge against the interest rate movements, then the number of contracts purchased
should be determined by a hedge ratio based on the delta value of the option.

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A. Discuss how the delta value of an option could be used in determining the number of contracts
purchased.

ALECTO 2013 PILOT EXAM QUESTION

Alecto Co, a large listed company based in Europe, is expecting to borrow €22,000,000, in 4 months’ time
on 1 May 20X2. It expects to make a full repayment of the borrowed amount nine months from now. Currently
there is some uncertainty in the markets, with higher than normal rates of inflation, but an expectation that
the inflation level may soon come down. This has led some economists to predict a rise in interest rates and
others suggesting an unchanged outlook or maybe even a small fall in interest rates over the next six months.
Although Alecto Co is of the opinion that it is equally likely that interest rates could increase or fall by 0.5% in
4 months, it wishes to protect itself from interest rate fluctuations by using derivatives. The company can
borrow at LIBOR plus 80 basis points and LIBOR is currently 3.3%. The company is considering using
interest rate futures, options on interest rate futures or interest rate collars as possible hedging
choices.
The following information and quotes from an appropriate exchange are provided on euro futures and options.
Margin requirements may be ignored.
Three-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25.
March 96.27
June 96.16
September 95.90
Options on three-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25. Option
premiums are in annual %.
CALLS PUTS
March June September Strike March June September
0.279 0.391 0.446 96.00 0.006 0.163 0.276
0.012 0.090 0.263 96.50 0.196 0.581 0.754

It can be assumed that settlement for both the futures and options contracts is at the end of the month. It
can also be assumed that basis diminishes to zero at contract maturity at a constant rate and that time
intervals can be counted in months.
Required
a. Briefly discuss the main advantage and disadvantage of hedging interest rate risk using an interest
rate collar instead of options (4 marks)
b. Based on the three hedging choices Alecto Co is considering and assuming that the company does
not face any basis risk, recommend a hedging strategy for the €22,000,000 loan. Support your
recommendations with appropriate comments and relevant calculations in €. (17 marks)
c. Explain what is meant by basis risk and how it would affect the recommendation made in part (b)
above. (4 marks)

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MASSIE (SEP/DEC 2015)

The Armstrong Group is a multinational group of companies. Today is 1 September. Massie Co is one of
Armstrong Group’s subsidiaries based in Europe.
The most significant transaction which Massie Co is due to undertake with a company outside the Armstrong
Group in the next six months is that it is due to receive €25 million from Bardsley Co on 30 November. Massie
Co’s treasury manager intends to invest this money for the six months until 31 May, when it will be used to
fund some major capital expenditure. However the treasury manager is concerned about changes in interest
rates. Predictions in the media range from a 0.5% rise in interest rates to a 0.5% fall.
Because of the uncertainty, the treasury manager has decided to protect Massie Co by using derivatives.
The treasury manager wishes to take advantage of favourable interest rate movements. Therefore she is
considering options on interest rate futures or interest rate collars as possible methods of hedging, but not
interest rate futures. Massie Co can invest at LIBOR minus 40 basis points and LIBOR is currently 3.6%.
The treasury manager has obtained the following information on euro futures and options. She is ignoring
margin requirements.
Three-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25
September 95.94
December 95.76
March 95.44

Options are 3-month euro futures, €1,000,000 contract, tick size 0.01% and tick value €25. Option
premiums are in annual %
CALLS STRIKE PUT
September December March September December March
0.113 0.182 0.245 96.50 0.0002 0.123 0.198
0.017 0.032 0.141 97.00 0.139 0.347 0.481
It can be assumed that settlement for the contracts is at the end of the month. It can also be assumed that
basis diminishes to zero at contract maturity at a constant rate and that time intervals can be counted in
months.
Required
Based on the choice of options on futures or collars which Massie Co is considering and assuming the
company does not face any basis risk, recommend a hedging strategy for the €25m receipt. Support your
recommendations with appropriate comments and relevant calculations. (14 marks)
ILLUSTRATION
2018 DECEMBER
4 Wardegul Co, a company based in the Eurozone, has expanded very rapidly over recent years by a
combination of acquiring subsidiaries in foreign countries and setting up its own operations abroad. Wardegul
Co’s board has found it increasingly difficult to monitor its activities and Wardegul Co’s support functions,
including its treasury function, have struggled to cope with a greatly increased workload. Wardegul Co’s
board has decided to restructure the company on a regional basis, with regional boards and appropriate
support functions. Managers in some of the larger countries in which Wardegul Co operates are unhappy

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with reorganisation on a regional basis, and believe that operations in their countries should be given a large
amount of autonomy and be supported by internal functions organised on a national basis.
Assume it is now 1 October 2017. The central treasury function has just received information about a future
transaction by a newly-acquired subsidiary in Euria, where the local currency is the dinar (D). The subsidiary
expects to receive D27,000,000 on 31 January 2018. It wants this money to be invested locally in Euria, most
probably for five months until 30 June 2018.
Wardegul Co’s treasury team is aware that economic conditions in Euria are currently uncertain. The central
bank base rate in Euria is currently 4·2% and the treasury team believes that it can invest funds in Euria at
the central bank base rate less 30 basis points. However, treasury staff have seen predictions that the central
bank base rate could increase by up to 1·1% or fall by up to 0·6% between now and 31 January 2018.
Wardegul Co’s treasury staff normally hedge interest rate exposure by using whichever of the following
products is most appropriate:
– Forward rate agreements (FRAs)
– Interest rate futures
– Options on interest rate futures
Treasury function guidelines emphasise the importance of mitigating the impact of adverse movements in
interest rates. However, they also allow staff to take into consideration upside risks associated with interest
rate exposure when deciding which instrument to use.
A local bank in Euria, with which Wardegul Co has not dealt before, has offered the following FRA rates:
4–9: 5·02%
5–10: 5·10%
The treasury team has also obtained the following information about exchange traded Dinar futures and
options:
Three-month D futures, D500,000 contract size
Prices are quoted in basis points at 100 – annual % yield:
December 2017: 94·84
March 2018: 94·78
June 2018: 94·66
Options on three-month D futures, D500,000 contract size, option premiums are in annual %
Calls Strike price Put
December March June December March June
0·417 0·545 0·678 94·25 0·071 0·094 0·155
0·078 0·098 0·160 95·25 0·393 0·529 0·664
It can be assumed that futures and options contracts are settled at the end of each month. Basis can be
assumed to diminish to zero at contract maturity at a constant rate, based on monthly time intervals. It can
also be assumed that there is no basis risk and there are no margin requirements.

Required:
(a) Recommend a hedging strategy for the D27,000,000 investment, based on the hedging choices
which treasury staff are considering, if interest rates increase by 1·1% or decrease by 0·6%. Support
your answer with appropriate calculations and discussion. (18 marks)
(b) Discuss the advantages of operating treasury activities through regional treasury functions
compared with:
– Each country having a separate treasury function.
– Operating activities through a single global treasury function. (7 marks)
(25 marks)

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JUNE 2015
4 For a number of years Daikon Co has been using forward rate agreements to manage its exposure to
interest rate fluctuations. Recently its chief executive officer (CEO) attended a talk on using exchange-traded
derivative products to manage risks. She wants to find out by how much the extra cost of the borrowing
detailed below can be reduced, when using interest rate futures, options on interest rate futures, and a collar
on the options, to manage the interest rate risk. She asks that detailed calculations for each of the three
derivative products be provided and a reasoned recommendation to be made.
Daikon Co is expecting to borrow $34,000,000 in five months’ time. It expects to make a full repayment of
the borrowed amount in 11 months’ time. Assume it is 1 June 2015 today. Daikon Co can borrow funds at
LIBOR plus 70 basis points. LIBOR is currently 3·6%, but Daikon Co expects that interest rates may increase
by as much as 80 basis points in five months’ time.
The following information and quotes from an appropriate exchange are provided on LIBOR-based $ futures
and options.
Three-month $ December futures are currently quoted at 95·84. The contract size is $1,000,000, the tick size
is 0·01% and the tick value is $25.
Options on three-month $ futures, $1,000,000 contract, tick size 0·01% and tick value $25. Option premiums
are in annual %.
December calls Strike price December puts
0·541 95·50 0·304
0·223 96·00 0·508
Initial assumptions
It can be assumed that settlement for both the futures and options contracts is at the end of the month; that
basis diminishes to zero at a constant rate until the contract matures and time intervals can be counted in
months; that margin requirements may be ignored; and that if the options are in-the-money, they will
exercised at the end of the hedge instead of being sold.
Further issues
In the talk, the CEO was informed of the following issues:
(i) Futures contracts will be marked-to-market daily. The CEO wondered what the impact of this would be if
50 futures contracts were bought at 95·84 on 1 June and 30 futures contracts were sold at 95·61 on 3 June,
based on the $ December futures contract given above. The closing settlement prices are given below for
four days:
Date Settlement price
1 June 95·84
2 June 95·76
3 June 95·66
4 June 95·74
(ii) Daikon Co will need to deposit funds into a margin account with a broker for each contract they have
opened, and this margin will need to be adjusted when the contracts are marked-to-market daily.
(iii) It is unlikely that option contracts will be exercised at the end of the hedge period unless they have
reached expiry. Instead, they more likely to be sold and the positions closed.
Required:
(a) Based on the three hedging choices available to Daikon Co and the initial assumptions given
above, draft a response to the chief executive officer’s (CEO) request made in the first paragraph of
the question.
(15 marks)

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(b) Discuss the impact on Daikon Co of each of the three further issues given above. As part of the
discussion, include the calculations of the daily impact of the mark-to-market closing prices on the
transactions specified by the CEO. (10 marks)
(25 marks)

2018 SEPTEMBER
Pault Co is currently undertaking a major programme of product development. Pault Co has made a
significant investment in plant and machinery for this programme. Over the next couple of years, Pault Co
has also budgeted for significant development and launch costs for a number of new products, although its
finance director believes there is some uncertainty with these budgeted figures, as they will depend upon
competitor activity amongst other matters.
Pault Co issued floating rate loan notes, with a face value of $400 million, to fund the investment in plant and
machinery. The loan notes are redeemable in ten years’ time. The interest on the loan notes is payable
annually and is based on the spot yield curve, plus 50 basis points.
Pault Co’s finance director has recently completed a review of the company’s overall financing strategy. His
review has highlighted expectations that interest rates will increase over the next few years, although the
predictions of financial experts in the media differ significantly.
The finance director is concerned about the exposure Pault Co has to increases in interest rates through the
loan notes. He has therefore discussed with Millbridge Bank the possibility of taking out a four-year interest
rate swap. The proposed terms are that Pault Co would pay Millbridge Bank interest based on an equivalent
fixed annual rate of 4·847%. In return, Pault Co would receive from Millbridge Bank a variable amount based
on the forward rates calculated from the annual spot yield curve rate at the time of payment minus 20 basis
points. Payments and receipts would be made annually, with the first one in a year’s time. Millbridge Bank
would charge an annual fee of 25 basis points if Pault Co enters the swap.
The current annual spot yield curve rates are as follows:
Year One Two Three Four
Rate 3·70% 4·25% 4·70% 5·10%
A number of concerns were raised at the recent board meeting when the swap arrangement was discussed.
– Pault Co’s chairman wondered what the value of the swap arrangement to Pault Co was, and whether the
value would change over time.
– One of Pault Co’s non-executive directors objected to the arrangement, saying that in his opinion the
interest rate which Pault Co would pay and the bank charges were too high. Pault Co ought to stick with its
floating rate commitment. Investors would be critical if, at the end of four years, Pault Co had paid higher
costs under the swap than it would have done had it left the loan unhedged.
Required:
(a) (i) Using the current annual spot yield curve rates as the basis for estimating forward rates,
calculate the amounts Pault Co expects to pay or receive each year under the swap (excluding the
fee of 25 basis points). (6 marks)
(ii) Calculate Pault Co’s interest payment liability for Year 1 if the yield curve rate is 4·5% or 2·9%, and
comment on your results. (6 marks)
(b) Advise the chairman on the current value of the swap to Pault Co and the factors which would
change the value of the swap. (4 marks)
(c) Discuss the disadvantages and advantages to Pault Co of not undertaking a swap and being liable
to pay interest at floating rates. (9 marks)
(25 marks)

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CURRENCY SWAPS is an arrangement whereby two organizations contractually agree to exchange

payments on different terms. The parties agree to swap equivalent amounts of currency for a period.

BENEFITS OF SWAP
▪ Flexibility: swaps are easy to arrange and are flexible since they can be arranged in any size and
are reversible
▪ Cost : transaction costs are low since there is no commission or premium to be paid
▪ Market avoidance: both parties can get the currency they require without subjecting themselves to
the uncertainties of the foreign exchange market
▪ Access to finance: the company can obtain debt finance in another country and currency where it
is little known and may have poorer credit rating.
▪ Financial restructuring: it may be used to restructure the currency base of the company’s liabilities
thereby reducing the exchange rate exposure
▪ Conversion of debt type: it enables the company also convert its interest rate from a fixed rate to
a floating rate and vice versa.
▪ Liquidity improvement; it could be used to absorb excess liquidity in one currency which is not
needed immediately, to create funds in another when there is a need.
▪ It is available for a longer period

DISADVANTAGES OF SWAP
▪ Risk of default by the other party to the swap (counterparty risk); if one party defaults, the other
party faces the risk of making the payment.
▪ Position or market risk: it may increase the financial risk of the company in a bid to make
speculative gains
▪ Sovereign risk; there may be a risk of political disturbances or exchange controls in the country
whose currency is being used for a swap
▪ Arrangement fees: there are fees that would be paid to the intermediary even though he accepts
no liability for the swap.

FOREX SWAP is a spot currency transaction coupled with an agreement that it will be reversed
at a pre-specified date by an offsetting forward transaction. It is also called a buy/sell swap or
sell/buy swap with no payment of interest rate.

2017 DECEMBER
Buryecs Co is an international transport operator based in the Eurozone which has been invited to take over
a rail operating franchise in Wirtonia, where the local currency is the dollar ($). Previously this franchise was
run by a local operator in Wirtonia but its performance was unsatisfactory and the government in Wirtonia
withdrew the franchise.
Buryecs Co will pay $5,000 million for the rail franchise immediately. The government has stated that Buryecs
Co should make an annual income from the franchise of $600 million in each of the next three years. At the
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end of the three years the government in Wirtonia has offered to buy the franchise back for $7,500 million if
no other operator can be found to take over the franchise.
Today’s spot exchange rate between the Euro and Wirtonia $ is €0·1430 = $1. The predicted inflation rates
are as follows:
Year 1 2 3
Eurozone 6% 4% 3%
Wirtonia 3% 8% 11%
Buryecs Co’s finance director (FD) has contacted its bankers with a view to arranging a currency swap, since
he believes that this will be the best way to manage financial risks associated with the franchise. The swap
would be for the initial fee paid for the franchise, with a swap of principal immediately and in three years’
time, both these swaps being at today’s spot rate. Buryecs Co’s bank would charge an annual fee of 0·5% in
€ for arranging the swap.
Buryecs Co would take 60% of any benefit of the swap before deducting bank fees, but would then have to
pay 60% of the bank fees.
Relevant borrowing rates are:
Buryecs Co Counterparty
Eurozone 4·0% 5·8%
Wirtonia Wirtonia bank rate Wirtonia bank rate
+ 0·6% + 0·4%
In order to provide Buryecs Co’s board with an alternative hedging method to consider, the FD has obtained
the following information about over-the-counter options in Wirtonia $ from the company’s bank.
The exercise price quotation is in Wirtonia $ per €1, premium is % of amount hedged, translated at today’s
spot rate.
Exercise price Call options Put options
7·75 2·8% 1·6%
7·25 1·8% 2·7%
Assume a discount rate of 14%.
Required:
(a) Discuss the advantages and drawbacks of using the currency swap to manage financial risks
associated with the franchise in Wirtonia. (6 marks)
(b) (i) Calculate the annual percentage interest saving which Buryecs Co could make from using a
currency swap, compared with borrowing directly in Wirtonia, demonstrating how the currency swap
will work. (4 marks)
(ii) Evaluate, using net present value, the financial acceptability of Buryecs Co operating the rail
franchise under the terms suggested by the government of Wirtonia and calculate the gain or loss in
€ from using the swap arrangement. (8 marks)
(c) Calculate the results of hedging the receipt of $7,500 million using the currency options and
discuss whether currency options would be a better method of hedging this receipt than a currency
swap. (7 marks)
(25 marks)

MAR/JUN 2019
2 Lurgshall Co is a listed electronics company. Lurgshall Co has recently appointed a new chief executive,
who has a number of plans to expand the company. The chief executive also plans to look carefully at the
costs of all departments

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TOPNOTCH INTEREST RATE MANAGEMENT

in Lurgshall Co’s head office, including the centralised treasury department.

The first major investment which the chief executive will oversee is an investment in facilities to produce
applications‑specific components. To finance the planned investment, it is likely that Lurgshall Co will have
to borrow money. It is now 1 May. At present, it seems that Lurgshall Co will need to borrow $84 million on 1
September, for a period of six months, though both the amount and the period of borrowing are subject to
some uncertainty. The treasurer plans to borrow the funds at a variable rate of LIBOR plus 50 basis points.
LIBOR is currently 4·5% but is expected to rise by up to 0·6% between now and 1 September.
So far, the possibility of hedging a rise in LIBOR of 0·6% using a forward rate agreement or September $
futures has been investigated. The results of the calculations for these instruments were as follows:
4–10 Forward rate agreement from Birdam Bank: 5·38%
Three-month traded September $ futures: 5·36%
Lurgshall Co’s treasurer also wants to consider using options on futures to hedge loans.
Although Lurgshall Co has not previously used swaps for hedging purposes, the treasurer has asked Birdam
Bank to find a counterparty for a potential swap arrangement.

Relevant information about options and swaps is as follows:

Options
The current price for three-month $ September futures, $2 million contract size is 95·05. The price is quoted
in basis points at 100 – annual % yield.
Options on three-month September $ futures, $2 million contract size, option premiums are in annual %
September calls Strike price September puts
0·132 95·25 0·411
It can be assumed that futures and options contracts are settled at the end of each month. Basis can be
assumed to diminish to zero at contract maturity at a constant rate, based on monthly time intervals. It can
also be assumed that there is no basis risk and there are no margin requirements.

Swap
Birdam Bank has found a possible counterparty to enter into a swap with Lurgshall Co. The counterparty can
borrow at an annual floating rate of LIBOR + 1·5% or a fixed rate of 6·1%. Birdam Bank has quoted Lurgshall
Co a notional fixed rate of 5·6% for it to borrow. Birdam Bank would charge a fee of 10 basis points to each
party individually to act as the intermediary of the swap. Both parties would share equally the potential gains
from the swap contract.

Treasury staffing
Lurgshall Co’s new chief executive has made the following comments: ‘I understand that the treasury
department has a number of day-to-day responsibilities, including investing surplus funds for the short-term
liquidity management and hedging against currency and interest rates. However, these tasks could all be
carried out by the junior, less experienced, members of the department. I do not see why the department
needs to employ experienced, expensive staff, as it does not contribute to the strategic success of the
company.’

Required:
(a) Compare the results of hedging the $84 million, using the options and the swap, with the results
already obtained using the forward rate agreement and futures, and comment on the results. Show
all relevant calculations, including how the interest rate swap would work. (15 marks)
(b) Discuss the advantages and disadvantages of using swaps as a means of hedging interest rate
risk for Lurgshall Co. (5 marks)
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TOPNOTCH INTEREST RATE MANAGEMENT

(c) Criticise the views of the chief executive about the work carried out by the treasury department
and the staff required to do this work. (5 marks)
(25 marks)

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 DELTA HEDGING

DELTA HEDGING
1. Price of the underlying asset = change in option value / change in asset price = delta
2. Time to expiry = change in option value / change in time to expiry = Theta
3. Volatility = change in option value / change in volatility = Vega
4. Interest rate = change in option value / change in interest rate = Rho
5. GAMMA = Change in option value / change in delta = Gamma

Delta of an option is defined as the change in the price of an option in proportion to the change in the value
of the underlying item. Delta = change in value of option / change in market value of underlying shares.
Option will go up (call) or down (put) if share price goes up.

Delta neutral position or hedging is a position where the delta value will not change in response to
changes in the value of the underlying asset. Gains and losses on assets are usually offset by gains and
losses on the options.

Dynamic delta hedging is the process of adjusting the balance of options and shares in the portfolio to
maintain a risk neutral position. The goal of a delta neutral hedge is to combine a position in an asset
with a position in an option to get a portfolio whose value does not change with changes in the value of
the asset. Buying is a long position +) and selling is a short position (-). For delta hedging, the total must
be equal to be zero.

The value of Nd1 can be used to indicate the amount of the underlying shares (or other instrument)
which the writer of an option should hold in order to hedge (eliminate the risk of) the option position.
Delta hedging allows us to determine the number of shares that we must buy to create the equivalent
portfolio to an option, and hedge it.

To eliminate borrowing risk, buy call options and to eliminate investment risk, sell call options.

Buying call options = buying share portfolio + borrowing at risk free rate

Buying call options + investing at risk free rate = Buying share portfolio

Investing at risk free rate = buying share portfolio – selling call options

Therefore we can eliminate investment risk by buying shares and selling call options, as an adverse
movement in the share price will be offset by a favourable movement in the option price. Delta hedging
tells us in what proportion shares should be purchased and call options sold.

DELTA VALUES

OUT OF THE MONEY AT THE MONEY IN THE MONEY

CALL OPTION 0 0.5 +1
PUT OPTION 0 -0.5 -1
The delta of one unit of a long position is +1 and -1 for one unit of a short position. The delta of a put option
is Nd1 - 1.and delta of a call option is Nd1.

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 DELTA HEDGING

A call option that is deeply ITM has a delta close to +1, while a put option that is deeply ITM has a delta
close to -1. A put option that is deeply OTM has a delta close to +0. A put option that is deeply ATM has a
delta close to +0.5 (call) or -0.5(put). Delta is always positive for calls and negative for put.

Long call options will have a delta between 0 and 1 while a long put option will have a delta value between
0 and -1.

CALCULATING DELTA FOR CALL OPTIONS

Amount of underlying to hold as a hedge = amount of underlying item to be hedged x N(d 1)

NUMBER OF CALL OPTIONS TO SELL = NUMBER OF SHARES HELD / ND1

If you already have call options, then you hedge by buying shares.

NUMBER OF SHARES TO HOLD = NUMBER OF CALL OPTIONS SOLD X ND 1

CALCULATING DELTA FOR PUT OPTIONS

Amount of underlying to hold as hedge = amount of underlying items to be hedged x N(-d1).

NUMBER OF PUT OPTIONS TO SELL = NUMBER OF SHARES HELD / N(-D1)

NUMBER OF SHARES TO HOLD = NUMBER OF PUT OPTIONS SOLD X N(-D1)

TIPS FOR CALCULATIONS UNDER DELTA HEDGING

❖ Number of call options required = number of shares / Nd1. ND1 represents the delta
of a call option.
❖ Number of Put options required = number of shares / (Nd1 – 1) (note the delta for a
put option is gotten by deducting the delta of a call option from 1)
❖ The delta of any security in this case shares is assumed to be 1 (whether buying or
selling)
❖ Buying of shares or options (long position) denotes a positive figure while selling
of shares or options (short position) denotes a negative figure.
❖ The sum of the portfolio delta (shares + options ) must be equal to zero for the
hedge to work. (Delta of share + delta of options = 0)
❖ Note , we are concerned with quantity and delta values. The prices are irrelevant for
Delta Hedging.
❖ Where the final result is positive, it signifies that we are buying but where the final
result is negative, it signifies that we are selling
❖ Note that the price of the shares or options is irrelevant for Delta Hedging
calculations.
❖ Number of contracts = number of options / contract size
❖ Where the delta of the option is not given, it should be calculated using the Nd1
formulae.

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 DELTA HEDGING

❖ Investing : buy shares and sell the call option or buy put option
❖ Disposal : sell shares and buy the call option or sell put option

ILLUSTRATION 1

What is the number of call options that you would have to sell in order to hedge a holding of
200,000 shares, if the delta value N(d1) of options is 0.8?. Assume that option contracts are for
the purchase or sale of 1,000 shares. Commented [H1]: This is contract size

SOLUTION

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares + 200,000 1 200,000
Call option X 0.8 0.8X
Total portfolio delta 200,000 + 0.8X
200,000 + 0.80X = 0 Commented [H2]: Note that the sum of the portfolio must be
zero for it to be risk neutral.
0.80X = - 200,000

X = -200,000 / 0.8 = -250,000 call options. The negative figure signifies that the investor must sell
250,000 call options.

OR Delta hedge: number of options = number of shares / Nd1 = 200,000 / 0.8 = 250,000 options.

Number of option contracts = number of options / contract size = 250,000 / 1,000 = 250 contracts.

For every $1 or ₦1 increase in the price of shares, the value of the call option would increase by
$800 per contract (0.8 x 1,000 = 800). However, since we were selling these contracts, the
increase in value of our holding of shares, 200,000 x $1 = $200,000, would be matched by the
decrease in our holding on option contracts; 250 x $800 = $200,000. (note that you will make a
loss if you are selling a call option and asset prices increase)

ILLUSTRATION 2 ON DELTA HEDGING

Ade owns 1,200,000 shares of GT bank stock currently selling at ₦40. A call option on GT bank with a
strike price of ₦40 is selling at ₦5 and has a delta of 0.60.

a. Determine the number of call options necessary to create a delta-neutral hedge.

b. If instead of using call options, the investor decides to make use of put options. How many Put
options will be needed?

SOLUTION

a. To attain a portfolio with a delta of zero, the investor needs to create a portfolio of bank’s shares
and call options on the shares. Let us take the number of calls as X.

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 DELTA HEDGING

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares + 1,200,000 1 1,200,000
Calls X 0.6 0.6X
Total portfolio delta 1,200,000 + 0.6X
1,200,000 + 0.60X = 0 Commented [H3]: Note that the sum of the portfolio must be
zero for it to be risk neutral.
0.60X = -1,200,000

X = -1,200,000 / 0.6 = -2,000,000 call options. The negative figure signifies that the investor must
sell 2,000,000 call options.

b. Let X represent number of put options, Delta of put = Nd1 – 1= 0.6 – 1 = -0.4

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares +1,200,000 1 1,200,000
Puts X -0.4 -0.4X
Total portfolio delta 1,200,000 - 0.4X
1,200,000 – 0.4X = 0

1,200,000 = 0.4X

X = 1,200,000 / 0.4 = +3,000,000 Put options. The positive figure signifies that the investor must Commented [H4]: Where there is no contract size, the options
are in units
buy 3,000,000 put options.

ILLUSTRATION 3

Osas has sold short 90,000 units of Topnotch plc shares. Call and Put options exist on the company’s
shares. You are aware that the position can be hedged using either call options or put options. (Nd1 is
assumed to be 0.45)

a. How many call options will be needed for delta neutral hedging
b. If put options are used, how many put options will be needed?

It is assumed that the calls and puts have the same characteristics.

SOLUTION

Call delta = Nd1 = 0.45 and Put delta = - Nd1 = 0.45 - 1 = -0.55

▪ To attain a portfolio with a delta of zero, the investor needs to create a portfolio of bank’s shares
and call options on the shares. Let us take the number of calls as X. Note that the quantity is negative
because the investor sold.

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares - 90,000 1 -90,000
Calls X 0.45 0.45X
Total portfolio delta -90,000 + 0.45X
-90,000 + 0.45X = 0

0.45X = 90,000

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 DELTA HEDGING

X = 90,000 / 0.45 = + 200,000 call options. The positive figure signifies that the investor must buy the
call options.

B PART OF THE ILLUSTRATION

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares -90,000 1 -90,000
Puts X -0.55 -0.55X
Total portfolio delta -90,000 - 0.55X
-90,000 – 0.55X = 0

-0.55X = 90,000

X = 90,000 /- 0.55 = -163,636 Put options. The Negative figure signifies that the investor must sell
163,636 put options.

ILLUSTRATION 4

Uche has sold 1,000,000 units of a company’s security at ₦25 per share. You have also written (sold)
500,000 put options on the company’s shares at ₦2.50 per unit. You have decided to hedge your position
with a call option having the same characteristics as the put option. The delta of the call option is 0.5.
How many units of the call option will be needed for delta neutral hedging.?

SOLUTION

Call delta = 0.5 and Put delta = delta of call option – 1 = 0.5 – 1= -0.5; X will represent the number
of calls needed.

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares -1,000,000 1 -1,000,000
Puts -500,000 -0.5 +250,000
Calls X 0.5 0.5X
Total portfolio delta -750,000 + 0.5X
-750,000 + 0.5X = 0

0.5X = 750,000

X = 750,000 / 0.5 = +1,500,000 call options. (buy call options since result is positive).

Note that the given price of the securities is irrelevant and the call & put options do not need to be of same
characteristics.

ILLUSTRATION 5

Topnotch has the following three positions in options on a stock.

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 DELTA HEDGING

▪ A long position in 200,000 call options with strike price of ₦55 and expiration date in 3 months. Commented [H5]: Buying position
The delta of each option is 0.48.
▪ A short position in 400,000 call options with strike price of ₦56 and expiration date in 5 months.
The delta of each option is 0.55.
▪ A short position in 100,000 put options with strike price of ₦56 and expiration date in 2 months.
The delta of each option is -0.65.

What position should the financial institution take on the underlying stock in order to neutralise delta
risk.

SOLUTION

SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA

Shares X 1 X
Call +200,000 0.48 +96,000
Call -400,000 0.55 -220,000
Put -100,000 -0.65 +65,000
Total portfolio delta X – 59,000
Let X represent the number of stocks

X – 59,000 = 0, therefore X = + 59,000 (the company should buy 59,000 units of the stock since it is
positive)

EXPECTED LOSS AND PROBABILITY OF DEFAULT

Credit risk reflects the expected loss from a loan. The expected loss is a function of the loss given default
(LGD) and the probability of default (POD). The loss given default is the amount that could be lost if a
lender defaults. It is not necessarily the amount of the loan as the lender might hold some form of collateral
or the borrower may be able to pay a percentage of the amount owed.

PROBABILITY OF DEFAULT; the value of Nd2 is the probability that a call option will not be in the
money at the exercise date i.e the probability that it will not be in the money 1 – N(d2)

EXPECTED LOSS; cash loan means the shareholders are given a put option on firm’s assets written by
lenders. The expected loss on the debt is the value between the value of an asset and the face value of debt
to shareholders as provided by lender. Expected loss (put option) can be calculated using put call parity.

Value of Put = value of call + PV of exercise price – current market price of underlying item

LOSS GIVEN DEFAULT = expected loss / probability of default

EXPECTED LOSS = loss given default x probability of default

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 DELTA HEDGING

MAY 2019 ILLUSTRATION 5B

Osas has sold short 110,000 units of Topnotch plc shares. Call and Put options exist on the
company’s shares. You are aware that the position can be hedged using either call options
or put options. (Nd1 is assumed to be 0.45)

If put options are used, how many put options will be needed?

It is assumed that the calls and puts have the same characteristics.

SOLUTION

Call delta = Nd1 = 0.45 and Put delta = - Nd1 = 0.45 - 1 = -0.55

▪ To attain a portfolio with a delta of zero, the investor needs to create a portfolio of
bank’s shares and call options on the shares. Let us take the number of calls as X.
Note that the quantity is negative because the investor sold.
SECURITY QUANTITY DELTA PER UNIT TOTAL DELTA
Shares -110,000 1 -110,000
Puts X -0.55 -0.55X
Total portfolio delta -110,000 - 0.55X
▪ -110,000 – 0.55X = 0
▪ -0.55X = 110,000
▪ X = 110,000 /- 0.55 = -200,000 Put options. The Negative figure signifies that the investor must
sell 200,000put options.

QUESTION 6 MAY 2016 ON OPTION VALUATION

a. You work in the corporate finance department of a major bank. The bank has invested in 20,000,000
shares of Ode Oil Plc. You are concerned about the recent volatility in Ode Oil Plc’s share price due to the
recent instability in the global oil market. You plan to protect the bank’s investment from a possible fall in Ode
Oil Plc’s share price for the next three months and you do not plan to sell the shares a t present.

You have the following additional information:

Ode Oil Plc’s current share price N10
Call option’s current share price N11
Option expiry 3 months
Interest rate (annual) 8%
Ode Oil Plc’s share annual standard 64%
deviation
Required:
How many call options do you need to buy or sell in order to delta-hedge the bank’s position. Please be
specific.
Note: Delta may be estimated using N(d1) (7 Marks)

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 DELTA HEDGING

SOLUTION
SECURITY QTY DELTA TOTAL DELTA
Shares 20,000,000 1 20,000,000
Call option X 0.47 0.47X
20,000,000 + 0.47X

20,000,000 + 0.47X = 0
X = -20,000,000 / 0.47 = -42, 553,191 call options to be sold.
CALCULATE D1
D1 = IN[So / E] + [r + 0.5σ2]T / σꝨT
D1 = IN[10/11] + [0.08 + {0.5 x 0.642] x 0.25 / 0.64 x Ꝩ0.25 = -0.0953 + 0.0712 / 0.32 = -0.0753 = -0.07
Nd1 = 0.4721

ILLUSTRATION 5 MAY 2019 ICAN PAST QUESTION

You are the portfolio manager of an asset management company based in Kano. Your
company has in its portfolio 27,750,000 shares of Yaro plc; a company listed on the Nigerian
Stock Exchange. The shares are currently trading at N3.60 per share.

Your company plans to sell the shares in six months’ time to pay dividend and you plan to
hedge the risk of Yaro’s shares falling by more than 5% from their current market value. A
decision has therefore been taken to buy an over the counter option to protect the shares. A
merchant bank has offered to sell an appropriate six month option to your company for
N1,250,000.

Yaro’s share price has annual standard deviation of 13% and the risk-free rate of 4% per
year.

Required :

a. Evaluate whether or not the price at which the merchant bank is willing to sell the
option is a fair price
b. Explain briefly (without any calculations) how a decrease in the value of each of the
following variables is likely to change the value of a call option.
i) Volatility of the stock price {2 marks}
ii) Risk – free rate {2 marks} {Total 15 marks}

CALL OPTION
FACTORS increase decrease
Asset price Option value increase Option value decrease

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 DELTA HEDGING

Exercise price Option value decrease Option value increase

Volatility Option value increase Option value decreases
Time to expiry Option value increase Option value decreases
Risk free rate Option value increase Option value decreases

APPLICATION OF BLACK SCHOLES MODEL FOR VALUATION

This model can be used to value equity and also assess default risk of debt. These applications are based
on the idea that when a company borrows money, the shareholders acquire a call option and a put option
written by the lenders on the underlying assets of the business with an exercise price equal to the face value
of debt.

A call option has an option to default on a loan it borrows which reflects in higher interest rates.

Equity in a firm is a residual claim as equity holders lay claim to all cash flows left over after other financial
claims of holders have been satisfied. If the firm is liquidated, equity investors receive whatever is left in the
firm after all outstanding debts and other financial claims are paid off.

The principle of limited liability protects equity investors in publicly traded firm if the value of the firm is less
than the value of the outstanding debt, however and they cannot lose more than their investment in the firm.

CALL OPTION

When a firm borrows money, the lender acquires the firm’s assets while the shareholders acquire an option
to buy them back by paying off the debt. Call option of assets with exercise price equal to face value of debt.

If the value of the assets is worth more than the face value of the debt (the exercise price), the shareholder
will exercise the option by paying the debt at the exercise date (redemption date). The shareholders will allow
the option to lapse (by bankruptcy) if the value of the assets is worth less than the face value of the debt
(exercise price).

PUT OPTION

Shareholders acquire a put option on the assets of the company where the exercise price (face value of debt)
is more than the firm’s asset. This is based on the fact that shareholders will not exercise the call options if
the firm’s assets are worth less than the face value of the debt.

MORE ON REAL OPTION IN VALUATION: VALUATION OF EQUITY

CONVENTIONAL investment appraisal techniques such as NPV often do not capture the full strategic
benefits of a project in terms of either features of a project that allow risk to be managed or features that allow
further follow-on gains to be made.

The value of a firm can be thought of in these terms:

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 DELTA HEDGING

▪ If the firm fails to generate enough value to repay its loans, then its value = 0; shareholders have the
option to let the company die at this point.
▪ However, if the firm generates enough value, then the extra value belongs to the shareholders and
in this case, shareholders can pay off the debt (exercise price) and continue in their ownership of the
company.

Black scholes model can be applied because shareholders have a call option on the business. The protection
of the limited liability creates the same effect as the call option because there is an upside if the firm is
successful, but shareholders lose nothing other than their initial investment if it falls. So the value of a
company can be calculated as the amount that you would pay as a premium for this call option.

If, at expiry of the debt, the value of the company is greater than the face value of debt, the option is in the
money, otherwise if the value of the firm is less than the face value of the debt, then the debt is out of the
money and equity is worthless.

Prior to the expiry of the debt, the call option (value to the equity holders) will also have a time value attached
to it. Within the BSOP model, N(d1) the delta value, shows how the value of equity changes when the value
of the company’s asset changes. N(d2) depicts the probability that the call option is in the money, then 1 -
N(d2) depicts the probability of default. Therefore the BSOP model and options are useful in determining the
value of equity and default risk.

Option pricing can be used to explain why some companies facing severe financial distress can still
have positive equity values.

A company facing severe financial distress would presumably be one where the equity holders’ call option is
well out of money and therefor has no intrinsic value. However as long as the debt on the option is not at
expiry, then that call option will still have a time value attached to it. The time value of an option indicates that
even though the option is currently out-of-money, there is a possibility that due to the volatility of asset values,
by the time the debt reaches maturity, the company will no longer face financial distress and will be able to
meet its debt obligations.

ILLUSTRATION ON EQUITY VALUATION USING BSOPM

A firm has assets currently valued at $100m, variance of 0.16 . The face value of the debt is $80m (it is a
zero coupon debt with 10 years left to maturity). 10 year treasury bond rate is 10%.

Required

a. Determine the market value of equity, the market value of debt and the yield to maturity on the
company’s debt
b. Now assume that the total value of the company is $50m, holding other factors constant, what is the
revised value of equity. Comment on your result.
c. What are the key simplifying assumptions in the above calculation

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SOLUTION

▪ Identify the variables; Pa or So = value of the firm = $100m, Pe or E = exercise price = value of debt
= $80m; t = time to expiration of the debt = 10 years, volatility = ᴠ0.16 = 0.4, r = 0.10
▪ Calculate d1 = in (100/80) + (0.10 + 0.5 x 0.42) x 10 / 0.16 x ᴠ10 = 1.5994
▪ Calculate d2 = 1.5994 - (0.40 x ᴠ10) = 0.3345
▪ Nd1 = 0.4441 + 0.94(0.4452 – 0.4441) + 0.5 = 0.9451
▪ Nd2 = 0.1293 + 0.45(0.1331 – 0.1293) + 0.5 = 0.6310
a. Value of equity = call value = (100 x 0.9451) – (80 x e-0.10 x 10 x 0.6310) = $75.94
Value of debt = value of company – value of equity = 100m – 75.94 = $24.06m
Yield to Maturity is the interest rate that makes the bonds current value of $24.06m to grow and
become $80m after 10 years ; 24.06(1 + YTM) 10 = 80; YTM = 10ᴠ(80/24.06) – 1 = 12.77%
b. The price of the underlying asset is now $50m, and repeat the above calculations
▪ Calculate d1 = in (50/80) + (0.10 + 0.5 x 0.42) x 10 / 0.16 x √10 = 1.0515
▪ Calculate d2 = 1.0515 - (0.40 x √10) = -0.2135
▪ Nd1 ={ 0.3531 + 0.15(0.3554 – 0.3531)} + 0.5 = 0.8534
▪ Nd2 =0.5 - { 0.0832 + 0.35(0.0871 – 0.0832)} = 0.4154
▪ Value of equity = call value = (50 x 0.8534) – (80 x e-0.10 x 10 x 0.4154) = $30.44
▪ Value of debt = 50 – 30.44 = ₦19.56

The first implication of viewing equity as a call option is that equity will have value because of the probability
that the value of the underlying asset may increase over the exercise price in the remaining life of the option.

c. The key assumptions are

▪ There are only two claim holders in the firm; debt and equity
▪ There is only one issue of debt outstanding and can be redeemed at face value
▪ The debt has a zero coupon and no special feature.
▪ The value of the firm and the variance can be estimated
▪ The conflict between equity and bond holders arises because equity is a call option on the value
of the firm and its value will increase with increased volatility

EXPECTED LOSS AND PROBABILITY OF DEFAULT

Credit risk reflects the expected loss from a loan. The expected loss is a function of the loss
given default (LGD) and the probability of default (POD). The loss given default is the amount
that could be lost if a lender defaults. It is not necessarily the amount of the loan as the lender
might hold some form of collateral or the borrower may be able to pay a percentage of the
amount owed.

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 DELTA HEDGING

PROBABILITY OF DEFAULT; the value of Nd2 is the probability that a call option will not be
in the money at the exercise date i.e the probability that it will not be in the money 1 – N(d2)

EXPECTED LOSS; cash loan means the shareholders are given a put option on firm’s assets
written by lenders. The expected loss on the debt is the value between the value of an asset
and the face value of debt to shareholders as provided by lender. Expected loss (put option)
can be calculated using put call parity.

Value of Put = value of call + PV of exercise price – current market price of underlying item

LOSS GIVEN DEFAULT = expected loss / probability of default

EXPECTED LOSS = loss given default x probability of default

ILLUSTRATION

A company has assets valued at ₦500m and zero coupon bond with a face value of ₦400m. The bond
matures in 5 years. The variance of the assets is 0.16. risk free rate is 5% continuously compounded.

Required : estimate the following using BSOP model

a. The probability of default

b. The recovery value of the assets
c. The present value of the present loss
d. The expected loss

SOLUTIONS

• Probability of default = N[-d2] = 1 – Nd2

• D1 = IN[500/400] + {0.05 + [Ꝩ0.16)2 ] x 5 / {Ꝩ0.16 x Ꝩ5} = 0.9762
• D2 = 0.9762 - {Ꝩ0.16 x Ꝩ5} = 0.0818
• Nd1 = 0.5 + {0.3340 + 0.62[0.3365 – 0.3340] = 0.8356
• Nd2 = 0.5 + {0.0319 + 0.18[0.0359 – 0.0319] = 0.5326
• 1- Nd1 = 1 – 0.8356 = 0.1644
• 1 – Nd2 = 1 – 0.5326 = 0.4674
• Probability of default is 46.74%

B PART

Recovery value = N[-d1]/N[-d2] x Asset value = 0.1644 / 0.4674 x 500 = N175.87m

C PART

This is same as loss given default = current market value of the bond less recovery value
GRACE MAKES THE DIFFERENCE Page 12
 DELTA HEDGING

Current market value of the bond = Ee-rt = 400 x e[- 0.05 x 5] = N311.52m

Present value of possible loss = N311.52 – N175.87 = N135.65m

D PART

Expected loss = probability of default x loss given default = 46.74% x 135.65m = NN63.40m

GRACE MAKES THE DIFFERENCE Page 13

 ADJUSTED PRESENT VALUE

Adjusted Present Value (APV) method is designed to address all of the weaknesses of NPV as it evaluates
the project and the impact of the financing separately. APV is used if a new project has a different financial
risk (debt-equity ratio) from the company that is the overall capital structure of the company changes.

APV (value of a geared product) = investment decision (value of an all equity financed project) + financing
decision (present value of financing side effects).

APV is a valuation method introduced in 1974 by Stewart Myers with the idea of valuing the project as if
it were all equity financed (ungeared) and to then add the present value of the tax shield of debt and
other side effects. It calculates the NPV of the project as if it is all equity financed (base case NPV) and
then adjusting it for the benefits of financing.

INVESTMENT DECISION (Estimating Base Case NPV discounted using the ungeared cost of equity)

The project is evaluated as though it were being undertaken by an all equity company with all financing
side effects ignored. Use a beta that reflects just the business risk (Beta asset)

FINANCING DECISION

This evaluates the financing aspect of the project. It considers the issue cost, tax reliefs and any savings
arising as a result of the financing. As all financing cash flows are low risk, they are discounted at either
the cost of debt before tax or the risk free rate.

CALCULATIONS UNDER APV

In APV, we are calculating two things the BASE CASE NPV and the FINANCING EFFECT

Under BASE CASE NPV, you are calculating the normal NPV but the discount factor should be the
ungeared cost of equity (K iE). The ungeared cost of equity can be determined in any of the following ways
based on the information in the question:

▪ Where the company is entering into a new business (diversifying) and the geared cost of equity
of the proxy company is given; the ungeared cost of equity of a proxy company in the line of the
new business can be calculated using Modigliani & Millers theory (KE = K iE + (K iE - Kd) VD(1 –
t)/VE, , where KE is the geared cost of equity, Ki E is the ungeared cost of equity, t is tax rate, Vd is
value of debt and VE is the value of equity. The discount factor (KiE) would be calculated from the
formulae above.

▪ Where the company is entering into a new business (diversifying) and the proxy company is
ungeared ; the ungeared cost of equity of the proxy company can be directly taken, if the proxy
company is all equity financed.
▪ Where the company is entering into a new business and the beta equity of a proxy company is
given, it should be degeared and the ungeared cost of equity calculated using CAPM ;

1
 ADJUSTED PRESENT VALUE

KiE = RF + βA (RM – RF) where Rm is market returns, RF is risk free rate, βA is beta asset and KiE is
ungeared cost of equity. (note that it is beta asset that you need, so you only degear but do not
regear).
▪ Where the company is entering into a new business and the beta asset of a proxy company is
given, you use the beta asset to calculate the ungeared cost of equity based on CAPM.
▪ Where the company is evaluating an existing business line, then it is their own geared cost of
equity or beta equity that would need to be adjusted. (where it is an existing business, no proxy
company or industry is required).

FINANCING EFFECT

The following should be considered when calculating the present value of the financing effect

1. ISSUE COST refers to the cost that would be required to raise the capital (debt and equity) and
assumed to be incurred in year 0. The issue cost on debt is usually assumed to be tax allowable
but this should be stated where the examiner is silent. Where it is tax allowable, the tax savings
on issue cost would be enjoyed based on the tax information. It is usually a percentage of the
gross finance. The challenge here is that the gross finance is hardly available in the scenario, and
so the following methods can be used to calculate issue cost.
▪ Issue cost = %issue cost X Gross Finance Where Gross finance is clearly given
▪ Where Gross finance is not given, we work with the net finance. The net finance is the amount
to be raised (when stated) or a combination of the initial outlay and initial working capital in
year 0 (where amount to be raised is not stated). Net finance could be initial outlay only when
the examiner says working capital can be financed internally.
I. Issue cost = issue cost % / 100% - issue cost% x Net finance or
II. Gross Finance = 100% / 100% - issue cost% x Net Finance; the Issue cost can now be
calculated as issue cost% x Gross finance calculated.
2. TAX SHIELD OR TAX SAVINGS ON INTEREST ANNUALLY = TAX RATE X INTEREST annually. Tax
shield refers to the tax savings that arises annually as a result of the interest payment that is tax
allowable. The total interest on the debt is calculated and multiplied with the tax rate before
determining the present value of the savings.
The total debt or finance is assumed to be a combination of the net finance and issue cost (where
the issue cost is financed internally, it would not be part of the debt to be raised).

You have to carefully look at the

Type of debt (is it a debt where part of the capital is paid annually along with the interest?, if yes,
then an amortization table would be required to get the annual interest);
The tax information (confirm if losses would be relieved using future profits and if tax is in
arrears);
The currency (confirm if the currencies are more than one; in that case it is an international
investment decision);
The tax rate (tax rate of your company);

2
 ADJUSTED PRESENT VALUE

The maturity of the debt (confirm the number of years to recognize when calculating PV of the
debt which may be different from the useful life of the project).
3. INTEREST SAVINGS AND TAX PAYMENT ON THE INTEREST SAVINGS ANNUALLY: interest savings
arises annually when there is a subsidized loan (that is a loan with a lower interest rate).
Interest savings = (normal rate of interest – subsidized interest rate) x Subsidized debt.
The tax payment on interest savings would be based on the tax rate and the tax timing
information. (Is the tax same year or in arrears)
4. DISCOUNT FACTOR: the PV of financing should be discounted using the riskfree rate or the pre-
tax cost of debt. (normal borrowing rate before tax).

ADVANTAGES OF APV

▪ It gives a clear understanding of the elements involved in the decision as it uses a step-by-step
approach.
▪ It can evaluate any type of financing package
▪ It is more straight forward
▪ It also helps in evaluating abnormal transaction cost such as issue cost
▪ It is not easily manipulated as it evaluates using two independent discount factors

DISADVANTAGES OF APV

▪ It ignores bankruptcy risk, tax exhaustion and agency cost

▪ It assumes that debt is risk free and irredeemable
▪ It aligns with the M&M theory which may be unrealistic.

TIPS TO NOTE IN APV CALCULATIONS

▪ Where there is information on issue costs or subsidized debt, the APV method should be used to
evaluate the project even where it is not clearly stated.
▪ The discount rate for the base case NPV should be the ungeared cost of equity of the company
or a proxy company in a similar line of business to the new venture.
▪ The effect of financing should be discounted using the pre-tax cost of debt or risk free rate
(always state the rate used)
▪ Tax savings should be recognised on issue cost if required and if not should be stated as an
assumption that tax on issue cost has been ignored.
▪ Tax shield and tax payment on interest savings will be based on the tax information whether in
arrears or on actual year basis
▪ Where cost of debt is not given, it is assumed that it is equal to the risk free rate.
▪ Discussions on assumptions should be practical and detailed to gain meaningful marks in the
exams

3
 ADJUSTED PRESENT VALUE

ILLUSTRATION 1 (MAY 2016 ICAN PAST QUESTION)

Katam plc has adopted a strategy of diversification into many different industries in order to reduce risk
for the company’s shareholders. This has resulted in frequent changes in the company’s gearing level
and widely fluctuating risks of individual investments. Presently the company has a target debt to asset
ratio i.e D/(D + E) of 25%, an equity beta of 2.25 and a pre-tax cost of debt of 5%.
On January 1, 2016 Katam plc with a year end of December 31, is considering the purchase of a new
machine costing N750 million which would enable it to diversify into a new line of business. The new
business will generate sales of N522.5 million in the first year, growing at 4.5% per annum. A constant
contribution margin ratio of 40% can be expected throughout the 15 year life of the project. Incremental
fixed costs will be N84.32 million into the first year growing by 5.4% per annum.
A regional development bank has offered a 10-year loan of 3% interest to finance 40% of the cost of the
machine. The balance of 60% will be financed equally by a 10-year commercial loan (with annual interest
of 5%) and a fresh round of equity.
The issue cost on the commercial loan will be 1% and the new equity will incur issue cost of 3%. All issue
costs are the gross amount raised for the respective capital. Issue costs on debt are allowed for tax
purposes.
A firm that is already in the business of the new project has a gearing ratio of 20% (debt to asset) and
cost of equity of 18.1%. its corporate debt is risk-free.
Tax rate of 30% is payable in the year profit is made. Tax depreciation of 20% on cost is available on the
new machine. Katam plc has weighted average cost of capital of 14% and a cost of equity of 17.5%. the
risk-free rate is 4% and the market risk premium is 7%.
You are required to:
a. Estimate the Adjusted Present Value (APV) and advise whether the project should be accepted (21
marks)
b. Explain the circumstances under which the use of APV is appropriate
c. State the major advantages and limitations of the use of APV method (9 marks)

ILLUSTRATION 2 (QUESTION 1 NOVEMBER 2019 ON ADJUSTED PRESENT VALUE)

Agbeloba Limited {AL} an unlisted company based in Akure, Nigeria. Over the years, the company has been
producing and selling agricultural support tools. AL is now considering the production and sale of yam
pounders.
Although this is a completely new venture for AL, it will be in addition to the company’s core business, AL’s
directors plan to develop the project for a period of four years and then sell it for N24 million to a group of
young investors.

4
 ADJUSTED PRESENT VALUE

The government is excited about the project and has offered AL a subsidized loan of up to 80% of the
investment funds needed at the beginning of the project, at a rate of 200 basis points below AL’s borrowing
rate. Currently AL can borrow at 300 basis points above the five year government debt yield rate.
A feasibility study commissioned by the Directors at a cost of N5 million has produced the following
information
1. The company can buy an existing suitable factory at a cost of N16.5 million payable now.
2. N4.5 million is required now to buy and install the necessary plant and machinery:
3. The company will produce and sell 1,300 units in the first year. Unit sales will grow by 40% in each
of the next two years before falling to an annual growth rate of 5% for the final year.
4. Unit selling price for the first year will be N3,750 but this will increase by 3% per year thereafter
5. In the first year, total variable cost per unit will be N1,800 but this will increase by 8% per year
thereafter.
6. In the first year, the fixed overhead costs will be N3.75million of which 60% are centrally allocated
overheads. The fixed overhead cost will increase by 5% per year after the first year.
7. AL will require working capital of 15% of the anticipated sales revenue for the year, at the beginning
of each year. The working capital is expected to be released at the end of the fourth year when the
project is sold.
8. AL’s tax rate is 25% per year on taxable profits. Tax is payable in the same year as when the profits
are earned. Tax allowable depreciation is available on the plant and machinery on a straight line
basis. It is anticipated that the value attributable to the plant and machinery after four years is
N600,000 of the price at which the project is sold. No tax allowable depreciation is available on the
factory.
9. AL uses 12% as a discount rate for new projects but feels that this rate may not be appropriate for
this new type of investment. It intends to raise the full amount of funds through debt finance and take
advantage of the government’s offer of a subsidized loan.
10. Issue costs are 4% of the gross finance required. It can be assumed that the debt capacity available
to the company is equivalent to the actual amount of debt finance to be raised for the project.
11. Although no other companies produce yam pounders in the country, Casscare plc {CL}, a listed
company produces cassava crushing machines, using almost similar technology to that required for
yam pounder. CL’s cost of equity is estimated to be 14% and it pays tax at 28%. CL has 15 million
shares in issue trading at N2.53 each and N40 million bonds trading at N94.88 per N100.
12. The five year government debt yield is currently estimated at 4.5% and the market risk premium at
4%

Required
a. Evaluate on financial grounds, whether AL should proceed with the project (28 marks)
b. Discuss the appropriateness of the evaluation method used and explain any assumptions made in
part a above. (5 marks)
c. Provide examples of ethical issues that might affect capital investment decisions, and discuss the
importance of such issues for strategic financial management (7 marks) {40 marks}

5
 ADJUSTED PRESENT VALUE

ILLUSTRATION 3 ACCA PAST QUESTION AMENDED

Tippletine Co is based in Valliland. It is listed on Valliland’s stock exchange but only has a small number of
shareholders.
Its directors collectively own 45% of the equity share capital.
Tippletine Co’s growth has been based on the manufacture of household electrical goods. However, the
directors have taken a strategic decision to diversify operations and to make a major investment in facilities
for the manufacture of office equipment.
Details of investment
The new investment is being appraised over a four-year time horizon. Revenues from the new investment
are uncertain and Tippletine Co’s finance director has prepared what she regards as cautious forecasts. She
predicts that it will generate $2 million operating cash flows before marketing costs in Year 1 and $14·5 million
operating cash flows before marketing costs in Year 2, with operating cash flows rising by the expected levels
of inflation in Years 3 and 4.
Marketing costs are predicted to be $9 million in Year 1 and $2 million in each of Years 2 to 4.
The new investment will require immediate expenditure on facilities of $30·6 million. Tax allowable
depreciation will be available on the new investment at an annual rate of 25% reducing balance basis. It can
be assumed that there will either be a balancing allowance or charge in the final year of the appraisal. The
finance director believes the facilities will remain viable after four years, and therefore a realisable value of
$13·5 million can be assumed at the end of the appraisal period.
The new facilities will also require an immediate initial investment in working capital of $3 million. Working
capital requirements will increase by the rate of inflation for the next three years and any working capital at
the start of Year 4 will be assumed to be released at the end of the appraisal period.
Tippletine Co pays tax at an annual rate of 30%. Tax is payable with a year’s time delay. Any tax losses on
the investment can be assumed to be carried forward and written off against future profits from the
investment.
Predicted inflation rates are as follows:
Year 1 2 3 4
8% 6% 5% 4%

Financing the investment

Tippletine Co has been considering two choices for financing all of the $30·6 million needed for the initial
investment in the facilities: $20m will be financed by the bank loan while the balance will be financed by the
subsidized loan.
– A subsidised loan from a government loan scheme, with the loan repayable at the end of the four years.
Issue costs of 4% of the gross finance would be payable. Interest would be payable at a rate of 30 basis
points below the risk free rate of 2·5%. In order to obtain the benefits of the loan scheme, Tippletine Co would
have to fulfill various conditions, including locating the facilities in a remote part of Valliland where
unemployment is high.
– Bank loan repayable in equal annual instalments over the projects life, interest payable at 8% per
year.(which is the normal cost of borrowing) The loan has an issue cost of 4%,
Other information
Humabuz Co is a large manufacturer of office equipment in Valliland. Humabuz Co’s geared cost of equity is
estimated to be 10·5% and its pre-tax cost of debt to be 5·4%. These estimates are based on a capital
structure comprising $225 million 6% irredeemable bonds, trading at $107 per $100, and 125 million $1 equity
shares, trading at $3·20 per share. Humabuz Co also pays tax at an annual rate of 30% on its taxable profits.
Required:
6
 ADJUSTED PRESENT VALUE

(a) Calculate the adjusted present value for the investment and conclude whether the project should
be accepted or not. Show all relevant calculations. (20 marks)

ILLUSTRATION 4
The selection of appropriate discount rates for capital investments has frequently
been a problem for the finance director of Relevant plc. The company had
adopted a strategy of diversification into many different industries, in order to
reduce risk for the company’s shareholders. This has resulted in frequent changes
in the company’s gearing level and widely fluctuating risks of individual
investments.
The current project under appraisal, an investment in the fast food industry where
Relevant has no other investments, is expected to generate pre-tax operating
cash flows of ₦8,400,000 in the first year, rising by 5% per year for the five-year
expected life of the project. After five years, the land and buildings are expected
to have a realizable value of ₦25,000,000 (after any tax effects), the same as their
original cost, but in order to continue operations, major new investments in
equipment would be required at that time. Other non-current assets would have
negligible value after five years. The total initial outlay of the project (net of issue
costs) is ₦46,000,000, and all but the land and building attracts a 25% per year
capital allowance on a reducing balance basis.
The project will be financed by a ₦16,000,000 fixed rate loan from a regional
development agency at a subsidized rate of 6% per year, 3% less than Relevant
could borrow in the capital market. The remainder of the finance would be
provided by an underwritten rights issue at a 10% discount on current market price
with total underwriting and issue costs of 5% of gross proceeds. The investment is
believed to add ₦20 million to the company’s debt capacity.
Current financial data for Relevant and the Fast food industry includes:

RELEVANT FAST FOOD INDUSTRY

AVERAGE
P/E RATIO 12 20
DIVIDEND YIELD 5% 3%
EQUITY BETA 1.1 1.4
DEBT BETA 0.2 0.25
DEBT/EQUITY RATIO
BOOK VALUES 1.1 : 1 1.6:1
MARKET VALUES 0.4: 1 1:1
SHARE PRICE ₦4.70 NA
NUMBER OF ORDINARY NA
SHARES

7
 ADJUSTED PRESENT VALUE

The corporate tax rate is currently 30% per annum and tax is payable one year
in arrears. Treasury bills are currently yielding 5% per year after tax and the return
required by well diversified investors is 12.5% per year.

Required
a. Provide a reasoned explanation as to whether you would support the
company’s strategy of diversifying into many different industries (4 marks)
b. Prepare a report for the Finance director of Relevant plc advising on the
financial viability of the proposed fast food investment. Include in the report
an assessment of the limitations of the method of appraisal that you have
used. Supporting calculations should form an appendix to your report
(16 marks)
c. Discuss the types of non-financial, ethical and environmental issues that
might influence the objectives of companies, and consider the impact of
these issues on the achievement of primary financial objectives such as the
maximization of shareholders wealth (10 marks)
d. According to International Valuation Standards (IVS) 200 ; Business
valuations and business interest, there are different levels at which value
can be expressed including enterprise value, total invested capital value,
operating value and equity value. Explain the different values according to
the standard showing the most common sources of data if the market
approach is applied (10 marks)
(40 marks)

8
BUSINESS VALUATION AND ACQUISITION

ILLUSTRATION 1 [ICAN MAY 2021 AMENDED]

Vmobile is a listed telecommunications company. The company is considering the purchase of Airtell, an
unlisted company that has developed, patented and marketed a secure, medium range, wireless link to
broadband. The wireless link is expected to increase Airtell’s revenue by 25% per year for three years,
and by 10% per year thereafter. Airtell is currently owned 35% by its senior managers, 30% by a venture
capital company, 25% by a single shareholder on the board of directors, and 10% by about 100 other
private investors.
The board of directors is concerned about the appropriate price to pay for Airtell. As a starting point, it
has been decided to provide a range of valuations based on different industry recognized techniques.
Summarized Financial statements of Airtell for the last two years are shown below:
STATEMENT OF PROFIT OR LOSS FOR THE YEARS ENDED 30 JUNE (₦000)
2020 2019
Sales revenue 112,400 101,090

Operating profit before exceptional items 6,510 4,100

Exceptional items (10,025) -
Interest paid (net) (1,400) (890)
Profit/ [loss] before taxation (4,915) 3,210
Taxation (1,050) (890)
Profit after taxation (5,965) 2,320
NOTE: Dividend 1,000 500

STATEMENT OF FINANCIAL POSITION AS AT 30 JUNE (₦000)

2020 2019
Non-Current Assets (Net)
Tangible assets 27,150 25,240
Goodwill 850 1,000
Current Assets
Inventory 17,000 13,900
Receivables 13,790 12,560
Cash at bank and in hand 240 240
Total Assets 59,030 52,940

EQUITY and LIABILITIES

Called up share capital (25k par) 20,000 10,000
Retained profit 5,185 17,150
Other Reserves 6,245 1,675
Total equity 31,430 28,825
Current liabilities- payables 27,600 24,115
59,030 52,940

GRACE MAKES THE DIFFERENCE 1

BUSINESS VALUATION AND ACQUISITION

Additional information relating to Airtell:

I. If the acquisition succeeds, there will be revenue synergy leading to increase in annual sales
revenue of Airtell of 25% for three years, and of 10% per year thereafter.
II. Non-cash expenses, including depreciation, were ₦4,100,000 in 2020.
III. Corporate taxation is at the rate of 30% per annum.
IV. Capital expenditure was ₦5m in 2020, and is expected to grow at approximately the same rate
as revenue.
V. Working capital, interest payments and non-cash expenses are expected to increase at the same
rate as revenue.
VI. Airtell has a patent with current market value of ₦50 million. This has not been included in non-
current assets.
VII. Operating profit is expected to be approximately 8% of revenue in 2021, and to remain at the
same percentage in future years
VIII. Dividends are expected to grow at the same rate as revenue
IX. The realizable value of existing inventory is expected to be 70% of its book value
X. The estimated cost of equity of Airtell is 14%
XI. The average PE ratio of listed companies of similar size to Airtell is 30:1.
XII. Average earnings growth in the industry is 6% per year.

Required
a. Prepare a report that
I. Estimates the value of Airtell using
▪ Asset based valuation [8 marks]
▪ PE ratios [6 marks]
▪ Dividend based valuation [6 marks]
▪ The present value of expected future cash flows (5 marks)
b. The directors of V-mobile are considering issuing same N100 nominal value ten year bonds to
finance the purchase of Airtell. To make the bonds look attractive to potential investors, the bonds
are to be issued at a discount of 10%. Based on V-mobile’s credit rating, investors are expected to
require a return of 7% per year from such bonds.
You are required:
To estimate the coupon rate that Vmobile will have to pay on these bonds in order to satisfy the
investors [5 marks] [40 marks]

ILLUSTRATION 2
TT plc is a major major manufacturer of consumables. It is considering making a bid for the entire share
capital of P limited operating in the flexible packaging industry.

GRACE MAKES THE DIFFERENCE 2

BUSINESS VALUATION AND ACQUISITION

A decision has been taken to value the company using Free Cash Flow to the Firm. You have been able to
project the following financial statements
P LIMITED; PROJECTED INCOME STATEMENT
YEAR 1 ₦m YEAR 2 ₦m YEAR 3 ₦m
Net sales 33,388 35,884 38,018
Cost of goods sold (27,614) (29,514) (30,994)
Other expenses (3,094) (3,234) (3,410)
EBITDA 2,680 3,136 3,614
Depreciation (2,110) (2,200) (2,286)
EBIT 570 936 1,328
Interest on Debt (216) (204) (172)
Earnings before tax 354 732 1,156
Taxes (134) (278) (440)
Net profit 220 454 716

PROJECTED STATEMENT OF FINANCIAL POSITION

YEAR 0 ₦m YEAR 1 ₦m YEAR 2 ₦m YEAR 3 ₦m
Cash 480 506 566 624
Trade receivables 4,464 4,580 4,740 4,820
Inventory 6,284 6,068 6,072 6,200
Non-current assets 10,848 11,024 11,574 11,868
Total Assets 22,076 22,178 22,940 23,512
Trade payables 7,862 8,108 8,644 9,230
Customers deposit for goods 2,422 2,386 2,256 2,100
Short term debt 1,928 1,662 1,644 1,130
Non-current debt 2,422 3,930 3,850 3,780
Equity 5,872 6,092 6,546 7,262
Total liabilities and Equity 22,076 22,178 22,940 23,512
Effective tax rate is 38%.
The table below shows the main listed comparable companies in the packaging industry, with some
associated financial details:
COMPARABLE EQUITY BETA EFFECTIVE TAX RATE DEBT/EQUITY RATIO
XX PLC 1.10 33% 0.8
YY PLC 0.95 35% 0.6
ZZ PLC 1.20 35% 1.0
TK LTD 0.98 37% 0.7
The D/E ratio and the effective tax rate of P limited are 0.55 and 38% respectively. The company has before
tax cost of debt of 6% with beta of debt of 0.2. Risk free rate is 3% and the expected equity risk premium is
6%.
Required

GRACE MAKES THE DIFFERENCE 3

BUSINESS VALUATION AND ACQUISITION

a. Estimate the appropriate WACC for TT limited. Show all workings.

b. Calculate the free cash flow to the firm for years 1,2 and 3
c. What is the market value of the company assuming free cash flow to the firm will grow by 2% from
year 4.
d. Explain the major limitations of your estimate in c above

ILLUSTRATION 3
Black plc, an unlisted company, designs and develops tools and parts for specialist machinery. The company
was formed four years ago by six friends who own 20% of the equity capital in total, and a consortium of
business angel organizations, who own the remaining 80% in equal proportions. Black plc also has a large
amount of debt finance in the form of variable loan notes. Initially, the amount of annual interest payable on
these loans was low and allowed Black plc to invest internally generated funds to expand its business.
Recently, though, due to a rapid increase in interest rates, there has been limited scope for future expansion
and no new product development.
The board of directors, consisting of the six friends and a representative from each business angel
organization, met recently to discuss how to secure the company’s future prospects. Two proposals were put
forward as follows:
PROPOSAL 1
To accept a takeover offer from White plc, a listed company, which develops and manufactures specialist
machinery tools and parts. The takeover offer is for N2.95 cash per share or a share for share exchange
where two White plc shares would be offered for three Black plc. White plc would need to get the final approval
from its shareholders, if either offer is accepted.
PROPOSAL 2
To pursue an opportunity to develop a small prototype product that barely breaks-even, but gives the
company exclusive rights to produce a follow-on-product within two years.
The meeting concluded without agreement on which proposal to pursue.
After the meeting, White plc was consulted about the exclusive rights. White plc’s directors indicated they
had not considered the rights in their computations and were willing to continue with the takeover offer on
the same terms without them.
Currently White plc has 10 million shares in issue and they are trading for N4.80 each. White plc’s price to
earnings ratio is 15. It has sufficient cash to pay for Black plc’s equity and a substantial proportion of its debt,
and believes that this will enable Black plc to operate on a P/E level of 15 as well. In addition to this, White
plc believes that it can find cost based synergies of N150,000 after tax per year for the foreseeable future.
White plc’s current profit after tax is N3,200,000.
The following financial information relates to Black plc and to the development of the new product
BLACK PLC FINANCIAL INFORMATION

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BUSINESS VALUATION AND ACQUISITION

Extract from the most recent income statement N’000

Sales Revenue 8,780
Profit before interest and tax 1,230
Interest [455]
Tax [155]
Profit after tax 620
Dividends Nil

Extract FROM THE RECENT STATEMENT OF FINANCIAL POSITION

N’000
Net non-current assets 10,060
Current assets 690
Total Asset 10,750

Share capital [40k share par value] 960

Reserves 1,400
Non-current liabilities: variable rate loans 6,500
Current liabilities 1,890
Total liabilities and capital 10,750
In arriving at the profit after tax amount, Black plc deducted tax allowable depreciation and other non-cash
expenses totaling N1,206,000. It requires an annual cash investment of N1,010,000 in non-current assets
and working capital to continue its operations.
Black plc’s profits before interest and tax in its first year of operation were N970,000 and have been growing
steadily in each of the following three years, to their current level. Black plc’s cash flows grew at the same
rate as well, but it is likely that this growth rate will reduce to 25% of the original rate for the foreseeable
future.
Black plc currently pays interest of 7% per year on its loans, which is 380 basis points over the government
base rate, and the corporate tax of 20% on profits after interest. It is estimated that an overall cost of capital
of 11% is reasonable compensation on an investment of this nature.
NEW PRODUCT DEVELOPMENT [PROPOSAL 2]
Developing the new follow-on-product will require an investment of N2,500,000 initially. The total expected
cash flows and present values of the product over its five-year life, with a volatility of 42% standard deviation
are as follows:
Year Now 1 2 3 to 7 [in total]
Cash flows N’000 - - [2,500] 3,950
Present values N’000 - - [2,029] 2,434

Required:
Prepare a report for the Board of Directors of Black plc that

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BUSINESS VALUATION AND ACQUISITION

I. Estimates the current value of Black plc share, using the free cash flow to firm methodology [6 marks]
II. Estimate the percentage gain in value to a Black plc share and a White plc share under each payment
offer [7 marks]
III. Estimates the percentage gain in the value of the follow-on product to a Black plc share based on its
cash flows and on the assumption that the production can be delayed following acquisition of the
exclusive rights of production. [7 marks]
IV. Discuss the likely reaction of White plc and Black plc shareholders to the takeover offer, including
the assumptions made in the estimates above and how the follow-on product’s value can be utilized
by Black plc. [7 marks] 30 marks

ILLUSTRATION 4
John is the CEO of Talkative Plc, a very large listed company in the telecommunications business. The
company is in a very strong financial position, having developed rapidly in recent years through a strategy
based upon growth by acquisition. The CEO has just attended a seminar on Corporate Valuation using
market value added (MVA) and he has instructed you as the CFO to value the next acquisition target
Topnotch, using MVA.
You have access to the following data of Topnotch
2014a 2015e 2016e 2017e 2018ff
Total assets (N m) 7,000 7,500 7,700 7,900 +1.5% p.a
Net profit after tax Nm 375 424 474 + 4% p.a
Net operating profit after tax Nm 563 742 955 +4% p.a
Risk free rate 4% 4% 4% 5%
Expected stock market return 8% 8% 8% 9%
Interest rate of debt 6.5% 6.5% 6.5% 7%
Free cash flow to the firm 225 400 525 +2.8% p.a
Dividend 100 100 150 ???
Debt/equity ratio 1.0 1.0 1.0 1.0 1.0
Tax rate % 28 28 28 38
Equity beta 1.2 1.2 1.2 1.1
Market value of debt equals book value of debt.
2014a= 2014 actual, 2015e= 2015 estimated, and 2018ff = 2018 and the following years.
Note where total asset is needed, make use of year- end figures.
Required
1. Which discount rate do you have to use, explain your decision (no calculation)
2. Calculate the appropriate discount rate
3. MVA uses EVA, explain MVA first then explain how to get EVA (no calculation)
4. Calculate EVA for 2015e, 2016e and 2017e
5. Explain the process to get value of equity using MVA

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6. Calculate the value of equity of Topnotch as at January 1 2015. Assume a two stage MVA where
stage 1 covers the period from 2015 to 2017 and stage 2 from 2018 and beyond. Predict a constant
growth of EVAs from 2018 which equals the growth rate of EVAs from 2017 to 2018.
7. Suppose that the valuation of equity by Dividend valuation model will show the same result as the
valuation of your MVA. How large must the growth rate of dividends be for an equivalent result of a
DVM from 2019 onward, if the 2018 dividend paid is equal to 2017 dividend paid?

ILLUSTRATION 5
Hapia Co a company dealing in the financial services & food manufacturing business is considering acquiring
Jeunsoke co an unlisted company involved in food manufacturing.
Hapia co has 2,000m shares in issue and currently trading at ₦2.50 each.
Jeunsoke co has 263 million shares in issue and the current market value of its debt is ₦400m. its most
recent profit before interest and tax was ₦132m, after deducting tax allowable depreciation and non cash
expenses of ₦27.4m. Jeunsoke makes an annual cash investment of ₦24.3m in non-current assets and
working capital. It is estimated that its cash flows will grow by 3% annually for the foreseeable future.
Jeunsoke’s current cost of capital is estimated to be 11%.
If Hapia co acquires Jeunsoke co, it is expected that the combined company’s sales revenue will be ₦7,351m
in the first year and annual pre-tax profit margin on sales will be 15.4% for the foreseeable future. After the
first year, sales revenue will grow by 5.02% every year for the next three years. It can be assumed that the
combined company’s annual depreciation will be equivalent to the investment required to maintain the
company at current operational levels. However in order to increase the sales revenue levels each year, the
combined company will require an additional investment of ₦109m in the first year and ₦0.31 for every ₦1
increase in sales revenue for each of the next three years.
After the first four years, it is expected that the combined company’s free cash flows will grow by 2.4%
annually for the foreseeable future. The combined company’s cost of capital is estimated to be 10%. It is
expected that the combined company’s debt to equity level will be maintained at 40:60, in market value terms,
after the acquisition has taken place.
Both Hapia and Jeunsoke pay corporation tax on profits at an annual rate of 20% and it is expected that this
rate will not change if Hapia co acquires Jeunsoke. It can be assumed that corporation tax is payable in the
same year as the profits it is charged on.
Hapia has proposed the following payment methods for the acquisition of Jeunsoke
I. A cash payment offer of ₦4.40 for each Jeunsoke share, or
II. Through a share for share exchange, where Jeunsoke shares are exchanged for a number of Hapia
co shares, such that 55% of the additional value created is allocated to Jeunsoke
III. A mixed offer of a cash payment of ₦2.09 per share and one Hapia co share for each Jeunsoke
share. It is estimated that the market price per share for Hapia co after the acquisition will be ₦2.60
per share

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IV. A share for share exchange of 5 new shares for every 2 shares in Jeunsoke.

Required
a. Estimate the value of equity of Hapia co and Jeunsoke co before the acquisition and of the combined
company after acquisition (10 marks)
b. Estimate the percentage gain in value for each Hapia share and Jeunsoke share under each of the
cash , share for share, share exchange and the mixed offer (10 marks)

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