BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Course Code Course Tile Course Developer/Writer

BHM 647 Capital Investment and Financial Decisions Dr. A. U. Nweze Enugu State University Technology, Enugu . Mr. E.U. Abianga National Open University Victoria Island, Lagos Dr. O.J. Onwe National Open University Victoria Island, Lagos S.O. Israel-Cookey National Open University Victoria Island, Lagos of

Course Editor

Programme Leader

Course Coordinator

NATIONAL OPEN UNIVERSITY OF NIGERIA

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

National Open University of Nigeria Headquarters 14/16 Ahmadu Bello Way Victoria Island Lagos Abuja Office No. 5 Dar es Salaam Street Off Aminu Kano Crescent Wuse II, Abuja Nigeria e-mail: centralinfo@nou.edu.ng URL: www.nou.edu.ng Published by: National Open University of Nigeria 2008 First Printed 2008 ISBN: 978-058-413-7 All Rights Reserved

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

CONTENTS
Module 1 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Module 2 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Module 3 Unit 1 Unit 2 Unit 3 Unit 4

PAGES

. 1 Conceptual Issue in Capital Investment...... 1 Decisions-types and Features and Tools for Decision Taking 8 The Payback Period.. 15 The Accounting Rate of Return... 23 Compounding and Discounting... 28 .. 39 The Net Present Value (NPV)... The Net Present Value (Annuity)... The Internal Rate of Return.... The International Rate of Return ... The Profitability Index... 39 46 51 59 64 45 50 58 63 67 7 14 22 27 38

.. 68 The Impact of Inflation on Investment Proposals ... Using Probability to Assess Impact of Risks on Capital Investments... Sensitivity Analysis. Capital Rationing. 68 - 74 75 - 85 86 - 95 96 -111

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MODULE 1
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Conceptual Issues in Capital Investment Decisions-types and features and tools for Decision taking The Payback Period The Accounting Rate of Return Compounding and Discounting

UNIT 1
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

CONCEPTUAL INVESTMENTS

ISSUES

IN

CAPITAL

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

Any discussion on investment must begin with this simple truth: Investment requires taking some risks. Your hope for investment success depends, in part, on your ability to control those risks without passing up reasonable rewards (Miller, 2003: 13). It therefore follows that investment involves some elements of sacrifice in anticipation of future returns.

2.0

OBJECTIVES

After studying this Unit, the reader should be able to: define investment; state the types of investment; identify some basic features of investment; and explain some conceptual issues in Investment.

3.0

MAIN CONTENT

Investment, in its broadest sense, means the sacrifice of current dollars (NNaira) for future dollars (naira). Two different attributes are
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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

generally involved: time and risk. The sacrifice takes place in the present and is certain. The rewards comes later, is at all and the magnitude is generally uncertain. In some cases, the element of time predominates (for example, government bonds). In other cases, risk is the dominant attribute (for example, call options on common stock). In yet others, both time and risk are important (for example, share of common stock) (William, F Sharpe, Garden J. Alexandra and Jeffery V. Bairley, 1995: 1). Viewed in this sense, marriage is an investment. Types of Investment Broadly speaking, investment may be classified into: a. b. c. d. Direct and Indirect Real assets (tangible) Paper assets (financial instrument)

Features of Investment Our discussions so far can be summarised by highlighting the essential features of investment. a. Investments are undertaken in anticipation of benefits which are not expected to accrue concurrently with the investment outlay. As a result of this inevitable time lag between outlay and benefit, almost every investment involves some risk, the risk that anticipated benefits may not ultimately be realised. Investments can be made in real or financial assets. Irrespective of the media, all investments can be measured in terms of the total outlay of funds. Unlike capital, investment is a flow variable. Consequently, it ought to be measured as a time-rate of change in capital stock. Since investment benefits accrue overtime, there is the expectation that the asset in which any investment is denominated shall be retained by the investor for some reasonable period. Hence the value of the asset should be carefully established at the time the investment is made. Every investment involves some forgoing some current capability for consumption. As a result of this feature, economists usually expect an identity between the level of savings and investment.

b.

c. d.

e.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Investment and Speculation According to Okafor (1983), the distinction between investment, and speculation is not easy to make by simply observing the overt actions of the individuals involved. He went further to provide a beautiful SUMMARY comparing the two as follows: Table 1: Investment and Speculation Compared Investment Less Moderate Speculation More, if not infinite. High

Possible considerations 1. Degree of risk assumed 2. Level of income/ profit expected 3. Income orientation 4. 5.

Income to accrue over Income to accrue time quickly and in a lump sum Major Future value of assets Direction and extent consideration and future earnings of expected price potential movement Nature of Regular income and Capital gains. income possible terminal capital gains.

Basis for Classifying Investments Broadly speaking, investments can be classified into two -investment in real assets and investment in financial assets. In the words of Okafor (1983) both types of investment can further be classified on the basis of a number of parameters. a. Magnitude of Outlay

Major investments could be distinguished from minor investments. In investment outlay, size is relative. An investment is major or minor depending on the relative proportion of the outlay to the total size of a firm. Thus whereas an investment of N20,000 could be considered a minor investment by a firm capitalized at N20 million, it is very major investment to a small firm with total assets valued at N40,000. b. Risk Environment of Investment

A distinction is made between investment under conditions of certainty, investments under conditions of risk, and investments under conditions

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

of uncertainty. The problem of risk and uncertainty will be discussed in the subsequent unit. c. Motivation for Investment

A distinction could be made among investments for asset replacement, capacity expansion or modernization, and investments for strategic purposes. d. Sequencing of Cash-flows

Conventional investments are distinguished from non -conventional investments on the basis of the timing and sequencing of cash-flow arising from the investment. The nature of both types of investment, and the differences between them, are discussed subsequently, in this course. e. Nature of Expected Benefits

A distinction exists between cost-saving and revenue-yielding, real asset investment. The former is illustrated by a firm that replaces old equipment in the hope of cutting operating costs over the life of the new equipment. In a revenue expansion programme, on the other hand, funds are invested in order to increase gross revenue either through additional sales volume or through increased price per unit of sales. When evaluating a cost-saving investment, the value of total costs saved is compared with the additional investment made. In the latter situation, the investor would have to compare the increased costs with the additional sales revenue. f. Relationship to other Investments

The costs and benefits of a given investment may or may not be affected by alternative investments. In this regard, dependent investments are different from independent investments. g. Investment in Real Assets

Investment in real assets takes one of three major forms, that is, investment in business fixed assets, investment in inventory and investment in residential construction. h. Investment in Projects

Real asset investment is either on single fixed assets or on a group of inter-related assets. Where the group of inter-related assets provides

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

facilities capable of completing a production or a service investment activity is described as a project. Investment such that the facilities provided by the component assets effective if operated as a unit. Hence the component necessarily be accepted or rejected as a set.

process, the projects are can only be assets must

Contrary to popular expectation, the basic difference between projects and single asset investments does not lie in the value of the investment outlay. The cost of a single turbine in a hydro-electricity generating plant could be many times the total investment outlay in a corn grinding mill. In terms of our definition, the latter is a project because it can complete a processing cycle. Outlay on the hydro-electricity generating turbine is not by itself a project. The distinction must, however, be given a common sense interpretation. It is wrong, for example, to regard the purchase of a single taxi cab as a project, though such a cab can operate as a unit. A project necessarily involves the interplay of a number of single assets. (Okafor 1983). Further Classifications 1. Conventional and Non-Conventional Investments

According to Okafor (1983), investment activities in which periods of net cash outflow are expected to precede periods of net cash inflows are described as conventional investments. Non-conventional investments, on the other hand, are those in which there is no specific pattern in the sequencing of cash flows. 2. Cash Flows

The definition of net cash inflow or outflow used above is not identical with the accounting concept of income or expenditure. Net cash inflow from an investment for any period includes both the accounting income for the period and the non-cash expenses charged to operating revenue in determining such income such as depreciation. 3. Dependent and Independent Investments

Two or more investments are economically independent if the expected cash flow from each would be unaffected whether or not the alternate investments are carried out concurrently. Investment proposals are dependent if they are either technically dependent or economically dependent. (Okafor, 1983).

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Degree of Dependence in Investments There are degrees of dependence of investment opportunities. In one extreme case, one investment (A) is so dependent on another (B) that the net benefits of A would be virtually insignificant unless both themes are carried out simultaneously. Given that situations, investment B is a prerequisite for A. Where the degree of dependence is reciprocal, the alternatives are complementary. The other extreme case of dependence occurs where the alternatives are so inter-related that the decision to carry out one implies ipso facto a rejection of the other. This is a case of mutual exclusion which occurs either because of technical dependence or because the alternative investments serve the same market which can only support one of the alternatives. Cases of mutual exclusion in investment alternatives abound in industry. Note Well The distinction between dependent and independent investments is important for one main reason. Whereas an independent investment is evaluated on the basis of its absolute cash-flows, a dependent investment must be evaluated on the basis of its incremental cash-flows.

4.0

CONCLUSION

From the foregoing discussions, one can therefore conclude that capital investments can contribute a lot towards national development. Accordingly we suggest that individual families, churches and states should embark on one form of investment or the other.

5.0

SUMMARY

In this unit, we learnt that capital investments involve making sacrifices today in anticipation of future benefits. We also learnt that investments could broadly speaking be divided into two namely Direct and Indirect investments or Real Assets (tangible) and paper Assets (Financial Instrument). We also looked at the features of investments and finally drew a line between investments and speculations.

6.0
1.

TUTOR - MARKED ASSIGNMENT

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

2. 3.

Discuss the similarities and major differences between investment in real assets and investment in financial assets. Evaluate at least five government policies currently in force, which either induce or stifle private investment.

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REFERENCES/FURTHER READINGS

Nweze, A.U. (2006). Investment Opportunities in the Nigerian Capital Market. Okafor, F.O. (1983). Investment Decision: Evaluation of Projects and Securities. London: Cassell Ltd.

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

UNIT 2
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

DECISIONS: TYPES, FEATURES AND TOOLS FOR DECISION-MAKING

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In real life situations, one is often faced with more than one possible course of action. These possible courses of action are known as alternatives, Faced with these alternatives, the question then that naturally arises is: Which alternative(s) do l embark upon? Collectively, all the steps and processes to be taken in order to arrive at the best possible course of action is known as decision making. This is the focus of this unit.

2.0

OBJECTIVES

After studying this unit, you should be able to: use tools for decision making at various levels; and define some "Decision Analysis" terms.

3.0

MAIN CONTENT

INTRODUCTION Decisions could be loosely grouped into five. They are: a. Routine Planning Decision - These decisions are often concerned with how to make the best use of scarce resources. Example budgeting. Non-Routine (Short-Run Problem) - These are "one-off" special decisions of a non-recurring nature, where cost- benefit analysis could quickly be carried out.

b.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

c.

Investment or Disinvestments Decisions - These decisions involve large cash outflows and the potential benefits are expected to accrue over a reasonably long period. Long-range Decisions - These are decisions that are not frequently made. In a way, therefore, they can be seen as quantitative policy decisions' (Shilling law, 1963). These decisions try to provide a continuing solution to a continuing or recurring problem(s). Control Decisions - These decisions involve evaluating performance provided a proper cost - benefit analysis is carried out before implementation (MAYO/BPP.1988:314)

d.

e.

Alternatively, Decisions could simply be categorised into two: a. b. Accept or Reject decisions; and Ranking decisions.

To facilitate our discussion, let's look at the various concepts in decision-making, starting with the concept of relevant costs. Concepts in Decision-Making: Relevant Cost According to the Official Terminology of the Chartered Institute of Management Accountants (CIMA), relevant costs are defined as cost appropriate to aiding the making of specific management decisions. MAYO/BPP (1988: 316) are of the view that the costs which should be used for decision making are often referred to as relevant costs. That is a relevant cost is a future cash flow arising as a direct consequence of a decision. a. b. Relevant costs are future costs. Past costs are only useful in so far as they provide information for predicting future costs. Relevant costs are cash flows. The following should be ignored. Depreciation/amortisation Notional rent or interest All overhead costs absorbed A relevant cost is one, which arises as a direct consequence of a decision.

c.

Differential Costs These are the differences in costs between two alternative courses of action. Example: Going to Lagos by road from Enugu costs N2,000 and

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

going by air costs N10,000 (say) the differential cost is therefore N(10,000 2,000) = N8,000. Incremental Cost These are relevant costs, which are simply the additional costs incurred as consequence of a decision. Example: in a decision, the cost of processing further is known as incremental cost and the associated benefit is known as incremental revenue. The difference between the incremental revenue and incremental cost forms a basis for the decision to process further. How does incremental cost differ from differential cost? Whereas differential costs compare the differences in cost between two alternative courses of action, incremental costs are ways of stating the relevant costs when three or more options are compared (MAYO/BPP, 1983: 318). Avoidable Costs They are defined as those costs that can be identified with an activity or sector of a business and which would be avoided if that activity or sector did not exist. Opportunity Costs An opportunity cost is the benefit forgone by choosing one opportunity instead of the next best alternative. Sunk Costs In the Holy Bible, the Gospel of St. Matthew, 22:14, Luke 14: 15 24, the parable of the Wedding Feast was told. According to the passage, those invited failed to come and the king said, now go to the main streets and invite to the feast as many people as you find (Matt. 22: 9). If we hold constant the moral or spiritual lessons, we can then extract the accounting information contained therein, that is: Realizing that the cooked food and meat and wine were all perishable possibly there were no refrigerators then the kind reasoned that all the food and meat were sunk costs (they had no viable alternative uses, if not consumed that day). Hence, he decided to invite other people to come and eat the food and meat, so that on the assessment day (Matt. 25: 31 46), he may be told, I was hungry and you fed me, thirsty and

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

you gave me a drink: I was a stranger and you received me in your home (Matt. 25: 35). The above vividly illustrates the concept of sunk cost defined as the cost of an asset which has no significant alternative uses. Examples include i. ii. Dedicated fixed assets Development costs already incurred.

Committed Costs A cost is said to be a committed cost if the cash outflow must necessary take place regardless of whatever decision is taken now about alternative opportunities. Notional (Imputed) Costs This is in line with the matching concept in accounting. It is a hypothetical account cost to reflect the use of a benefit for which no actual cash expense is incurred. Example: i. ii. Rent charged on a building owned by the organization Interest charged on own capital employed.

The Relevant Cost of Materials In the word of MAYO/BPP (1988: 322), the decision tree below shows how the relevant costs of materials can be identified, provided that the materials are not supplies and so do not have an internal opportunity cost.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Yes

Are the materials already in stock or contracted to buy in a purchase No agreement? No Relevant cost = future /current purchase cost of materials

Are the materials regularly used and replaced with fresh supplies when stocks run out? Yes Relevant cost = future/current purchase of materials Sracped if not used Do the materials have an alternative uses or would they be scrapped if not used?

Do the materials have an alternative uses or would they be scrapped if not used? Other used available Relevant cost = higher of value in other use or scrap value/disposal value

Relevant Costs in Non-Routine Decisions Types of Non-Routine Decisions i. When performing the manufacturing and selling functions, management is constantly faced with the problem of choosing between alternative courses of action. Typical questions include: what to make? How to make it? Where to sell the product? And what price should be charged? In the short run, management is typically faced with the following non-routine, non-recurring types of decision: Acceptance or rejection of special order Pricing standard products Make or buy Sell or process further Add or drop a certain product line Utilization of scarce resources

ii. iii. iv. v. vi. vii.

Relevant Costs Defined In each of the above situations, the ultimate management decision rests on cost data analysis. However, not all cost are of equal importance in decision-making, and managers must identify the costs that are expected future costs (and revenues) which differ between the decision alternatives.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

The Management Accountants Role in Short Term Decision Management Accountant has an important role in the problem-solving process, not decision-making but as collector and reporter of relevant data. His reports must provide valid data in numbers that measure the quantities pertinent to the decision at hand. Many managers want the management accountant to offer recommendations about the proper decisions even though the final choice always rests with the operating executives problem-solving is essential decision i.e. choosing among several courses of action. The management accountants role in problem solving is primarily that of technical expert on cost analysis. His responsibility is to be certain that the manger is guided by relevant data/information that would lead the manager to the best decision. Under the concept of relevant costs, which may be appropriately titled the incremental, differential, or relevant cost approach, or relevant cost approach, the decision involves the following steps: i. ii. iii. iv. gather all costs associated with each alternative drop the sunk costs drop those costs (not in absorption costing), that do not differ between alternatives select the best alternatives based on the cost data.

Feasibility and Viability Studies Before embarking on any capital investment, it is always advisable to conduct both feasibility and viability studies. Whereas feasibility study is aimed at establishing the practicability or workability of an investment, viability study tries to evaluate the degree of profitability. Feasibility Study This starts with environmental assessment (since certain investments can not take place in some environments). Other issues to be considered include: i. ii. iii. Management/personnel Availability of raw materials Market share assessment

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Viability Tests These tests are normally conducted using either the traditional techniques or the discounted techniques or both.

4.0

CONCLUSION

As soon as one is faced with many alternatives, decision-making comes in. The truth, therefore, is that decision making is future-oriented. Therefore, everything humanly possible must be done to ensure that only economically viable, socially desirable and technical feasible investment decisions are taken.

5.0

SUMMARY

This unit basically looked at the fundamental concepts in decisionmaking. The various types of decisions were also discussed. Feasibility and viability studies were equally considered.

6.0
1. 2. a. b. c. d. e.

TUTOR- MARKED ASSIGNMENT

7.0

REFERENCES/FURTHER READINGS

Nweze, A. U. (2004). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

UNIT 3
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

THE PAYBACK PERIOD

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

For an average rational investor, one question that must be considered before embarking on a capital investment is: how long shall it take to recover or recoup the amount to be invested? This explains why young man that wants to go into motorcycle (okada) business would first of all ask: how long shall it take to get back the cost of the motorcycle. Potential landlords also ask similar questions. This is where the payback period readily comes in.

2.0

OBJECTIVES

In this unit, you will be able to: define, apply and compute payback period; and outline merits and demerits of the payback period.

3.0

THE MAIN CONTENT

Payback Period Payback period is defined as the period, usually expressed in years, which it takes for the projects net cash inflows to recoup the original investment. Illustrations i. When the cash-flows form an annuity. The Payback Period is simply Cash outflow divided by Cash inflow. Example, Alhaji Haruna spent N10,000,000 to build a house and receives N1,000,000 annually as rent. The payback period is N 10m N1m = 10 years.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

ii.

When the cash inflows do not form an annuity. Ebele Nig. Ltd has the option of investing in any of the following three projects whose associated cash flows are presented thus: Year Project I Cash Flow N000 0 (15,000) 1 6,000 2 5,000 3 4,000 4 5 6 Project II Cash Flow N000 (15,000) 4,000 5,000 6,000 Project III Cash Flow N000 (15,000) 3,000 5,000 4,000 3,000 2,000 1,000

Required: Advise the company on which of the three projects to invest in (base your advice on the payback approach). Project I This project generated N15,000,000 in exactly three years. Therefore, the payback period is three (3) years. N:B: There were no other cash inflows after year three. Project II Again, the payback period is three (3) years since it took exactly three years to recoup N15,000,000. Also, no further cash inflows were recorded after the third year. Project III Even though the payback period for this project is 4 years, it recorded additional N2,000,000 and N1,000,000 in years 5 and 6 respectively. Advice: Choose either project (I or II).

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Solution Ebele Nig. Ltd Net Cash Flows Project I Year Cashflow Cumulativ e Cashflow N000 N000 0 (15,000) (15,000) 1 6,000 (9,000) 2 5,000 (4,000) 3 4,000 NIL 4 5 6 N.B: By usual notations: Year 0 = Now (the date of investment) Year 1 = the end of the1st year Year 2 = the end of the 2nd year And so on Any figure in a bracket means cash outflow A positive figure means cash inflow Merits and Demerits of Payback Period a. Merits i. Simple to calculate ii. Easy to understand iii. It does not recognize depreciation as an expense iv. It favours projects that have quick return potentials Demerits i. It completely ignores any other cash inflow once the payback period has been arrived at. ii. It ignores the timing of cash inflows. For example, in the above illustration, Projects I and II ranked equally even when it is obvious that the cash inflows for project I are better than that for project II. Project II Cashflow Cumulativ e Cashflow N000 N000 (15,000) (15,000) 4,000 (11,000) 5,000 (6,000) 6,000 NIL Project III Cashflow Cumulative Cashflow N000 N000 (15,000) (15,000) 3,000 (12,000) 5,000 (7,000) 4,000 (3,000) 3,000 NIL 2,000 2,000 1,000 3,000

b.

N.B: Because of its simplicity, the Payback Period Approach is undoubtedly the most commonly applied in practice.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Illustration Bola Plc is considering the following three projects whose associated cash flow are given thus: Year Project A N000 0 (500,000) 1 100,000 2 150,000 3 250,000 4 500,000 Project B N000 (500,000) 150,000 250,000 300,000 300,000 Project C N000 (500,000) 200,000 250,000 300,000 450,000

Required: Calculate the payback periods for each of the projects and advice Bola Plc accordingly. Solution Bola Plc. Project A The sum of the cash inflows for the first 3 years equal N500,000,000. The payback period is 3 years. Project B The sum of the cash inflows for the first 2 years is N400,000,000 and for the third year, the cash inflow is N300,000,000 even when only N100,000,000 was required to recoup the cost of the investment conclusively. Therefore, the payback period is 500,000,000 400,000,000 300,000,000 = 21/3 years

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Project C The sum of the cash inflow for the first 2 years is N450,000,000 and for the third year, the cash inflow is N3,000,000,000. Therefore, the payback period is 5,000,000,000 450,000,000 300,000,000 = Comments Since project C has the least payback period of 21/6 years compared with period B (21/3 years, or project A (3 years), the management of Bola Plc is advised to embark on project C. Illustration Modern Tech Services Ltd is considering two alternative projects for a business expansion programme in the Northern part of the country. The projects have the following naira cash flow profiles according to the data supplied by the companys accountant: Year 0 1 2 3 4 5 6 7 Required: a. b. Calculate the payback period for each project (10 marks) Based on payback periods, advice which of the two projects should be chosen (1 mark) c. State the advantage and disadvantages of the payback period criterion on investment appraisal (5 marks). (Total 16 marks) Project I -1 million -2 million -95 million .85 million .78 million .62 million .40 million .10 million Project II -3 million .20 million -50 million .65 million .75 million .80 million 1.90 million .20 million 21/6 years

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ICAN (May 1994) Mgt Acc Q7. Solution Project I Period Cash flow CF N000 (N) 0 (1,000) (1,000) 1 (2,000) (3,000) 2 950 (2,050) 3 850 (1,200) 4 780 (420) 5 620 200 6 400 600 7 100 700 PBP = 4 years + 420,000 620,000 = 46/7 years Project 2 Cash flow CF N000 (N) 0 (3,000) (3,000) 1 (200) (2,800) 2 500 (2,300) 3 650 (1,650) 4 750 (900) 5 800 (100) 6 1,900 1,800 7 200 2,000 PBP = 5 years + 100,000 1,900,000 = 5 years + 0.522631578 PBP = 5 years Period Project 1 = 46/7 years Project 2 = 5 years Advice From this, I advise modern technical service to accept project 1 because it has a shorter payback period (PBP) than project 2. Merits of PBP i. ii.
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1st position 2nd position

It is not very costly to adopt It is simple to understand and easy to calculate

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

iii. iv. v. vi.

It doesnt recognize depreciation as an expense It favours projects that have quick return potentials It is virtually suitable for many categories of management It gives an insight into the liquidity of the project.

Demerits of PBP i. ii. iii. iv. It ignores the cash inflows earned after the payback period It does not take the time value into consideration Payback periods are arbitrarily set by management, hence they are usually subjective. It is not consistent with the objective of maximizing the market value of the firms shares, as share prices are not dependent on the firms payback period.

4.0

CONCLUSION

Predicated on the foregoing discussions, one can now conclude that the payback period is a very simple method for evaluating capital investments the weaknesses notwithstanding.

5.0

SUMMARY

In this unit, we saw the definition of the payback period as a method for appraising capital investment. We also looked at the merits and demerits of the method and had some illustrations of both when the cash inflows form an annuity and when the cash inflows fail to form an annuity.

6.0

TUTOR-MARKED ASSIGNMENT

AKPEBOR OTUOKENA BEAUTY (AOB) Projects Initial costs (N) Expected life Scrap value expected Expected Cash Inflow End of year 1 2 3 4 5 A 400,000 5 years N20,000 N000 160 140 130 120 110 B 460,000 5 years N30,000 N000 200 140 100 100 100 C 360,000 4 years N16,000 N000 110 130 190 200 0

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The company estimates its cost of capital to be 18% and discount factors are: Year 1 2 3 4 5 Required i. Calculate the following The payback period for each project The Internal Rate of Return for each project The Net Present Value of each project (10 marks) Which project should be accepted? Give reasons (2 marks) (Total 15 marsk) (ICAN, November 2002) Mgmt Acc Q3. 0.8475 0.7182 0.6086 0.5158 0.4371

ii.

7.0

REFERENCES / FURTHER READINGS

Nweze, A. U. (2004). Profit Planning: A Quantitative Approach. Enugu: Mcal Communications. Osisioma, B. C. (1976). Studies in Accountancy: Text and Readings. Enugu: Acena Publishers. Pandey, I. M. (1988). Financial Management. Publishing House PVT Ltd. New Delhi: Vikas

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UNIT 4
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

ACCOUNTING RATE OF RETURN (ARR)

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

Oftentimes, Accountants are interested in profits maximization or more appropriately wealth maximization. But these profits are normally expressed as percentages of the amount invested. This way a benchmark could be set. This is where the Accounting Rate of Return becomes relevant. It has its origin from the concepts of Return of Investment (ROI) or Return on Capital Employed (ROCE).

2.0

OBJECTIVES

At the end of the unit, you are expected to: define Accounting Rate of Return (ARR); state the formulae for ARR; identify the investment criteria for ARR; and state the advantages and disadvantages of ARR.

3.0

MAIN CONTENT

Accounting Rate of Return (ARR) This is defined as the ratio of average annual profits after depreciation, to capital invested. This is the basic definition. Other variants exist. For example: i. ii. iii. Profits may be before or after tax Capital may or may not include working capital Capital invested may mean the initial capital investment or the average of the capital invested over the life of the project.

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From the above variations, one can state at a very high confidence level that the ARR (Accounting Rate of Return) and (Return on Capital Employed) could be used interchangeably. Illustration Modesta Nig. Ltd. is considering three projects each with an initial capital of N1,000,000 and a life of 10 years. The profits generated by the projects are estimated to be as follows: After Tax and Depreciation Profits Year Project A N000 1 100 2 100 3 100 4 100 5 100 6 100 7 100 8 100 9 100 10 100 Total 1000 Project B N000 175 175 100 100 75 75 75 75 75 75 1000 Project C N000 75 75 75 75 75 75 100 100 175 175 1000

Required: Calculate the Accounting Rate of Return (ARR) using i. ii. Initial Capital Average Capital

Solution Modesta Nig Ltd. i. Accounting Rate of Return on Initial Capital Project B N1,000,000 10 =100,000 100,000 1,000,000 = 10% Project C N1,000,000 10 = 100,000 100,000 1,000,000 =10%

Project A Average Profits N1,000,000 10 = 100,000 100,000 ARR 1,000,000 = 10%

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

ii.

Accounting Rate of Return on Average Capital Project B N1,000,000 2 = 500,000 100,000 500,000 = 20% Project C 1,000,000 2 = 500,000 100,000 500,000 = 20%

Project A Average Profits N1,000,000 2 = 500,000 ARR 100,000 500,000 = 20%

N.B: Calculation of average capital. Given a scrap value of ZERO, then the average capital investment is calculated thus: Sum of the terms No of Terms Sum = 1,000,000 + 0 = 1,000,000 No of terms = 2 (that is, 1,000,000 and 0) Average = 1,000,000 2 = N500,000 By way of formulas therefore, Average capital = Initial Capital 2 Where the scrap value is not ZERO, then the average capital becomes: Initial Capital + Scrap Value 2 ARR: Merits and Demerits Merits 1. 2. Simple to calculate Easy to Understand

Demerits 1. 2. 3. 4. It ignores the time value of money. For example, the above three projects are ranked equally even when there are obvious differences in the timing of cash flows. It recognizes depreciation as an expense. There are many variations of accounting rate of return. Accordingly, it lacks objectivity.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

4.0

CONCLUSION

Even though the Accounting Rate of Return (ARR) does not recognize the time value of money, it remains a very valuable method for evaluating capital projects. This is simply because it is very much associated with the concept of Return on Investment or Return on Capital Employed which is used to evaluate divisional performance.

5.0

SUMMARY

In this unit, we discussed the basic definition of Accounting Rate of Return (ARR) and also looked at the other variants of the definition. Such variants include i. ii. The definition of profits: is it Profit before Tax (PBT) or Profit after Tax (PAT)? The definition of capital: is the working capital included or not? Is it the initial capital or the average capital?

6.0

TUTOR-MARKED ASSIGNMENT

Duro Plastic Plc is considering investment in two mutually exclusive projects A and B, each having a life span of 5 years and no residual value. Project A Project B N N Initial Investment Net Cash Inflows Year 1 Year 2 Year 3 Year 4 Year 5 250,000 80,000 60,000 65,000 70,000 75,000 320,000 70,000 75,000 80,000 85,000 85,000

The criteria for accepting or rejecting a project are: a. Accounting rate of return on average capital employed should not be less than 15%. b. Payback period should not be more than four years, and c. Profitability index based on net present value should not be less than 3% using a discounting rate of 12%. You are required to present necessary calculations to show whether the above projects A and B are acceptable to the company or not.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

7.0

REFERENCES/FURTHER READINGS

Copeland, R. M. and Dascher, P. E. (1979). Management Accounting. Canada: John Willey and Sons Inc. Fregman, J. M. (1985). Accounting for Management Analysis. Homewood Illinois: Richard D. Urwin. Horngren, C. T. and Foster and Datar, S. M. (1997). Cost Accounting: A Management Emphasis. New Delhi: Prentice Hall.

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UNIT 5
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

COMPOUNDING AND DISCOUNTING

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In Investment decisions, it is generally believed that money has time value. Hence, we often talk of future value (when we are compounding) or present value (when we are discounting). This is so because N1.00 received today is worth more than N1.00 receivable tomorrow. Yes, even if we hold constant the application of time value of money, the saying that a bird at hand, is worth more than one million in the bush becomes relevant. It is for this reason that we now talk about compounding and discounting.

2.0

OBJECTIVES

At the end of studying this unit, you will be able to: define compounding and discounting in investment decisions; compute the formulae for compounding and discounting; compute simple discounting factors; compute annuity factors (present values); and solve some practical problems involving compounding and discounting.

3.0

MAIN CONTENT

What are the Components of Cash flows? The following components according to Lucey (1988) are typical cash flow items. a. i. ii. Cash Inflows The project revenue Government grants

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

iii. iv. v. b. i. ii. iii. iv. v.

Resale or scrap value of assets Tax receipts Any other cash inflows caused by accepting the project. Cash Outflows Initial investment in acquiring the assets Project cost (labour materials sets) Working capital investment Tax payments Any other cash outflow caused by accepting the project

Time Value of Money Suppose you are given the option of receiving either N100,000 (one hundred thousand naira) today or N120,000 (one hundred and twenty thousand naira) at the end of the year. Which option would you choose given that the prevailing interest rate is at 10% per annum and that the risk of default is ZERO? Given that redeeming the N120,000 in a years time has a probability of 1 (ONE), that is, it must necessarily be redeemed, then the question of a bird at hand is worth more than 10 (TEN) in the bush becomes inapplicable. In that case, we are left with only rational reasoning. To reason rationally, one has the option of asking any of the following questions:
i. ii.

At 10% per annum, how much is N100,000 worth in a years time? Or At 10% per annum, how much is N120,000 receivable in a years time worth TODAY?

Answers While the first question addresses a concept known COMPOUNDING, the second centres on DISCOUNTING. Option 1:
Option 2:

as

In a years time, N100,000 at 10% per annum will worth N100,000 x 1.1 = N110,000. The present value (todays value) of N120,000 receivable in a years time at 10% per annum is N120,000 (1.1)-1 = N109,091.

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Analysis Either way, the option of receiving N120,000 in a years time has a higher value than receiving N100,000 TODAY. What if the option was between receiving equal amounts say N120,000 either TODAY or in a years time? Obviously, the question becomes easy since any rational being would opt for receiving the money TODAY. Hence, N10,000 received TODAY is worth more than N10,000 received tomorrow. This is the concept of time value of money. Comment For investment appraisal, DISCOUNTING is preferred to COMPOUNDING. Put differently, for investment appraisal, our FOCAL DATE should be TODAY AND NOT TOMORROW! Compound Interest According to the New Websters Dictionary (1995: BD 25), compound interest is interest upon principal plus accrued interest. Put differently, compound interest is generally calculated for long term loans and the interest payable in one period forms a part of the principal in the coming or subsequent periods; which itself earns interests for other periods. The ultimate effect is that at the end of each period, the principal keeps increasing following the addition of interest earned in the preceding period. Interests are usually calculated and added to the principal at the end of each regular interval usually called the conversion intervals or periods. The conversion period/intervals may be one year (annually), six months (semi-annually), four months (term), three months (quarterly), monthly, weekly, daily or even hourly. Usual Notations Initial Principal Rate of interest That is, Nominal interest rate Number of conversion intervals per year Rate of interest per conversion period = = = = = P Jm pr (J, M) J per year M I

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Period for which principal is invested = conversion interval Accumulated amount after k conversion, periods = Sk Accumulated amount at the end of the term = S From the above notation, interest rate per conversion interval is equal to nominal interest rate divided by number of conversions per year. There 1 = j/m. Also, the accumulated amount at the end of the first conversion period is equal to the principal at the beginning of the first conversion period plus interest earned at the first conversion period, that is: S1 = P + pi = P(1 + i)

Similarly, the accumulated amount at the end of the second conversion period is given as: = S1 + S,I = S1 (1 = i) = P(1 + i) (1 + i) = P(1 + i) Similarly, S3 = S2S2i = S2 (1 + i) = P(1 + i)2 (1 + i) = P(1 + i)3 It can be observed from the expressions of S1, S2 and S3 that they form a sequence in which the power of (1 + i) is equal to the number of conversion intervals. Therefore, the accumulated amount at the end of k conversion period gives us: Sk = P (1 + i)k Similarly, the accumulated amount at the end of the conversion period N where n is the number of terms Sn = P(1 + i)n N.B: If there are M conversion intervals per year than the number of conversions in the period of T years is TM. Illustration Find the accumulated amount of the following:
a. b. c.

S2

N250,000 after a period of 3 years at J = 6% and M = 2 N325,000 at the end of 6 years and 3 months at J4 = 0.10 N275,000 after the period of 31/2 years at J4 = 8%

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

N250,000 after the period of 10 years at 6% converted quarterly. Solution

a.

P = I = But S = Substituting, S = = = P = n = S = Substituting, P = = = P n S S = = = = = = = = = = =

N250,000 n = TM 3 x 2 = 6 JM = 3% = 0.03 P(1 +i)n 250,000 (1.03)6 250,000 x 1.194052297 N298,513.07 N325,000; t = 61/4; J4 = 10% 61/4 x 4 = 25 and 1 = 10/4 = 2.50% P(1 + i)n 325,000 (1.025)25 325,000 x 1.853944098 N602,531.82 N275,000; t = 31/2 years, J12 = 8% 41 and i = 8/12 P (1 + i)n 275,000 (1.006666666)42 275,000 x 1.321900923 N363,522.75 250,000; t = 10 years, j = 6% 4 40, i = 6/4= 1.5% 250,000 (1.015)40 N453,504.60

b.

c.

d.

P M n S

Annuity According to the New Websters Dictionary (1995: BD5), annuity is a series of payment for a fixed future period or for lie, payable monthly, semi-annually, annually or at any other specified intervals. It is frequently used to describe a part of the retirement allowance derived from the accumulated contributions made by the members, contributions which is called a pension. Put differently, an annuity is a sequence of equal payments made at equal time intervals. Example: a. b.
32

The payment of a sum of money at the end of each month as rent Mortgage payments

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

c. Installment payments (hire purchase, lease). Payment Intervals This is the time interval between two consecutive payments. Term of an Annuity This is the time period from the payment interval preceding the first payment to the date of the last payment. Amount of an Annuity (A) This is the total equivalent value of all payments on the day of the last payment at a given rate of interest. Present value of an Annuity (A) This is the total equivalent value of all payments at the beginning of the term given a rate of interest. Simple Annuities These are annuities in which the payment intervals and conversion COINCIDE. Under the simple annuity, payments are made at the end of the payment intervals. Formulae Lets recall that since annuity is a sequence of equal payment made at equal time intervals, it therefore becomes a geometric series in which: a. b.
c.

the first term, a = 1 the common rate, r = 1 + i the last term, 1 = (1 + i)n-1

Usual notations: R N A S I = = = = = regular payments number for regular payment present value of an annuity amount of the annuity interest rate per payment interval

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Time Diagram

(n-3)(n-2)(n-1)n Term Lets assume that our focal date is the date of the last payment (n). By the concept of equivalent values, lets identify the two sets of obligation. First Set of Obligation The accumulated sum (S) on the date of the last payment (n) is: S (1 + i)0 = S Second Set of Obligation This is the future value of all the regular payments. That is: R (1 + i)n-1 + R(1 + i)2 + R(1 + i)n-3 + R(1 + i)n-4 + R(1 + i) + R (1 + i)0 = R[1 + i)n-1 + (1 + i)n-2 + (1 + i)n-3 + (1 + i)n-4 + (1 + i) + 1] Rewrite the terms in the reverse order. R [1 + (1 + i) + + (1 + i)n-3 + (1 + i)n-2 + (1 + i)n-1] The above, has therefore metamorphosed into a geometric series in which: i. ii.
iii.

The first term, a = 1 The common ratio, r = 1 + i The last term, I = (1 + 1)n-1

* The last term has (n 1) and not n since no payment was made in the nth period. Therefore, the sum of the series, S is the same as the sum of the geometric series given a a rI = a(rn 1) 1r r1 for r > 1 Sn =

34

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

By substituting a rI 1r In the above equation 1 (1 + I) (1 + I)n-1 = 1 (1 I) 1 (1 + 1)n -i

On the multiplying both sides by 1, we have: (1 + i)n 1 i Sn = RI (1 + I)n 1I i For given values of I and n (1 + I)n 1 I (As in annuity table) This is a constant and therefore denoted as S nI (usually referred as S angle n at i". Therefore, instead of writing S = R[(1 + i)n 1 I S = RSn I. Present Value, A Assume that t = 0, value of all regular payment made to repay, for instance, a loan at the beginning of the term = R (1 + i)-1 + R (1 + i)2 + + R(1 + I)-n A = R[(1 + i)-1 + (1 + i)-2 + + (1 + i)-n]. Again, the above series becomes a geometric progression whose first term (a) = (1 + i)-1 Common ratio (r) = (1 + i)-1 But Sn = a(1 rn) 1- r for r < 1 substituting A = (1 + i)-1 [1 (1 + i)-1(n)] 1 (1 + i)-I

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

(1 + i)-1 [1 (1 + i)-n] 1 1/1+i = (1 + i) 1 [1 (1 + i)n] 1+i1 1+i = (1 + i)-1 [1 (1 + i)-n] i 1+i = (1 + i)-1 [1 (1 + i)-n] x 1 + i i -n = 1 (1 + i) i A = R[1 (1 + i)-n] i = Ran i A = Tutorial Notes a. b. Ordinary annuity certain: This is an annuity in which the payments are made at the end of the payment intervals. Students are urged to display each annuity on a time line with the interest period (IP) as the unit of measure marking at least the beginning of the term (0 and the scale) and the end of the term (n on the scale) and a few other periods. Difficulties with annuities arise from a failure to keep two facts in mind when using the formula: a. The formula S = Rsn i, gives the amount of an annuity just after payment has been made. b. The formula A = Ran i give the value of annuity one period before the first payment was made. If an unknown is associated with the amount of an annuity, take a focal date of t = n in which case the amount is known (given or inferred). If an unknown is associated with the present value of an annuity, take the focal date of t = 0 in which case the present value is known (given or inferred).

c.

d. e.

Illustration For the past ten years, Austin has been depositing N50,000 at the end of each year in a savings account, which pays 15 percent per annum. How much was to his credit just after the 10th deposit? Solution R = 50,000
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BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

i = 0.15 n = 10 (by usual notation) S = R[(1 + I)n 1] i Substituting S = = = = Illustration Today, Uche purchased an annuity of N250,000 per year for 15 years from an insurance company, which uses 3% compound annually. If the first payment is due in one year, what did the annuity cost him? Solution R = N250,000 i = 0.03 n = 15 A = R[1 (1 + i)-n] I Solution N250,000 [1 (1.03)-15] 0.03 = N250,000 x 11.93793509 = N2,984,483.77 N50,000 [(1.15)10 1] 0.15 N50,000 [4.0455577 1] 0.15 N50,000 x 20.3037184 N1,015,185.91

4.0

CONCLUSION

In financial mathematics in general, and in capital investment appraisal in particular, the twin concepts of compounding and discounting are so fundamental that they can not be done away with. This is because of the all-important concept of time value of money. Accordingly, one is advised to understand this foundation aspect of capital investment appraisal technique.

5.0

SUMMARY

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

In this unit, we looked at a wide range of concepts in financial mathematics. These concepts include: i. cashflows ii. time-value of money iii. compound interest and annuity We also looked at the various formulae for computation.

6.0
1.

TUTOR-MARKED ASSIGNMENT
Assuming that Prof. Bello decides to deposit in his Savings Account N10,000.00 at the end of every 6 months for 5 years, followed by deposits of N15,000 at the end of every 6 months for 12 years and N30,000 at the end of every 6 months for 8 years. If the back pays interest at 7 per cent per annum, compounded semiannually, how much will he collect at the end of 25 years? Ifebuche Local Government built a bridge that will need no repairs until the end of the next 5 years when N30,000 will be required for repairing. After that, it is estimated that N30,000 will be needed at the end of each year for the next 20 years. You are required to find the present value of the upkeep of the bridge, if money is worth 10 percent per annum.

2.

7.0

REFERENCES/FURTHER READINGS

Ayres, F. (1980). Mathematics of Finance. Schar Sevies. Nweze, A. U. (2004). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.

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MODULE 2
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 The Net Present Value (NPV The Net Present Value (Annuity) The Internal Rate of Return The International Rate of Return The Profitability Index

UNIT 1
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

NET PRESENT VALUE I

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

Discounted Cash-flow (DCF I) Against the backdrop that the traditional techniques ignore the timing of cash-flow, a new approach known as the discounted cash-flow has been developed. This approach uses cash-flows rather than accounting profits. According to Lucey (1988), accounting profits are invariably calculated for stewardship purposes and are period-oriented (usually monthly, quarterly or annually) thus necessitating accrual accounting with its attendant conventions and assumptions. Therefore, for investment appraisal purposes, a project-oriented approach using cashflow is to be preferred since it disallows depreciation as an expense and also recognizes the timing of cash flows.

2.0

OBJECTIVES

After studying this unit, the reader should be able to: define Net Present Value (NPV); compute and apply the formula for simple NPV; and express the investment criteria under NPV.

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3.0

MAIN CONTENT

Assumptions Underlying the Basic Discounted Cashflow Appraisal According to Lucey (1988), certain assumptions are made initially so that the underlying principles can be more easily understood. These are as follows: a. b. c. d. Uncertainty does not exist Inflation does not exist The appropriate discount rate to use is known A perfect capital market exists, that is unlimited funds can be raised at the market rate of interest.

Later, each of the above assumptions will be isolated and handled accordingly. Net Present Value (NPV) Net present value (NPV) is defined as the difference between the present value of cash inflows and those of the cash outflows all discounted at the cost of capital. According to Okafor (1983: 222), the net present worth of a project is the present value of the discounted net proceeds anticipated throughout the economic life of the project. The cash outflows and inflows are discounted using the same rate of discount. The algebraic sum of the discounted stream of cash-flows is the net present value (NPV). That is
NPV = n FC t (1 + K ) t

t=0 where

NPV = net present value CFt = net cash flow at time t K = discount rate For most conventional investments, the net cash outflow would occur at the initial period, that is, at t = 0. In such cases, the equation becomes:

NPV t=0

CFi CF0 (1 + K ) i

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

The present value of one ratio today, is of course N1. Therefore, CF0, would be equal to the initial cost of the project. Decision Rule The general criteria under the NPV appraisal techniques are: i. ii. iii. INVEST: if NPV > 0. That is, invest if the NPV is positive. DONT INVEST: if NPV < 0. That is, do not invest if the NPV is negative. Remain indifferent: if NPV = 0. That is, you may or may not invest if the NPV = 0.

According to Okafor (1983: 223), choosing among alternative and mutually exclusive projects, the decision rule is to rank them according to their relative net present worths. The project with the highest NPV is presumed to be the most preferable. Illustration 1 Ayodele Engineering Co. is trying to decide which type of machine tool to buy, of the two types available. Type A costs N10,000,000 and the net annual income from the first three years of its life will be N3,000,000, N4,000,000 and N5,000,000 respectively. At the end of this period, it will be worthless except for scrap value of N1,000,000. To buy a type A tool, the company would need to borrow from a Finance Group at 9%. Type B will last for three years too, but will give a constant net annual cash flow if N3,000,000 it costs N6,000,000 but credit can be obtained from its manufacturer at 6% interest. It has no ultimate scrap value. Which investment would be the more profitable? Give reason for your answer. Solution Ayodele Engineering Company Type A Year 0 1 2 3 Cash flow N000 (10,000) 3,000 4,000 6,000 NPV Discount (9%) N000 1.000 0.917 0.842 0.772 Factor Net Present Value N000 (10,000) 2,751 3,368 4,632 N751

N.B: 6,000 = 5,000 cashflow + 1,000 scrap value.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Type B Year 0 1 2 3

Cash flow N000 (6,000) 3,000 3,000 3,000 NPV

Discount Factor Net (6%) Present Value N000 N000 1.000 (6,000) 0.943 2,829 0.890 2,670 0.840 2,520 N2,019

Alternatively, for project B, since the cash inflows form an annuity, we then use annuity factor. For n = 3, r = 6%, the annuity factor is: 1 (1.06)-3 0.06 = 2.673

The NPV = 3000 x 2.673 6000 = 2019. Thus, we can see that type B has a far higher NPV and this will be the better investment. Illustration 2 Femi Nig. Ltd is proposing to purchase a new machine for N20,000,000 which will have a life of 6 years. The cash inflows estimated to be generated by the machine are as follows: Year 1 = N12,400,000; Year 2 = N6,000,000; Year 3 = N7,100,000; Year 4 = N2,203,000 and Year 5 = N2,774,000 and removed in year 6 an estimated net cash outflow of N1,477,000. The companys cost of capital is 15%. Should investment be proceeded with? Solution Femi Nig. Ltd

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Year Cashflow N000 0 (20,000) 1 12,400 2 6,000 3 7,100 4 2,203 5 2,774 6 -1,477

15% Discount N000 1.000 0.870 0.756 0.658 0.572 0.497 0.432

Net PV at 15% N000 (20,000) 10,788 4,536 4,672 1,260 1,379 -638

Net Profit Value (NPV) =

+ 1,997

The NPV is positive, hence go for the project.

4.0

CONCLUSION

In this unit, we looked at one of the most fundamental methods for appraisal capital projects the Net Present Value (NPV). This approach must be understood and applied most religiously.

5.0

SUMMARY

In this unit, we took a cursory look at the Net Present Value (NPV) method of capital investment approach. We started with the basic definition and formula. We also looked at the computational technique and the investment criteria.

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6.0
1.

TUTOR-MARKED ASSIGNMENT
Because of public credit policy binding in the current year, Omoloju Ltd is unable to raise all the funds it requires for investments, which must be made in the current year. There are investments opportunities open to it this year, but it can only finance one to them. The projects cash flows are as follows: Year 0 1 2 3 4 A (500,000) 300,000 300,000 300,000 (100,000) B (350,000) 100,000 260,000 200,000 50,000 C (532,360) 350,000 300,000 200,000 10,000

Required: Assuming that the marginal cost of capital of Omoluju Ltd. is 28%, advice the company on which of the three investment opportunities to choose. 2. a. Write show notes on the following:

Net Present Value Payback Model The Internal Rate of Return (IRR) b. The following information relate to three possible capital projects: Because of capital rationing, only one project can be accepted by the management of Akpebor Otuokena Beauty (AOB): Projects Initial costs (N) Expected life Scrap value expected Expected Cash Inflow End of year 1 2 3 4 5 A 400,000 5 years N20,000 N000 160 140 130 120 110 B 460,000 5 years N30,000 N000 200 140 100 100 100 C 360,000 4 years N16,000 N000 110 130 190 200 0

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

The company estimates its cost of capital to be 18% and discount factors are: Year 1 2. 3. 4. 5. Required i. Calculate the following: ii. The payback period for each project The Internal Rate of Return for each project The Net Present Value of each project (10 marks) 0.8475 0.7182 0.6086 0.5158 0.4371

Which project should be accepted? Give reasons (2 marks) (Total 15 marks) (ICAN, November 2002) Mgmt Acc Q3.

7.0

REFERENCES/FURTHER READINGS

Horngren, C. T. and Foster and Datar, S. (1997). Cost Accounting: A Managerial Emphasis. New Delhi: Prentice Hall. Lucey, T. (1984). Costing: An Instructional Manual. Eastheigh Hanks: DPP. Lucey, T. (1985). Management Accounting. London: DPP. Matz, A. and Usry, M. T. (1976). Cost Accounting: Planning and Control. Cincinnati Ohio: Southern Western Pub. Co. MAYO Association and B. P. Publications Ltd. (1988). Management Accounting. Lagos/London. Okafor, F. O. (1983). Investment Decisions: Evaluation of Projects and Securities. London: Cassell. Nweze, A. U. (2000). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.

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UNIT 2
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

NET PRESENT VALUE II

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In the previous section, we looked at Investment Appraisal involving the computation of Net Present Value (NPV) in situations where the cash inflows were not regular or constant. In that case, we used ordinary present value discounting factors. But, in situations where the cash inflows are constant, the time and effort shall be considerably minimized if we use the annuity factor present value instead. For periods less than 5, the beauty of this short cut may not be appreciated. However, with long periods, this short cut shall then become indispensable.

2.0

OBJECTIVES

After studying this unit, you should be able to: explain the concept of annuity; quote and apply the annuity factor present value; and solve practical questions involving annuity (lease rentals, hire purchase).

3.0

MAIN CONTENT

We had earlier prepared the ground for this all-important aspect of capital investment technique (see Unit Six). Illustration Obumneme Group of Companies lease land and erects building on it, financing the construction from term loans. The buildings are rented out by the company which can borrow and invest money at 15 percent per annum. As the companys financial controller, you have been approached to advise it on how best to use a site it leased 25 years ago for 80 years,
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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

from Obumnenye Local Government for an initial premium of N50,000,000 and annual ground rent of N6,000,000. When the lease expires, the building will revert to the Local Government. The following options are available to the company on the use of the site in question.
a.

b.

The site could be out-leased for the remaining years at an annual rent of N40,000,000. A house could be constructed quickly on the site with the following estimated costs and income Building and other capital expenditure Annual management and maintenance fee Annual rental income (till the lease expires) N500,000,000 N150,000,000 N250,000,000

c.

Blocks of flats could be constructed on the site. However, this would entail a long development period and rents would not be collected till after 5 years time. The estimated costs and income for this option are given as follows: Building and other capital expenses = N250,000,000 per year (amounting to N1,250,000.00) Annual management and maintenance costs of N200,000,000.00 and annual rental income of N550,000,000.00 (for the 50years after completion)

Solution This is an interesting question that brings out some cost/management concept clearly. These are:
i.

ii.

iii. iv.

The initial premium of N50,000.00. This cost is already incurred hence it is both sunk and irrelevant. Accordingly, we shall disregard it in our analysis. The annual ground rent of N6,000.00. This cost is yet to be incurred. Hence, it is a relevant cost. However, since it must necessarily be incurred regardless of the option embarked upon, it becomes a common cost. Accordingly, including or excluding it in our analysis shall not affect our decision. We shall exclude it. The net cash inflows in each case form an annuity. Hence, we shall use annuity table (present value) instead of ordinary present value table. Relevant period.

The land was rented 25 years ago for 80 years. The relevant period therefore is from TODAY (the 25th year) to the 80th year. That is, 55 years.

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Therefore, the annuity factor at 15 percent for 55 years, a55(0.15) is calculated thus: The formula is = 1 (I + r)-n r

where n = the number of periods r = the interest rate Substituting 1 (1.15)-55 = 0.15 6.6636

Option C however takes the form of a deferred annuity since the building would take 5 years to complete and cash inflows can only take place as from the 6th year. This we can represent on a number line thus: <----3.3522 -------------->5<-------3.3114------>55 a5 0.15 a55 0.15 difference = = = 3.3522 and 6.6636 3.3114

Therefore, the annuity factor for the deferred annuity is 3.3114. Anchored on foregoing comments, we then proffer our solution thus: Option A: Out-lease the site for remaining years Since the yearly income is N40,000,000 for 55 years, the present value is N40,000,000 x 6.6636 = N266,544,000.00. Option B: Quick construction of a house at the site This is purely theoretical, as house can not be so quickly built. Yes, even at the transfiguration of our Lord Jesus Christ, (Matt. 17: 1 8; Mark 9: 2 8 and Luke 9: 28 36), Peter said, We will make three tents, one for you, one for Moses and one for Elijah (Luke 9: 33). Assuming that it is possible to quickly construct a house, then the cost of the house N500,000,000 took place in year zero. Also, since the annual management and maintenance fee is N150,000,000 and the annual rental income is N250,000,000, the net annual cash inflow is N100,000,000 (i.e. N250,000,000 N150,000,000). Therefore, the NPV is N100,000,000 x 6.6636 N500,000,000 = N166,360,000.

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Option C: Construction of Block of Flat Since the construction would last for 5 years @ N250,000,000 per annum, the present value of the cost of the block of flats is: N250,000,000 x 3.3522 = N838,050,000 Also, given that annual management and maintenance costs N200,000,000 and annual rental income of N550,000,000 shall commence after 5 years, the annual net cash inflows of N350,000,000 (N550,000,000 N200,000,000) form a deferred annuity whose present value is N350,000,000 x 3.3114 = N1,158,990,000 This leaves us with an NPV of N320,940,000 (That is N1,158,990,000 N838,050,000). SUMMARY Option A: Option B: Option C: NPV = N266,544,000 NPV = N166,360,000 NPV = N320,940,000

Therefore, since option C has the highest NPV, that option is the most preferable and hence recommended. N.B: We most logically assumed the 25th year as our Focal Date.

4.0

CONCLUSION

Bearing in mind that multiplication, is the SUMMARY of addition, we now developed a formula for present value when the cash inflow is constant and hence forms an annuity. This method provides a very beautiful short-cut, particularly when we are talking of a large number of periods. This method should also be understood in hire purchase and finance lease computations.

5.0

SUMMARY

In this unit, we essentially looked at the application of annuity factor (present value) in capital investments.

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6.0

TUTOR-MARKED ASSIGNMENT

Ola Nig. Ltd. invested N10m in a project that gives it N1m per annum for 40 years. If the cost of capital is 10 per cent per annum, compute the Net Present Value.

7.0

REFERENCES/FURTHER READINGS

Horngren, C. T. and Foster and Datar, S. (1997). Cost Accounting: A Managerial Emphasis. New Delhi: Prentice Hall. Lucey, T. (1984). Costing: An Instructional Manual. Eastheigh Hanks: DPP. Lucey, T. (1985). Management Accounting. London: DPP. Matz, A. and Usry, M. T. (1976). Cost Accounting: Planning and Control. Cincinnati Ohio: Southern Western Pub. Co. MAYO Association and B. P. Publications Ltd. (1988). Management Accounting. Lagos/London. Okafor, F. O. (1983). Investment Decisions: Evaluation of Projects and Securities. London: Cassell. Nweze, A. U. (2000). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.

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UNIT 3
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

INTERNAL RATE OF RETURN I

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In our previous sections, we looked at various investments appraisal techniques. While the payback period tried to answer the question of how long it would take for the cost of the investment to be recovered or recouped, the Net Present Value (NPV) on the other hand centred on wealth maximization on absolute naira. Yet, there is another method that sets a hurdle rate, internally, before investment can take place. This is called the Internal Rate of Return (IRR). This is the focus of this unit.

2.0

OBJECTIVES

After studying this Unit, the reader should be able to: define Internal Rate of Return (IRR); state IRR formula and how to derive unknown values within a range; outline the investment criteria under the IRR; and state the merits and demerits of IRR.

3.0

MAIN CONTENT

Internal Rate of Return According to Okafor (1983: 224), the IRR criterion follows the basic principles of the NPV method. Unlike the NPV method, the IRR does not use an exogenously determined (exogenously to the project being considered) discount rate. Rather, the principle is to find a rate of discount that will match the discounted value of cash inflows and outflows. The rate of discount, which achieves that equality, is the internal rate of return.

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Put differently, the internal rate of return is the rate at which NPV is zero;the rate at which the present value of the cash inflows is equal to those of the outflows, and the hurdle rate or the break-even rate. According to Lucey (1988: 414), alternative names for the IRR include DCF yield, marginal efficiency of capital, trial and error method, discounted yield and the actuarial rate of return. According to Okafor (1983: 224) and Van Home (1986: 130), the IRR is derived mathematically by solving the following equation for r:

(I = r)
t= 0

CFt

=0

For conventional projects, the equation becomes:

(I = r)
t= 0

CFt

= CF0

Investment Criteria under the IRR Approach Under the IRR, the investment criteria are: i. ii. iii. INVEST IF IRR > Cost of capital. That is invest if the internal rate of return is more than the cost of capital. DO NOT INVEST IF THE IRR < Cost of capital. That is, do not invest if the internal rate of return is less than the cost of capital. Remain INDIFFERENT if IRR = Cost of capital.

Illustration I Refer to illustration two under Unit Six. Compute the Internal Rate of Return. Solution Trial and Error: Let us try 20% since 15% gives NPV of N1,997,000 Year Cash-flow 20% Discount Net Present N000 N000 N000 0 -20,000 1,000 -20,000 1 12,400 0.833 10,329 2 6,000 0.694 4.164 3 7,100 0.579 4,111 4 2,203 0.402 1,061

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5 6 Let us try 22%

2,774 -1,477

0.402 .0335

1,061 -495 285

Year Cash-flow N000 0 -20,000 1 12,400 2 6,000 3 7,100 4 2,203 5 2,774 6 -1,477

20% Discount N000 1,000 0.820 0.672 0.551 0.451 0.370 0.303

Net Present N000 -20,000 10,168 4.032 3,912 994 1,026 -447 -315

Since IRR lies between positive and negative numbers, it should lie between + 286 and 315. Hence, using the formula to calculate the IRR, we have:
IRR = x + a ( y x) a+b

where x Y a b II IRR

= = = = = =

the lower rate of interest used the higher rate of interest used the absolute NPV at X% the absolute NPV at Y% modulus i.e. assume every figure to be positive. Internal Rate of Return

Using the above formula, we have 20% + [285/(285 + 315)] x (22 20) = 20 + (285 x 2)/600 = 20 + 0.95 IRR = 20.95% This is the highest cost of capital, which could be used on the project. As a check, calculate the NPV with 20.95% as your cost of capital.

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Proof: Year 0 1 2 3 4 5 6 Illustration II Haruna Nigeria Ltd.

Femi Nig. Ltd. Cash-flows N (20,000) 12,400 6,000 7,100 2,203 2,774 (1,477) DF @ 20.95% 1.000 0.827 0.684 0.565 0.467 0.386 0.319 PV N (20,000) 10,255 4,104 4,012 1,029 1,071 (471) 0

An investment is being considered for which the net cash flows have been estimated as follows: Year 0 Year 1 Year 2 Year 3 Year 4 N N N N N -9,500 3,000 4,700 4,800 3,200 What is the NPV if the discount rate is 20%? Is the project acceptable? Calculate the IRR. Solution From the table, at r = 20% The discount factors are 0.833, 0.694, 0.579 and 0.482 NPV = -9500 + (0.833 x 3000) + (0.694 x 4700) + (0.597 x 4800) + (0.482 x 3,200) = + N582. Since, the NPV is positive, the project is acceptable. To calculate the IRR, we try higher rate say 25%. The NPV if r = 25% is calculated thus: Year Cashflow N000 0 -9500 1 3,000 2 4,700 3 4,800 4 3,200 That gives NPV = -323.
55

20% Discount N000 1,000 0.8000 0.6400 0.5120 0.4096

Net Present N000 -9,500 2,400 3,008 2,458 1,311

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

The IRR can be calculated as follows: IRR = 20% + 5% (582) = 23.22% 905 a b c d where Is a discount rate, which gives a positive NPV? In this example, 20% gives N-582. b. Is the difference between (a) and the rate, which gives a negative NPV? In this exampled, 25% - 20% = 5%. c. Is the positive NPV at the discount rate chosen in (a)? I this example, it is 582? d. Is the total range of NPV at the rates chosen? In this example, + 582 to 323 = 905? (Lucey 1988: 415)
a.

Illustration III MPC (Megini Prince Chima) has been looking for a suitable investment which will give a target internal rate of return of 17 to 20%. An investment adviser has offered the company a project, the details of which are given below: Pineapple Squash Bottling Project Initial investment involves purchase of machinery for N1,800,000 and installation expenses of N310,000. The plant can produce N100,000 cartons of pineapple squash per annum, during the first two years, rising to125,000 cartons per annum, for the next three years. Cost of production of each carton, excluding depreciation costs is N21 and the selling price will be N27. The plant will be scrapped at the end of the 5 th year and is expected to have negligible scrap value. You are required to calculate the actual internal rate of return of the above project. You may ignore the effect of taxation. Solution Present Value factor = (1 + r)n where r is the rate; and n is the number of year.

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Solution i. Pineapple Squash Bottling Project Year PV Factor 17% 0 (211,000) 1.000 1 60,000 0.855 2 60,000 0.731 3 75,000 0.624 4 75,000 0.534 5 75,000 0.456 Net present value Cashflow N Present Value (211,000) 51,300 43,860 46,800 40,050 34,200 5,210 PV Factor 20% 1.000 0.833 0.694 0.579 0.482 0.402 Present Value (211,000) 49,980 41,640 36,150 36,150 30,150 (9,655)

Cash-flow years 1 and 2 (N27 21) x N10,000 = N60,000 Cash-flow years 3, 4, and 5 (N27 21) x N12,5000 = N75,000 N/B: This is a neat way of determining the cash inflows. Actual Rate of Return = a + c C+d (b a)

Where a = the low discount rate b = the high discount rate c = the low rate of present value d = the high rate of net present value 17 + = = 5210 (20 17) 5210 + 9655 17 + 5210 x 3 14865 17 + 1.05 =

18%

4.0

CONCLUSION

This method, Internal Rate of Return is also very important. Even with the possibility of multiple rates, it is still very important.

5.0

SUMMARY

In this unit, we looked at the various definitions of Internal Rate of Return (IRR). We also discussed the computational techniques and the investment criteria.
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6.0

TUTOR-MARKED ASSIGNMENT

International Oil Ltd., a refinery consortium, which specializes in the Running of Refinery Plant in Africa, is considering setting up a Refinery Plant in Port Harcourt. Information available shows that only two types of refineries can thrive in the Nigerian environment. These include: FCC Based Refinery Hydro-cracking type The following investment information are also available in respect of the two projects: Fluid Catalytic Cracking (FCC) Refinery Cost of installation N2,600 million annual productivity 100 million metric (Average) tons (MT) Plant life (years) 15 Processing fees N/Mt 5.00 (by the refinery Commencement of Year 3 production Annual operating cost N30 million other information i. ii. Hydro Cracking Refinery (HC) N1,500 million 60 million metric tons (MT) 16 5.00 Year 3 N20 million

Cost of capital is assumed to be 15% Cash outflow for the Refineries are set out below: FCC Million HC Million 500 400 1,000 900 600 200 500 ---2,600 million 1,500 million

Year Immediately Year 1 Year 2 Year 3 Ignore taxation

You are required to: a. b. Determine the approximate IRR of the two Refinery Projects (8 marks) Determine the more viable of the two refineries (4 marks)

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

c.

Determine other factors that need to be considered in the construction and management of the refinery plant (4 marks) Total (16 marks) Rate of Discount 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 0.870 .756 .658 .572 .497 .432 .376 .324 .284 .247 .215 .187 .163 .141 .123 .107 .093 .081

(ICAN, May 1997, Q5).

7.0

REFERENCES/FURTHER READINGS

Horngren, C. T. and Foster and Datar, S. (1997). Cost Accounting: A Managerial Emphasis. New Delhi: Prentice Hall. Lucey, T. (1984). Costing: An Instructional Manual. Eastheigh Hanks: DPP. Lucey, T. (1985). Management Accounting. London: DPP. Matz, A. and Usry, M. T. (1976). Cost Accounting: Planning and Control. Cincinnati Ohio: Southern Western Pub. Co. MAYO Association and B. P. Publications Ltd. (1988). Management Accounting. Lagos/London. Okafor, F. O. (1983). Investment Decisions: Evaluation of Projects and Securities. London: Cassell. Nweze, A. U. (2000). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.
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UNIT 4
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

INTERNAL RATE OF RETURN II

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In the very previous unit, we saw that the computation of IRR involved a lot of trial and error except when we are using computers. Therefore, any discussion that could considerably reduce the quantum of trial and error shall be a welcome development. Accordingly, this unit concerns itself with developing short cuts to trial and error approach.

2.0

OBJECTIVES

After studying this unit, you should be able to: outline the steps to be adopted in order to find an alternative to pure trial and error in applying the IRR method; read up the annuity table; apply the annuity table in solving IRR problems; and Explain that at times IRR could yield to multiple rates.

3.0

MAIN CONTENT

Is there any short cut to IRR Computation? Since the calculation of IRR is based on trial and error, any technique to minimize the extent of the trial and error would be highly appreciated. The following steps would be helpful. Step 1: Step 2: Step 3: Sum up the cash inflows Find the average of the cash inflows. Let this be x Give that the cash outflow occurred in year zero and taking year zero as the focal date, we then establish an equation of values, Thus x and i = CFO
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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Where x = the average of cash inflows And i = annuity factor for a given value of n and i CFO = cash outflow in year 0. Step 4: From the annuity table (present value) read up the nearest (most approximate) rate whose annuity factor at the given value of n is very close to the quotient. Step 5: Compute the NPV using the rate as the discount rate. Step 6: If the NPV derived from Step 7: Above is positive, a higher rate of discount is tried and if negative a lower rate is tried. Step 8: Upon arriving at two rates one having a positive NPV and the other a negative NPV resort to interpolation viz:
IRR = x + a ( y x) a+b

where IRR = internal rate of return x = the lower rate a = NPV at x y = the higher rate b = NPV at y II = modulus sign (meaning assume every figure to be positive). Illustration Anulika Nig. Ltd is considering investing in a project whose cash flows were as follows: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 N000 N000 N000 N000 N000 N000 -144 +15 +25 +35 +45 + 60 Given that the cost of capital is at 10% per annum, should Anulika Nig. Ltd. invest in it or not using the IRR approach? Solution To minimize the extent of the trial and error, the above eight steps are then sequentially followed thus: Step 1: Step 2: Sum up the cash inflows N(15,000 + 25,000 + 3,500 + 45,000 + 60,000) = N180,000 Find the average of the cash inflows: the average is N180,000 5 = N36,000

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Step 3:

Given that the outflow occurred in year zero and taking year zero as the focal date, we then establish an equation of values, thus: X an i = CFO

Substituting 36,000 as 5 i = 144,000 5 i = 4.00 a Step 4: From the annuity table (present value) read up the nearest (most approximate) rate whose annuity factor at the given value of n is very close to the quotient, CFO: X

Substituting 144,000: 36,000 = 4.00 From the annuity table (present value) given that n = 5 and a5 i = 4.00 The nearest values of i are 7% (4.100) and 8% (3.993). Step 5: Step 6: The rate obtained in Step 4 above becomes the base rate. In this case 8% Compute the NPV using the base rate at the discount rate. Year Cash-flow N000 0 -144 1 15 2 25 3 35 4 45 5 60 Step 7: DCF @ 8% N000 1,000 0.926 0.857 0.794 0.735 0.681 NPV = Present Value N000 -144.00 13.89 21.43 27.79 33.08 40.86 -6.95

If the NPV derived in Step 6 above is positive, a higher rate of discount is tried and if negative, a lower rate is tried.

Accordingly, lets try lower rate say 6%

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

Year Cash-flow N000 0 -144 1 15 2 25 3 35 4 45 5 60 Step 8:

DCF @ 8% N000 1,000 0.943 0.890 0.839 0.792 0.747 NPV =

Present Value N000 -144.00 14.15 22.25 29.37 35.64 44.82 -2.23

Upon arriving at two rates, one having a positive NPV and the other a negative NPV resort to interpolation viz:
IRR = x + a ( y x) a+b

where IRR = internal rate of return x = the lower rate a = NPV at x y = the higher rate b = NPV at y II = modulus Substituting: IRR = 6 + 2.23 (8 6) 2.23 + 6.95 = 6 + 2.23 x 2 9.18 = 6 + 0.4858 = 6.486 As a check, lets now compute the NPV given that the discount rate = 6.486%. Year Cash-flow N000 0 -144 1 15 2 25 3 35 4 45 5 60 * DCF @ 6.486% N000 1,000 0.9391 0.8819 0.8282 0.7777 0.7304 NPV = Present Value N000 -144.00 14.0865 22.0475 28.987 34.999 43.824 -0.056*

For all practical purposes, the NPV at IRR should be zero. However, occasionally, one could record a negligible negative or positive NPV (-0.056 in this case) due to rounding off error.
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4.0

CONCLUSION

Having seen that the computation of Internal Rate of Return (IRR) is essentially anchored on trial and error method, an attempt was made to develop a short cut that is reliable.

5.0

SUMMARY

In this unit, we saw a short-cut to their trial and error approach to IRR computations.

6.0

TUTOR-MARKED ASSIGNMENT

Recompute illustrations 2 and 3 (Unit Nine) by applying the short cut.

7.0

REFERENCES/FURTHER READINGS

Horngren, C. T. and Foster and Datar, S. (1997). Cost Accounting: A Managerial Emphasis. New Delhi: Prentice Hall. Lucey, T. (1984). Costing: An Instructional Manual. Eastheigh Hanks: DPP. Lucey, T. (1985). Management Accounting. London: DPP. Matz, A. and Usry, M. T. (1976). Cost Accounting: Planning and Control. Cincinnati Ohio: Southern Western Pub. Co. MAYO Association and B. P. Publications Ltd. (1988). Management Accounting. Lagos/London. Okafor, F. O. (1983). Investment Decisions: Evaluation of Projects and Securities. London: Cassell. Nweze, A. U. (2000). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.

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UNIT 5
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

PROFITABILITY INDEXES

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

As scientific as the Net Present Value (NPV) approach to investment appraisal may appear to be, it has one major limitation it fails to consider the quantum of capital that generated the NPV. This is a major weakness since ordinarily a higher capital base will generate a higher NPV. Logically, therefore, a relative NPV or better still, an NPV per unit of capital base would give a better evaluation results. This is where the Profitability Index (PI) comes from.

2.0

OBJECTIVES

After going through this Unit, you should be able to: explain the meaning of profitability index (PI); state the formulae for PI; apply the formulae for PI; outline the merits and demerits of PI; and compare the IRR method with the NPV method.

3.0

MAIN CONTENT

Profitability Index or Excess Present Value Index (EPV I) There are two possible formulae to calculate this index: a. According to Okafor (1983: 229), the profitability index (PI) of a project is the ratio of the sum of the present values of all its cash inflows to the sum of the present values of its cash outflows, i.e. PIi Where = Pvi Ci

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

PIi = profitability index of project i Pvi = sum of present value of cash inflows from project I Ci = sum of present value of cash outflows of project i. b. According to Lucey (1988: 419), the EPVI is merely a variant of the basic NPV method and is the ratio of the NPV of a project to the initial investment. i.e. EPVI = NPV Initial Investment

Thus, the index is a measure of relative and not absolute profitability. Because of this, it suffers from the same general criticisms when used for ranking purposes as the IRR. Decision Rule The decision rule for the profitability index is: a. b. c. Accept only projects that profitability index of more than 1 (one) Reject projects that have profitability index of less than one Remain indifferent if the index is zero.

For the excess present value index, the decision rule is: a. b. c. Accept only project whose EPVI is positive Reject projects whose EPVI is negative Remain indifferent if the EPVI is zero.

Illustration Akachukwu Company is considering five different investment opportunities. The companys cost of capital is 12 percent. Data on these opportunities under consideration are given below: Project Investment PV at N000 12% N000 a. 35,000 39,325 b. 20,000 22,930 c. 25,000 27,453 d. 10,000 10,854 e. 9,000 8,749 i. 66

NPV IRR Profitability N000 N000 Index N000 4,325 16 1.12 2930 15 1.15 2,453 14 1.10 854 18 1.09 (251) 11 0.97

Rank the five projects 1 descending order of Preference, according to NPV (Net Present Value)

BHM 647

CAPITAL INVESTMENT AND FINANCIAL DECISIONS

ii.
iii.

IRR (Internal Rate of Return) Profitability Index.

Which ranking would you prefer? Based on your answer in part 2, which projects would you select if N55,000,000 is the limit to be spent?

Solution i. Akachukwu Company Order of Preference NPV IRR Profitability Index a. 1 2 2 b. 2 3 1 c. 3 4 3 d. 4 1 4 e. 5 5 5 ii. The profitability index approach is generally considered the most dependable method of ranking projects competing for limited funds. It is an index of relative attractiveness, measured in terms of how much you get out for each naira invested. Based on the answer in part 2, projects (a) and should be selected, where combine NPV would be N7,255 (N2,930 + N4,325) with the limited budget of N55,000,000.

iii.

4.0

CONCLUSION

Net Present Value (NPV) has one major weakness when one is faced with two or more projects it fails to take in to consideration the quantum of capital outlay that generated the NPV. This is a weakness because huge capital outlays are likely to have huge NPV relative to small capital outlay. This is where the Profitability Index (PI) comes in. hence, PI is defined as NPV per unit of capital.

5.0

SUMMARY

In this Unit, we looked at the basic definition of Profitability Index. We also looked at the computational techniques and the investment criteria.

6.0

TUTOR-MARKED ASSIGNMENT

United Development Corporation has N2.5million naira available for investment in projects. The following projects are under consideration.

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Project No Initial N 1. 800,000 2. 600,000 3. 700,000 4. 900,000 5. 300,000 6. 950,000

Annual N 230,000 190,000 210,000 240,000 92,000 300,000

Life 6 years 6 years 6 years 6 years 6 years 6 years

The corporation expenses a minimum rate of return of 18%. Projects Nos. 2 and 5 are complimentary to each other. They have to be accepted together or rejected together. Projects Nos. 2 and 5 are mutually exclusive due to their nature. You are required to: a.
b.

Calculate profitability of all the six projects (6 marks) Advise the Corporation on selection of projects to maximize profitability bearing in mind that only N2.5 million capital is available (6 marks)

Note: Present value of an annuity of N1 for the next 6 years at 18% is N3.497 (ICAN, Nov. 1999, Q3).

7.0

REFERENCES/FURTHER READINGS

Horngren, C. T. and Foster and Datar, S. (1997). Cost Accounting: A Managerial Emphasis. New Delhi: Prentice Hall. Lucey, T. (1984). Costing: An Instructional Manual. Eastheigh Hanks: DPP. Lucey, T. (1985). Management Accounting. London: DPP. Matz, A. and Usry, M. T. (1976). Cost Accounting: Planning and Control. Cincinnati Ohio: Southern Western Pub. Co. MAYO Association and B. P. Publications Ltd. (1988). Management Accounting. Lagos/London. Okafor, F. O. (1983). Investment Decisions: Evaluation of Projects and Securities. London: Cassell. Nweze, A. U. (2000). Profit Planning: A Quantitative Approach. Enugu: MCal Communications.
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MODULE 3
Unit 1 Unit 2 Unit 3 Unit 4 The Impact of Inflation on Investment Proposals Using Probability to Assess Impact of Risks on Capital Investments Sensitivity Analysis Capital Rationing

UNIT 1
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

THE IMPACT OF INFLATION ON CAPITAL INVESTMENT DECISIONS PROPOSALS

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

Inflation can be simply defined as an increase in the average price of goods and services. The accepted measure of general inflation in Nigeria is the Retail Price Index (RPI) which is based on the assumed expenditure patterns of an average family. General inflation is a factor in investment appraisal but of more direct concern is what may be termed specific inflation i.e the changes in prices of the various factors which make up the project being investigated, e.g wage rates, sales prices, material costs, energy costs, transportation charges and so on. Every attempt should be made to estimate specific inflation for each element of the project in as detailed a manner as feasible. General, overall estimates based on the RPI are likely to be inaccurate and misleading. Synchronised and Differential Inflation Differential inflation is where costs and revenues change at differing rates of inflation or where the various items of cost and revenue move at different rates. This is normal but the concept of synchronised inflation - where costs and revenues rise at the same rate - although unlikely to be

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encountered in practice, is useful for illustrating various facets of projects appraisals involving inflation. Money cash flows and Real Cash Flows Money cash flows are the actual amounts of money changing hands whereas real cash flows are the purchasing power equivalents of the actual cash flows. In a world of zero inflation there would be no need to distinguish between money and real cash flows as they would be identical. Where inflation does exist then a difference arises between money cash flows and their real value and this difference is the basis of the treatment of inflation in project appraisal

2.0

OBJECTIVES

After studying the unit, you will be able to: define inflation; explain the meaning of money and real cash flows; and explain the effects of inflation on investment appraisal.

Dealing with Inflation The following example will be used to illustrate the way that inflation with in investment appraisal. Example One A labour saving machine costs N24,000 p.a. at current wage rates. The machine is expected to have a 3 year life and nil scrap value. The firms cost of capital is 10%. Calculate the projects NPV: a. b. c. With no inflation With general inflation of 15% which wage rates are expected to follow (i.e synchronised inflation) With general inflation of 15% and wages rising at 20% p.a. (i.e differential inflation)

Solution a. NPV - No inflation = -60,000 + 24,000 A3]10% -60,000 + 24,000 x 2.487 = N312

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Project unacceptable as it has a negative NPV at companys cost of capital b. General inflation 15%, wages increasing at 15% Wage Savings p.a. with 15% Inflation 27,600 31,740 36,501

Wage Savings p.a. with no Inflation 24,000 24,000 24,000

With no inflation the appropriate discounting rate was 10%. With inflation at 15%, the 10% discounting rate is sufficient to bring cash sums arising at different periods into equivalent purchasing power terms. Without inflation N1 now was deemed equivalent to N1.10 (1.15) = N1.265, thus the discount rate to be used is 26%. Project NPV with 15% Synchronised Inflation Year 0 1 2 3

Cash Flow -60,000 +27,600 +31,740 +35,501 Project unacceptable

26% Discount 1,000 0.792 0.624 0.494 PV =

Present -60,000 21,859 19,806 18,031 N304

It will be seen that the answers with no inflation and with 15% synchronised inflation are virtually the same, (the difference being due to roundings in three figure tables). This equivalence is to be expected, as with synchronised inflation the firm, in real terms is no better or no worse off. c. Project with 15% general inflation and wages rising at 20% p.a. (differential inflation. Wage per annum 24,000(1.20) 24,000(1.20)2 24,000(1.20)3 = 27,600 = 31,740 = 36,501

Year 1 2 3

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Project NPV with Differential Inflation Year 0 1 2 3

Cash Flow -60,000 +28,800 +34,560 +41,472 Project acceptable

26% Discount 1.000 0.792 0.624 0.494 PV =

Present -60,000 22,810 21,565 20,487 N4,862

Thus it will be seen that with differential inflation the project is acceptable. In this case this is to be expected because it was a labour saving project so that in real terms, the firm is better off if the rate of wage inflation is greater than the general rate of inflation. Frequently, differential inflation works to the disadvantage of the firm, for example, when costs are rising faster than prices. Each case is different and detailed, individual analysis is required - not generalised assumptions. Money and Real Discount Rates The 26% discount rate used in Example 1 was a money discount factor and was used to discount the money cash flows of the project. The relationship between real and money discount factors is as follows: Real discount factors = 1 + Money discount factor - 1 1 + Inflation Rate

Using the data from example 1 the real discount factor can be calculated. Real discount factor 1 + 0.265 - 1 = 0.1 i.e 10% 1 + 0.15 In this case, of course, the real discount factor was already known and the above calculation was for illustrative purposes only. The real discount factor can be used for project appraisal providing that the money cash flows are first converted into real cash flows by discounting at the general inflation rate as follows. Example Two Re-work part (c) of Example one using real cash flows and the real discount factor. =

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Year

Money Cash Flow -60,000 +28,800 +34,560 +41,472

0 1 2 3

Real Cash Flow Evaluation General 26% Inflation Discount 15% discount 1.000 -60,000 1.000 0.870 25,056 0.909 0.756 26,127 0.826 0.658 27,289 0.751 PV =

Present

-60,000 22,776 21,581 20,494 4,851

From which it will be seen that (table rounding differences apart) the two methods give identical results. Thus it will be seen that there are two approaches to investment appraisal where inflation is present. Single Discounting: Two stage Discounting: Money cash flows discounted by money discount factor. Money cash flows discounted by general inflation rate and then the real cash flows produced discounting by real discount factor.

The two approaches produce the same answer because the money discount factor includes the inflation allowance. Because of this and because money cash flows are the most natural medium in which estimates will be made, it is recommended that money cash flows should be discounted at an appropriate money discount factor. Take great care never to discount money cash flows by a real discount factor or real cash flows by a money discount factor. If real cash flows are directly provided in a question take care to discount once only using a real discount factor. Illustration A firm is considering a project with a cash outlay of N1,000,000 now and 5 yearly cash flows of N500,000. a. b. What is the NPV at 10% ? What is the NPV assuming a general inflation rate of 8% and an increase in cash flows to N510,000 per annum?

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Solution a. Given that the cash inflow is constant, we now apply the annuity factor (present value). At 10% per annum for 5 years the annuity factor present value is arrived by evaluating 1 - (1.10)-5 0.10 = 3.79

NPV = = =

(1,000,000) + 3.79 x 500,000 (1,000,000) + 1,895,393 + N895,393

b.

Discount rate with 8% Inflation = 1.10(1.08) = 1.188 = 19% With cash outlay at N1m and cash inflow at N510,000 for 5 years discount rate at 19% Annuity factor (Present value) 1 - (1.19)-5 0.19 = 3.058

The NPV

= = =

(1,000,000) x 3.058 x 510,000 (1,000,000) x 1,559,393 559,393

4.0

CONCLUSION

Because price levels always change continuously there is need to evaluate investments under inflationary trends.

5.0

SUMMARY

In this unit, are looked at the basic definition of inflation and other associated terms namely. i. ii. iii. iv. Retail Price Index (RPI) Specific inflation Synchronised and Differential Inflation Money Cash flows and Real cash flows.

We also had some illustrations on how to evaluate investments under inflationary trend.

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6.0

TUTOR-MARKED ASSIGNMENT

Chief Ugwoke is considering a project with a cash outlay of N5,000,000.00 now and 5 yearly cash inflows of N2,500,000.00. What is the APV assuming a general inflation rate of 8% and an increase in cash flow to N2,550,000.00

7.0

REFERENCES/FURTHER READINGS

Lucey, T. (2002). Quantitative Techniques, London: MPG Books Ltd. Nweze, A.U. (2004). Quantitative Approach to Accounting. Enugu: Amazing Grace Publishers. Management

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UNIT 2

THE USE OF PROBABILITIES TO ASSESS THE IMPACT OF RISK ON CAPITAL INVESTMENTS

CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0 Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

In this unit, we shall look at the Probability Estimate of Cash flows. Environmental Conditions Investment decisions are carried out under one of three possible environmental conditions: i. ii. iii. i. Conditions of certainty Conditions of risks and Condition of uncertainty Condition of Certainty

Condition of certainty can be said to prevail where a potential investor has full knowledge of the ultimate outcome of an investment opportunity. This implies a. b. Perfect knowledge, from the outset of the exact nature and timing of the stream of cash flow to be expected from the investment opportunity. The expectation (belief) that the anticipated (ultimate) outcome would not be subject to change. Situation of single value expectations are however rate in the investment world (Okafor, 1983). Condition of Risks

ii.

Where an investor knows exactly the range of possible outcome to expect from an investment opportunity as well as the likelihood

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(probability) of each outcome, the investor is exposed to a condition of risk. Since conditions of certainty are rare in the investment world, this part of the text would focus mainly on conditions of risk and uncertainty. After all, freedom from uncertainty is a luxury rarely enjoyed by the contemporary management. Methods of Incorporating Uncertainty and Risk when Appraising projects The major business risk faced by business organizations in the appraisal of long-term capital project is the possibility that actual outcome of such investments will deviate from forecasts used in the appraisal overtime. The methods of analyzing risk and/ or uncertainty for capital expenditure projects include the following: i. ii. iii. iv. v. vi. vii. viii ix. x. xi. risk premium method Adjusted payback period Simulation modelling Probability estimates of cash flows Sensitivity analysis Certainty equivalent Standard deviation of the expected Net present value. Worst possible and best possible outcomes Portfolio theory Decision tree Finite horizon method

2.0

OBJECTIVES

After studying this unit, you should be able to: define probability; define and apply the following terms, namely, expected value, standard deviation and co-efficient of variation as applied in investment appraisal; and evaluate investments by applying probability estimates.

3.0

MAIN CONTENT

This section is best discussed with an illustration from one

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Illustration The General Manager of a company is confronted with the option of embarking on one project out of the two projects are as follows: Project A Project N'000 Probability 20 0.40 22 0.30 30 0.30 Project B Profit N'000 Probability 10 0.20 27 0.70 35 0.10

Prepare a report advising the General Manager on which of the two projects to embark upon. Consider the use of coefficient of variation in choosing among the two projects. Source: Management Accounting, ACA, Nov. 1988 Q7 Comment The above problem is based on the probability estimates of cash flows. Accordingly, we shall use the problem to illustrate probability estimates in greater details. Probability Estimate of Cash Flows Probability has been defined as the qualification of uncertainty. Probabilities have values ranging from zero (0) to one (1). A probability of zero means that the event CAN NEVER take place. For example, flying to the moon unaided. This we can express as p (flying to the moon unaided) = 0. A probability of one means hat the event MUST SURELY take place. For example, every mortal MUST die. This we can express as P (dying) = 1 Going down the memory lane, lets now use our knowledge of statistics to establish the formulae for probability approach to uncertainty. Frequency Distribution Since the value of probabilities can only lie between 0 and 1, it follows that the probabilities of any given event MUST necessarily sum up to 1 (one).

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That means, given a set of cash flows with their associated probabilities, the sum of probabilities and hence the sum of the frequencies must necessarily be 1. Hence, f = p = 1 It will be recalled that for a grouped data, n = f. Hence, for our probability estimates of cash flows. n = f = p = 1. Average (Expected value) For a grouped data, the average (x), is given as X = X = px = px (Since p = 1). f p In probability estimates of cash flows, the average is known as the expected value. Hence our expected value, EV is given as _ EV = px = X Standard Deviation For grouped data, the standard deviation, d, is given as d = f (X - X) f For probability estimates of cash flows, our formular for standard deviation becomes: d = f (X - X) f = = f (X - EV) p f (X - EV) (Since p = 1).

Interpretation of the Value of Standard Deviation Since the residuals (the extent to which the various observed values of Y deviate from the regression line) are assumed to have a constant variance, the higher this constant variance, the more widely the various observed values of Y are SCATTERED, AND hence the higher the standard deviation.

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It therefore follows that the higher the standard deviation the higher the risk. This can further be illustrated using our experience in soccer. When a team concedes an indirect kick (very close to the 18) many of the players would come together and form a wall on defense. This way, they are NOT widely scattered and the standard deviation is low and as a corollary, the risk of conceding a goal is equal reduced. POSERS: What do you think is the relationship between distant marriage and the chances of extra-marital affairs? Which one is easier - breaking a stick of broom or breaking a bunch of brooms? Let's now solve the problem at hand-bearing the above discussion in our mind. Solution a. Expected Value (EV) of Profits EV = px where p = probability Project N'000 20,000 22,000 30,000 Comment Based on the expected value of profits, it would appear that Project B should be favoured to Profit A because Project B has a higher expected value of profits. This measure, however does not take account of the risk in the projects, as measured by the dispersion of the outcome, so that a better measure such as standard deviation of the outcome, which takes the risks in project into accounts is considered in selecting the better of the projects. Project A Probability Expected Profit Value N N'000 0.40 8,000 10,000 0.30 6,600 27,000 0.30 9,000 35,000 23,600 Project B Probability Expected Value 0.20 2,000 0.70 18,900 0.10 3,500 24,400

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b.

Standard Deviation of Profits

Standard deviation d is calculated by using the formula: d d d x p = = = = = p (X - X)2 p (X - EV)2 Standard figures profit figures probability PX N 8,000 6,600 9,000 23,600 = = Y-Y - 4400 - 2600 10600 Variance = = X-X N - 36000 - 1600 + 6400 Variance = (X - X)2 N 12,960,000 2,560,000 40,960,000 P(X - X)2 N 5,184,000 768,000 12,288,000 18,240,000

Project A X Prob N N 20,000 0.40 22,000 0.30 30,000 0.30 0

d = Variance Y N 10000 27000 35000 Prob. N 0.20 0.70 0.10 0 PY 2000 18900 35000 24400

18240000 N427.838301 (Y - Y)2 270,360,000 6,760,000 112,360,000 P (Y - Y)2 41,472,000 47,320,000 11,236,000 57,440,000

d = Variance Comment

57440000 N7578.918

The above shows that Project A has a lower degree of riskiness in absolute terms than Project B. The degree of riskiness measured by the standard deviation shows the degree of dispersion of the profits of the projects around the means profit or the expected value of profits of the projects. Since project A shows a lower degree of dispersion in absolute terms, the Project is considered less risky than Project B, which shows a higher standard deviation of A Projects. This measure, however, is not a relative measure as it does not take the size of the projects or the expected value of the projects into consideration. A more reliable relative measure is the coefficient of variation, which relates the standard deviation of the size of the project and its expected value.
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Co-efficient of Variation The formular for calculating the co-efficient of variation = d x 100 X 1 where d = standard deviation X = mean or expected value of profits. Co-efficient of Variation PROJECT A N4,270.83130 N23,600 = 0.18096 Comment From the above, it may be concluded that Project B is considered risker than Project A, and should therefore be foregone in preference to Project A. (MAYO). Illustration The USMAN Nig. Ltd is a considering a major investment in a new productive process. The total cost of the investment has been estimated N2,000,000 but if this were increased to N3,000,000 productive capacity could be substantially increased. Because of the nature of the process once the basic plant has been established, to increase capacity at some future date is exceptionally costly. One of the problems facing management is that the demand for process output is very uncertain. However, the market research and finance departments have been able to produce the following first estimates. Investment A (N3m) Demand Annual Net Probability Cash Inflow (NM) 0.3 yrs 1 - 4 1.0 5 - 10 0.7 0.5 yrs 1 - 4 0.8 5 - 10 0.4 0.2 yrs 1 - 10 0.1 Cost of Capital 15% Investment B (N2m) Demand Net Cash Probability Inflow (NM) 0.4 yrs 1 - 4 5 - 10 0.4 yrs 1 - 4 5 - 10 0.2 yrs 1 - 4 Cost of Capital 0.6 0.2 0.6 0.2 0.2 15% PROJECT B N7,578.91813 N24,400 = 0.31061

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You are required to prepare a statement, which clearly indicates the financial implications of each of the projects. Select the better investment. Solution to Illustration USMAN Nig. Ltd. Investment A Cash Annuity Flow Factor Nm 1-4 1.0 2.8550 5 - 10 0.7 2.164 Year Probability 2 Investment A Year Cash Annuity Flow Factor Nm 1-4 0.80 2.855 5 - 10 0.40 2.164 Probability 3 Investment Investment A: Years 1 - 10. N0.10m x 5.019 = N50.19m B: Years 1 1 Investment B Present Year Cash Annuity Value Flow Factor Nm Nm 2.855 1 - 4 0.60 2.855 0.860 5 - 10 0.50 2.164 3.150 Present Value Nm 1.713 0.433 2.146 Present Year Value Nm 2.855 1-4 1.515 5 - 10 4.370 Investment B Cash Annuity Flow Factor Nm 0.60 2.855 0.50 2.164 Present Value Nm 1.713 1.082 2.795

Expected NPV (Possible Outcome x Prob): Investment A 1. N4.370 x 0.30m = N1.311 2. N3.1496 x 0.50m= N1.5748 3. N0.5019 x 0.20m= N0.10038 Total present value = N3.0000m Less initial outlay = (N0.01382m) Investment B N2.795 x 0.040m = N1.118m N2.1458 x 0.40m = N0.85832 N1.0038 x 0.20m = N0.20076 N21.1708m (N0.177708m)

Decision: Accept Investment B with a positive NPV.

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4.0

CONCLUSION

In this unit, we have learnt the environmental conditions under which investment decisions. We also learnt the methods of analyzing risk and / or uncertainty for capital expenditure projects.

5.0

SUMMARY

In this unit, we defined probability; applied some terms such as expected value, standard deviation and co-efficient of variation as applied in investment appraisal; and evaluated investments by applying probability estimates.

6.0
1.

TUTOR-MARKED ASSIGNMENT
Two components are assembled to make a finished product. There is a 0.2 probability that the first component will cost N50 and 0.8 probability it will cost N60, while there is a 0.3 probability that the second component will cost N90 and 0.7 probability ti will cost N120. The assembly cost is N21. Compute the expected cost of the finished product. (6 marks) Company ABC has predicted its costs and sales in respect of a product selling for N10 will be as follows; Marginal cost per unit Fixed Cost N15,000 N20,000 Sales Unit N4,000 N6,000 Probability 0.6 0.4 Probability 0.8 0.2 Probability 0.5 0.5 (12 marks) (Total 18 marks) ICAN, Nov. 1998, Mgt Acc Q6.

a. b. i. ii. iii

Compute the profit expectation

2.

Baro Pharmaceutical Nig. Ltd. can purchase the patents and the manufacturing rights of any one of the three drugs. The costs of the rights are: Drug X = N260,000 Drug Y = N380,000

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Drug Z = N400,000 At the company's board meeting, the management accountant declared that it was general knowledge that the venture is a very short-term project. The fixed manufacturing and advertising cost of each venture will be: X N'000 240 100 Y N'000 40 60 Z N'000 40 40

Fixed manufacturing costs Advertising Costs

Sales and production will, once, known, dovetail and therefore, there will be no stock builds up. The sales price and variable costs per unit are: X N'000 680 280 Y N'000 630 220 Z N'000 260 140

Sales price per unit Variable cost per unit

However, the sales volume is the key factor. The company does not know what the sales level will be but it knows the various probabilities of what the sale level could be. Drug X, could be a complete flop, it could sell well, or it might sell very well. Drug Y is also quite variable whereas with Drug Z, the range of outcome is very small. The various possible sales volumes and their associated probabilities are as follows: Drugs X Sales Volume in Unit 0 2,500 4,000 Probability 0.1 0.4 0.5 Y Sales Volume in Unit 3,000 4,000 6,000 8,000 Probability 0.1 0.3 0.3 0.3 2 Sales Volume in Unit 7,000 8,000 9,000 Probability 0.8 0.1 0.1

The company now wishes to decide on which of the drugs it should manufacture and sell.

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Required Calculate the expected money value of each drug and on the basis of this, advise the board of which drug to produce. (16 marks) (ICAN, Nov. 2003, Mgt. Acc. Q2)

7.0

REFERENCES/FURTHER READINGS

Lucey, T. (2002). Quantitative Techniques, London: MPG Books Ltd. Nweze, A.U. (2004). Quantitative Approach to Accounting. Enugu: Amazing Grace Publishers. Management

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UNIT 3
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

SENSITIVITY ANALYSIS

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

Here managers try to identify the critical variables in their capital budgeting decisions. The variables are normally - the cash flows, cost of capital and the life of the product (time period). The objective is to find out how sensitive the project is to change in any or all these variables. Two ways can be identified for the treatment of sensitivity analysis. a. b. To alter the value of the variables arbitrarily and find out if the decision on the project will change. Alternatively, the analyst can calculate the percentage change in a variable that will result in a change of his decision on the project.

Shortcomings in Sensitivity Analysis (Multi-collinearity) The weakness of sensitivity analysis, include: In the sensitivity analysis, each element is varied individually. It is however, likely that interrelationships exist between many of the elements, and two or more elements will in reality vary simultaneously. "This is the problem of simultaneous relationships, or multi-collinearity, among the independent variables. It means simply that the independent variables are not really independent of one another, but rather have values that are jointly or simultaneously determined".

2.0

OBJECTIVES

After studying this unit, you should be able to: define sensitivity analysis; identify the key factors in any investment appraisal;

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re-evaluate investments by varying the key factors in turn, and assessing the effect on the investment; and identify the advantages and disadvantages of sensitivity analysis. Sensitivity Analysis This is a practical way of showing the effects of uncertainty by varying the values of the key factors (e.g. sales volume, price, rates of inflation, cost per unit) and showing the resulting effect on the project. The objective is to establish which of the factors affect the project most. When this is done it is management's task to decide whether the project is worthwhile, given the sensitivity of one or more of the key factors. It will be seen that this method does not ask for subjective probability estimates or likely outcomes, but attempts to provide the data upon which judgements may be made. The method is illustrated by the following example. Example 5 Assume that a project (using single valued estimates) has a positive NPV of 25,000 at a 10% discounting rate. This value would be calculated by the normal methods using particular values for sales volume, sales price, cost per unit, inflation rate, length of life, etc. Once the basic value (i.e. the NPV of 25,000) has been obtained the sensitivity analysis is carried out by flexing, both upwards and downwards, each of the factors in turn. An abstract of the results of a sensitivity analysis for the project above might be as follows:

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Table 3 Sensitivity Analysis Abstract Original NPV = 25,000 A B C D Element Alteration Revised Increase to be from NPV + varied Basic Decrease Sales +15% 46,000 +21,000 Volume +10% 33,000 +8,000 (Basic -10% 17,000 -8,000 value 8,000 -15% 14,000 -11,000 units in Period 1 8,500 in -20% 9,000 -16,000 Period 2, etc) Sales +20% 42,000 +17,000 Price +10% 31,000 +6,000 (Basic -10% 17,000 -8,000 value 6 units -15% 11,000 -14,000 in Period 1 6.25 in -20% 2,000 -23,000 Period 2, etc) Cost/Unit +25% -12,000 -37,000 (Basic +10% 6,000 -19,000 Value 2.50 in -5% 34,000 +9,000 Period 1 2.60 in -10% 47,000 +22,000 Period 2, etc. E F Percentage Sensitivity Change Factor, i.e E/B 84 32 32 44 64 68 24 32 56 92 148 76 36 88 5.6 3.2 3.2 2.9 3.2 3.4 2.4 3.2 3.73 4.6 5.9 7.6 7.2 8.8

From such an analysis the more sensitive elements can be identified. Once identified further analysis and study can take place on these factors to try to establish the likelihood of variability and the range of values that might be expected so as to be able to make a more reasoned decision whether or not to proceed with the project.

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Advantages of Sensitivity Analysis a. b. c. Shows the effect on project outcome of varying the value of the elements which make up the project (e.g Sales, costs, etc). Simple in principle. Enables the identification of the most sensitive variables.

Disadvantages of Sensitivity Analysis a. b. c. Gives no indication of the likelihood of a variation occurring. Considerable amount of computation involved. Only considers the effect of a single change at a time which may be unrealistic.

Illustration Two Alhaji Shew Buraiman is contemplating investing in a project and the following tentative estimates have been made. Cash outlay Sales price/unit Unit cost Discount rate Life span of project Year 1 2 3 Required a. i. ii. iii. iv. v. Calculate the maximum tolerable unfavourable change in each of the areas (as a percentage of the original estimated value) in Sales unit Unit cost Sales volume Initial outlay Project file Comment on the results. Could sales volume be treated separately in this analysis? b. Now assume that the government anti-inflationary policy allows sales prices to rise by 10% per annum compound, and unit costs are expected to rise at annual rate of 20% compounded (both N100,000 (in year 0) N30 N20 10% p.a. 3 yrs. Sales Volume 4,000 units 6,000 units 3,000 units

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starting in year 0). What initial cash subsidy would be necessary to retain the viability of the project? Discounting Factor at 10% Year 0 1 2 3 PV 1.000 0.909 0.826 0.751

Source: Financial Management, ACA, Nov. 1988m Q2 Solution to Illustration a. Computation of the Net Present Value (NPV) Cash Flow N (100,000) 40,000 60,000 30,000 Discount Factor (DF) at 10 1,000 0.909 0.826 0.751 Present (PV) (100,000) 36,360 49,560 22,530 N8,450

Year Value

0 1 2 3

Cash flows as computed viz: Sales Volume x (Sales Price - Unit Cost) Year 1 2 3 D.F 0.909 0.826 0.751 Sales 120,000 180,000 90,000 PV of Sales 109,080 148,680 67,590 325,350 Costs (N) 80,000 120,000 60,000 PV of Costs 72,720 99,120 45,060 216,900

i.

Sensitivity to price = NPV x PV of sales

100 1

Substituting 8,450 325,350 x 100 1

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Comment Sales price should not be reduced by more than 2.60% otherwise the project becomes unacceptable. ii. Sensitivity to Unit Cost = NPV x PV of sales 8,450 216,900 Comment The unit cost should not be increased by more than 3.8% otherwise the project becomes unacceptable. iii. Sensitivity to Sales Volume = NPV x PV of sales 100 1 x 100 1 100 1

Substituting

Where PV of contribution = 325,350 - 216,900 = 108,450 Substituting 8,450 108,450 7.8% x 100 1

= Comment

A fall in contribution beyond 7.8% level would make the project unacceptable. iv. Sensitivity of Initial Outlay = NPV x PV of initial Outlay = Comment The initial outlay should not increase beyond 8.45%. 8,450 x 100,000 100 1

100 1

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v.

Sensitivity of Project life.

Suppose the analyst assumes the project lasted for 2 years. Year 0 1 2 Cash Flow (N) (100,000) 40,000 60,000 DF @ 10% 1.000 0.909 0.826 PV (N) (100,000) 36,360 49,560 (14,080)

By Interpretation 2 + 14,080 (3 - 2) = 2.63 years 14,080 + 8,450 Sensitivity to Product Life 3 - 2.63 = 12.30% 3 Comment The maximum tolerable reduction in project life to retain viability is 12.3% vi. Alternative

Interpretation method for project life(Objections). A reduction of one year in life of the Project will lead to a rejection of the project since the NPV arrived at is negative N14,808. Unless the analyst assumes that the Net Cash inflows accrue evenly over the period, it is not advisable to interpolate. The analyst must assume that inflows after the initial outflow occur at the end of the years to which they relate. In this case, a reduction of the project life from three years to two years will be an unfavourable change and will alter our decision. The percentage change will be 3 - 2 x 100 = 33.33% 3 1 The maximum tolerable change = 33.33%

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General Comment The project is sensitive to all the factors tested above. The selling price and the unit cost should be watched, as the project is particularly sensitive to these. The other factors are relatively sensitive. In general, a slight change in the factors should have grave consequences on the viability of the project. The sales volume could be treated separately in the analysis. The sensitivity of sales volume could be calculated for each of the respective years. Year 1 NPV PV contributed (year 1) = 8,450 x 100 36,360 1 23.24% NPV x PV contributed (year 2) 8,450 x 100 49,560 1 17.05% NPV x PV contributed (year 3) = 8,450 x 100 22,530 1 37.50% 100 1 x 100 1

= Year 2

100 1

= Year 3

= b. Year 1 2 3

Incorporating Inflation Effects Sales (N) 4000 (1.1) x 30 = 132,000 6000 (1.1)2 x 30 = 217,800 3000 (1.1)3 x 30 = 119,790 Cost (N) 4000 (1.2) x 20 = 96,000 6000 (1.2)2 x 20 = 172,800 3000 (1.2)3 x 20 = 103,680

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Year 0 1 2 3

DF 10% 1.000 0.909 0.826 0.751

Cash Flow (100,000) 36,000 45,000 16,110

PV (N) (100,000) 32,724 37,170 12,099 (18,007)

4.0

CONCLUSION

In this unit, we tried to identify the critical variables in capital budgeting decisions. The variables are normally - the cash flows, cost of capital and the life of the product (time period). The objective is to find out how sensitive the project is to change in any or all these variables. Two ways were identified for the treatment of sensitivity analysis: (a) altering the value of the variables arbitrarily and finding out if the decision on the project will change; (b) alternatively, the calculating the percentage change in a variable that will result in a change of his decision on the project.

5.0

SUMMARY

In this unit, we defined sensitivity analysis; and identified the key factors in any investment appraisal. We also re-evaluated investments by varying the key factors in turn, and assessed the effect ton the investment, and identified the advantages and disadvantages of sensitivity analysis.

6.0

TUTOR-MARKED ASSIGNMENT

The initial subsidy needed to retain the viability of the project is N18,007. (MAYO ASSOCIATES) A company is considering the production of a new product. Dose. Relevant data about the product; as revealed by research carried out by the company's marketing manager is as follows: Contribution per unit Annual fixed costs Break even sales volume ..................... N 4 ..................... N 10,000 ..................... 2,500 units

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Probable Sales Schedule Units % 5,000 10 4,000 20 3,000 40 2,000 20 1,000 10 The management before accepting to produce this product is very much concerned about the possibility of risk of losses associated with the production taking into consideration the probable sale forecast as above. You are required i. ii. Q7 To advise the management whether to go ahead with the production of this product. Assume that the company will not mind 5% chance of the product turning out to make losses. To calculate the coefficient of variation of the probable sales to buttress our decision in (1) above. (10 marks). ICAN, Nov. 1994 Mgt Acc.

7.0

REFERENCES/FURTHER READINGS

Nweze, A.U. (2006). "Investment Opportunities in the Nigerian Capital Market". Okafor, F.O. (1983). Investment Decision: Evaluation of Projects and Securities. London: Cassell Ltd.

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UNIT 4
CONTENTS 1.0 2.0 3.0 4.0 5.0 6.0 7.0

CAPITAL RATIONING

Introduction Objectives Main Content Conclusion Summary Tutor-Marked Assignment References/Further Readings

1.0

INTRODUCTION

This is where the firm is unable to initiate all projects which are apparently profitable because insufficient funds are available. Under the assumptions given for the basic DCF model, a perfect capital market was presumed, that is as much finance as required could be raised at the market rate of interest. In imperfect capital market conditions, capital may be raised, but at increasing rates of interest; but there will be some point where there is an absolute limit to the amount that could be raised. This is known as external capital rationing. Alternatively, the effects of capital rationing may develop for internal purposes, for example, it may be decided that investment should be limited to the amount that can be financed solely from retained earnings or kept within a given capital expenditure budget. The external and internal factors which impose quantitative limits have led to two opposing view-points developing, known as the `hand' and `soft' views of capital rationing. The `hard' view is that there is an absolute limit on the amount of money a firm may borrow or raise externally whereas the `soft' view is that rationing by a quantitative limit such as an arbitrary capital expenditure budget should only be seen as a temporary, administratively expedient because such a limit is a not determined by the market (the assumption being that any amount of funds is available, at a price) and such a limit would not be imposed by a profit maximising firm. Whatever the causes of the limited capital supply available for investment purpose, it means that, not only must each project cover the cost of capital, but that the project or batch of projects selected must maximise the return from the limited funds available, i.e some form of ranking becomes necessary. Before considering solution methods some definitions need to be considered.

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a. b. c.

d.

Single period capital rationing - the term used where there is a limit on the funds available now but where it is anticipated that funds will be freely available in subsequent periods. Multi-Period Capital rationing - where the limitation of funds extends over a number of periods or possibly indefinitely. Divisible projects - projects where the whole project or any fraction may be under-taken. If a fractional part is undertaken, then it is assumed that the initial outlay and subsequent cash inflows and outflows are reduced pro rata. Although for most industrial projects this seems somewhat hypothetical, the assumption of divisibility is frequently made in solving capital rationing problems, particularly in examination questions. Indivisible projects - where the whole project must be undertaken or not at all.

2.0

OBJECTIVES

After studying this unit, you should be able to: define capital rationing; and evaluate projects and investments under inflationary trends. Project Selection under Capital Rationing Where capital rationing exists the normal DCF decision rule, i.e. accept all projects which have a positive NPV at the cost of capital is insufficient to make the appropriate project selection. The objective where capital rationing exists is to maximise the return from the batch of projects selected having regard to the capital limitation. This means that the investment decision changes from simply being `accept or reject' to what is in effect a ranking problem. Ways of achieving this objective are shown below for the following rationing possibilities (single or multi period capital with divisible projects), where some are mutually exclusive. Single Period Capital Rationing - Divisible Projects This is the simplest situation and the solution method is to rank the projects in order of their EVPI (i.e. NPV per of outlay as described earlier) and to choose projects, or fraction of a project, until the supply of capital for investment is exhausted.

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Example One Onwe Ltd has a cost of capital of 15% and has a limit of N100,000 available for investment in the current period. It is expected that capital will be freely available in the future. The investment required, the NPV at 15% and the EVPI for each of the 6 projects currently being considered are shown below. What projects should be initiated? Project Outlay N A 20,000 B 40,000 C 35,000 D 50,000 E 15,000 F 45,000 Solution Ranking by EVPI is C, B, D, A and E. Project F cannot be considered because it fails the initial hurdle of achieving a positive NPV.

NPV @ 15% N 8,000 28,000 37,500 31,500 3,500 -5,000

EPVI ( NPV ) Outlay 0.4 0.7 1.07 0.63 0.23 -0.11

Optimal Investment Plan Project C B D Fraction Undertaken 1.00 1.00 0.50 Investment N 35,000 40,000 25,000 N100,000 NPV 37,500 28,000 15,750 N81,250

It will be seen that this solution method uses the well known management accounting principle of maximising return per unit of the limiting factor - in this case NPV per N of capital available for investment. It will be recalled that this principle is appropriate where there is a single constraint only - in this case investment finance for one period. Single Period Capital rationing with Mutually Exclusive Divisible Projects Where two or more of the projects are mutually exclusive the solution method of ranking of EVPI can still be used but the projects have to be divided into groups each containing one of the mutually exclusive projects. This is shown below.
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Example Two Assume the same data as Example one except that projects B and D are mutually exclusive. What projects should be initiate? Solution It is necessary to divide the projects into two groups, rank by EVPI, select projects up to the capital limit and to compare the total NPV obtainable from each group. Project A B D E Group I Investment N 20,000 40,000 35,000 15,000 EVPI Project 0.4 0.7 1.07 0.23 A C D E Group II Investment N 20,000 35,000 50,000 15,000 EVPI 0.4 1.07 0.63 0.23

Ranking the groups and choosing the projects up to the investment limit produces the following: Group I Investment N'000 Fraction Project C B A E
100

Group II Investment N Fraction Project NPV NPV

1.00 1.00 1.00 1/3

35.00 40.00 20.00 5.00 N100.00

37.50 28.00 8.00 1.17 N74.67

C D A

1.00 1.00 3/4

35.00 50.00 15.00 N100.00

37.50 31.50 6.00 N75.00

It will be seen that, by a narrow margin, Group II with the proportions indicated has the greater NPV and would be chosen. Single Period Capital Rationing - Indivisible Projects Where projects have to be accepted in their entirety or not at all, then EVPI ranking procedure does not necessarily produce the optimal solution. Providing that relatively few projects are involved a trial and error approach can be used to find a solution. Where projects are indivisible then it is likely that some of the capital available for

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investment may be unused and in such circumstances a full analysis should include the returns from external investment of under-utilised funds. Example 9 Lloyds Ltd has a cost of capital of 10% and has a limit of 100,000 available for investment in the current period. Capital is expected to be freely available in future periods. The following indivisible projects are being considered. Investment NPV @ 10% Initial Project N N A 35,000 17,500 B 40,000 22,500 C 65,000 38,000 D 48,000 31,500 E 23,000 9,000 It is required to calculate the optimal investment plan: a. b. where there are no alternative investments available for any surplus funds where surplus funds can be invested to produce 12% perpetuity.

Solution a. Various combinations are tried to see which combination produces the maximum NPV.

Table 5 shows a few examples. Table 5 Project Combinations N AC ABE AD BD BE CE DE Total Outlay for Surplus Combinations Funds N N 100,000 98,000 2,000 83,000 17,000 88,000 12,000 63,000 37,000 88,000 12,000 71,000 29,000 Total NPV of Combinations N 55,500 49,000 49,000 54,000 31,500 47,000 40,500

It will be seen from Table 5 that the best investment plan is A and C which utilises all the funds available and produces a combined NPV of N55,500.
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When surplus funds can be invested externally each of the combinations in Table 5 which have surplus funds must be examined to see if the project NPV plus the return on external investment is greater than N55,500. Each N1,000 invested at 12% in perpetuity yields N200 NPV, i.e.
[

1,000 x .12] - 1,000 = N200 1

The project combinations and total NPV (Projects + External Investment) are shown in Table 6.
Table 6

Funds externally invested (N)

Project NPV (N)

= Total NPV (N)

External investment NPV (N)

Total Project Outlay (N)

ABE AD BD BE CE DE *

Multi-Period Capital Rationing This has been previously defined to be where investment funds are expected to be limited over several periods. In such circumstances it becomes difficult to choose the batch of projects (some starting immediately, some one period hence, two periods hence, etc.) which yield the maximum return and yet which remain with the capital limits.
102

Combination

98,000 83,000 88,000 63,000 88,000 71,000

2,000 17,000 12,000 37,000 12,000 29,000

400 3,400 2,400 7,400 2,400 5,800

+ + + + + +

49,000 49,000 54,000 31,500 47,000 40,500

49,400 52,400 56,400* 38,900 49,400 46,300

When external investment is considered then projects BD should be initiated and N12,000 invested externally to produce a total NPV of N54,500. It will be seen that this is slightly better than the AC combination shown in Table 5. Note: Although ranking by EVPI in conditions of single-period capital rationing with indivisible projects does not necessarily produce the correct ranking it usually provides an excellent guide to the best group of projects.

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CAPITAL INVESTMENT AND FINANCIAL DECISIONS

The problem becomes one of optimising a factor (e.g. NPV) where resources are limited, i.e. the funds available over the periods being considered. This will be recognised as a situation where Linear Programming (LP) can be used and LP has been used successfully in solving Multi-Period Capital Rationing problems. SELF-ASSESSMENT EXERCISE 1 Examine the balance sheet of two manufacturing companies, two commercial firms and two financial institutions. Make a list of all capital items in the balance sheet. In each case, determine the ratio of financial to real assets. Explain the differences, if any, in the ratios as between the various industrial groupings studied. SELF-ASSESSMENT EXERCISE 2 Udaku Plastics Products Limited is evaluating the proposal to purchase a new machinery for the current year. The relevant data are as follows: i. ii. iii. The cost of the machinery would be N200,000. It would be depreciated on a straight-line basis over five years with no salvage. The pre-tax annual cash inflow from this investment is N100,000 and the income tax rate is 45% paid the same year as incurred. All cash flows occur at year-end. The Company's investment policy is to embark on investments only if two of the following three conditions are satisfied: a. The after-tax accounting rate of return is at least 20% b. The payback period is less than four years c. The net present value of the new machine is favourable. The desired rate of return is 15% and the annuity table is as follows: Year 1 2 3 4 5 6 Required : (a) Present value of an annuity in arrears of 1 at 15% N870 1.626 2.284 2.856 3.353 3.785 As the Chief Accountant of Udaku Plastics Products Limited would you advise that the investment be undertaken. Why?

iv.

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(b)

How much would the company have had to invest four years ago at 15% compounded annually to have N300,000 now (16 marks). ICAN (May 1986) Mgt Acc Q2.

SELF-ASSESSMENT EXERCISE 3 i. Write short notes on the following: Net Present Value Model Payback Model The Internal Rate of Return (3 marks) The following information relate to three possible capital project: Because of capital rationing, only one project can be accepted by the management of Akpebor Otuokena Beauty (AOB) Nigeria Limited. PROJECTS A B 400,000 460,000 5 years 5 years N20,000 N30,000 N'000 N'000 1 160 200 2 140 140 3 130 100 4 120 100 5 110 100 C 360,000 4 years N16,000 N'000 110 130 190 200 0

ii.

Initial costs (N) Expected life Scrap value expected Expected cash inflow End of year

The company estimates its cost of capital to be 18% and discount factors are: Year 1 0.8475 2 0.7182 3 0.6088 4 0.5158 5 0.4371 Required i. Calculate the following The payback period for each project The Internal Rate of Return for each project The Net Present Value of each project. (10 marks) Which project should be accepted? Give reasons (2 marks) (Total 15 marks). ICAN (November 2002) Mgt Acc Q3.

ii.

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SELF-ASSESSMENT EXERCISE 4 FCE (Fredrick C. Egwuonwu) Plc has N500,000 available for investment The following projects are under consideration. Project Initial Net Cash Inflow During 6 Outlay Years Life A 140,000 N40,000 annually N80,000 for each of the first 3 B 180,000 years and N60,000 for each of the remaining 3 years N60,000 for each of the first 3 C 220,000 years and N80,000 for each of the remaining 3 years D 160,000 N300,000 annual amount for the first 3 years being 25% more than the annual amount for the next 3 years E 120,000 First year nil remaining years at N50,000 per annum The expected rate of return on capital is 15% Residual 5,000 Nil Nil

Nil Nil

With supporting calculation, advise management on which of the projects should be selected for investment. SELF-ASSESSMENT EXERCISE 5 Wolex Limited has commenced a review of the price being charged for a major product line. Over the past three years the product has had sales averaging 48,000 units per year at a standard selling price of N5.35. Costs have also been rising steadily over the past year and the company is considering raising this price to N5.85 or N6.35. The Sales Manager has produced the following schedule to assist with the decision: Price Estimates of demand Pessimistic estimate (probability 0.25) Most likely estimate (probability 0.55) Optimistic estimate (probability 0.20) N5.85k 35,000 40,000 50,000 N6.35k 12,000 20,000 40,000

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Currently the unit cost is estimated at N5.00; analysed as follows: Direct material Direct Labour Variable overheads Fixed overheads N 2.50 1.00 1.00 0.50 5.00

The management accountant is of the view that the most likely value for unit variable cost over the next year is N4.90 (subjective probability 0.75) but that it could be as high as N5.20 (probability 0.15) and it might even be as low as N4.75 (probability 0.10). Total fixed costs are currently estimated as N24,000 p.a. but it is estimated that the corresponding total for the ensuring year will be as follows: N25,000 with probability of 0.20 N27,000 with probability of 0.60 N30,000 with probability of 0.20 Demand quantities, unit costs and fixed costs can be assumed to be statistically independent. i. ii. iii. Analyse the above information in a way that will assist management in addressing the problem Give your views on the situation and advise on the new selling price. Calculate the expected level of profit that would result from selling price that you recommend. (15 marks). ICAN (Nov. 2002) Mgt.Acc.

Features of Investment Our discussions so far can be summarised by highlighting the essential features of investment. a. Investments are undertaken in anticipation of benefits which are not expected to accrue concurrently with the investment outlay. As a result of this inevitable time lag between outlay and benefit, almost every investment involves some risk, the risk that anticipated benefits may not ultimately be realised. Investments can be made in real or financial assets. Irrespective of the media, all investments can be measured in terms of the total outlay of funds.

b.

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c. d.

Unlike capital, investment is a flow variable. Consequently, it ought to be measured as a time-rate of change in capital stock. Since investment benefits accrue overtime, there is the expectation that the asset in which any investment is denominated shall be retained by the investor for some reasonable period. Hence the value of the asset should be carefully established at the time the investment is made. Every investment involves some forgoing some current capability for consumption. As a result of this feature, economists usually expect an identity between the level of savings and investment.

e.

Investment and Speculation According to Okafor (1983), the distinction between investment, and speculation is not easy to make by simply observing the overt actions of the individuals involved. He went further to provide a beautiful SUMMARY comparing the two as follows: Table 1: Investment and Speculation Compared Possible Investment considerations 1 Degree of risk Less assumed 2 Level of Moderate income/profit expected 3 Income Income to accrue over orientation time 4 Speculation More, if infinite. High not

Income to accrue quickly and in a lump sum Major Future value of assets and Direction and consideration future earnings potential extent of expected price movement Nature of Regular income and Capital gains. income possible terminal capital gains.

Basis for Classifying Investments Broadly speaking, investments can be classified into two -investment in real assets and investment in financial assets. In the words of Okafor (1983) both types of investment can further be classified on the basis of a number of parameters. a. Magnitude of Outlay
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Major investments could be distinguished from minor investments. In investment outlay, size is relative. An investment is major or minor depending on the relative proportion of the outlay to the total size of a firm. Thus whereas an investment of N20,000 could be considered a minor investment by a firm capitalized at N20 million, it is very major investment to a small firm with total assets valued at N40,000. b. Risk Environment of Investment

A distinction is made between investment under conditions of certainty, investments under conditions of risk, and investments under conditions of uncertainty. The problem of risk and uncertainty will be discussed in the subsequent unit. c. Motivation for Investment

A distinction could be made among investments for asset replacement, capacity expansion or modernization, and investments for strategic purposes. d. Sequencing of Cashflows

Conventional investments are distinguished from non -conventional investments on the basis of the timing and sequencing of cashflow arising from the investment. The nature of both types of investment, and the differences between them, are discussed subsequently, in this course. e. Nature of Expected Benefits

A distinction exists between cost-saving and revenue-yielding, real asset investment. The former is illustrated by a firm that replaces old equipment in the hope of cutting operating costs over the life of the new equipment. In a revenue expansion programme, on the other hand, funds are invested in order to increase gross revenue either through additional sales volume or through increased price per unit of sales. When evaluating a cost-saving investment, the value of total costs saved is compared with the additional investment made. In the latter situation, the investor would have to compare the increased costs with the additional; sales revenue realised.

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f.

Relationship to Other Investments

The costs and benefits of a given investment may or may not be affected by alternative investments. In this regard, dependent investments are different from independent investments. Investment in Real Assets Investment in real assets takes one of three major forms, that is, investment in business fixed assets, investment in inventory and investment in residential construction. Investment in Projects Real asset investment is either on single fixed assets or on a group of inter-related assets. Where the group of inter-related assets provides facilities capable of completing a production or a service process, the investment activity is described as a project. Investment projects are such that the facilities provided by the component assets can only be effective if operated as a unit. Hence the component assets must necessarily be accepted or rejected as a set. Contrary to popular expectation, the basic difference between projects and single asset investments does not lie in the value of the investment outlay. The cost of a single turbine in a hydro-electricity generating plant could be many times the total investment outlay in a corn grinding mill. In terms of our definition, the latter is a project because it can complete a processing cycle. Outlay on the hydro-electricity generating turbine is not by itself a project. The distinction must, however, be given a common sense interpretation. It is wrong, for example, to regard the purchase of a single taxi cab as a project, though such a cab can operate as a unit. A project necessarily involves the interplay of a number of single assets. (Okafor 1983). Further Classifications 1. Conventional and Non-Conventional Investments

According to Okafor (1983), investment activities in which periods of net cash outflow are expected to precede periods of net cash inflows are described as conventional investments. Non-conventional investments, on the other hand, are those in which there is no specific pattern in the sequencing of cash flows.

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2.

Cash Flows

The definition of net cash inflow or outflow used above is not identical with the accounting concept of income or expenditure. Net cash inflow from an investment for any period includes both the accounting income for the period and the non-cash expenses charged to operating revenue in determining such income such as depreciation. 3. Dependent and Independent Investments

Two or more investments are economically independent if the expected cash flow from each would be unaffected whether or not the alternate investments are carried out concurrently. Investment proposals are dependent if they are either technically dependent or economically dependent. (Okafor, 1983). Degree of Dependence in Investments There are degrees of dependence of investment opportunities. In one extreme case, one investment (A) is so dependent on another (B) that the net benefits of A would be virtually insignificant unless both of themes are carried out simultaneously. Given that situations, investment B is a prerequisite for A. Where the degree of dependence is reciprocal, the alternatives are complementary. The other extreme case of dependence occurs where the alternatives are so inter-related that the decision to carry out one implies ipso facto a rejection of the other. This is a case of mutual exclusion which occurs either because of technical dependence or because the alternative investments serve the same market which can only support one of the alternatives. Cases of mutual exclusion in investment alternatives abound in industry. Note Well The distinction between dependent and independent investments is important for one main reason. Whereas an independent investment is evaluated on the basis of its absolute cash-flows, a dependent investment must be evaluated on the basis of its incremental cash-flows. Feasibility and Viability Studies Before embarking on any capital investment, it is always advisable to conduct both feasibility and viability studies. Whereas feasibility study

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is aimed at establishing the practicability or workability of an investment, viability study tries to evaluate the degree of profitability. Feasibility Study This starts with environmental assessment (since certain investments can not take place in some environments). Other issues to be considered include: Management/Personnel Availability of Raw Material Market Share Assessment Viability Tests These tests are normally conducted using either the traditional techniques or the discounted techniques or both (See Unit).

4.0

CONCLUSION

From the foregoing discussions, one can therefore conclude that capital investments can contribute a lot towards national development. Accordingly we suggest that individuals, families, churches and states should embark on one form of investment or the other.

5.0

SUMMARY

In this unit, we learnt that capital investments involve making sacrifices today in anticipation of future benefits. We also learnt that investments could broadly speaking be divided into two namely Direct and Indirect investments or Real Assets (tangible) and paper Assets (Financial Instruments). We also looked at the features of investments and finally drew a line between investments and speculations.

6.0
1. 2. 3.

TUTOR-MARKED ASSIGNMENT
"There is no basic difference between the behaviour of speculators and those of are interested in making as much income as possible from a given capital outlay" Discuss. Discuss the similarities and major differences between investment in real assets and investment in financial assets. Evaluate at least five government policies currently in force, which either induce or stifle private investment.

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7.0

REFERENCES/FURTHER READINGS

Nweze, A.U. (2006). "Investment Opportunities in the Nigerian Capital Market". Okafor, F.O. (1983). Investment Decision: Evaluation of Projects and Securities. London: Cassell Ltd.

112