Finance Is One of The Most Difficult Subjects You Will Ever Love!

CORPORATE FINANCE
GRADE COMPONENTS
Diligence,
awarenes
s,attitude
10% Small quizes:
Group - Bonus: 0.25->1 point
project
Final 20% +Top 3 best performances.
exam
50% + Add to the midterm test.
Midterm
test
20%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
RECOMMENDED READING
• [1] Ross, S. A., Westerfield, R. W. and Jordan, B. D. (2019) Fundamentals of Corporate Finance. 12th ed.
New York: McGraw-Hill Education.

• [2] Brealey, R. A., Myers, S. C. and Allen, F. (2020) Principles of Corporate Finance. 13th ed. New York:
McGraw-Hill Education.

• [3] Trần Nguyễn Minh Hải, Nguyễn Đức Trung và ctg. (2021) Tài chính doanh nghiệp. Trường ĐH Ngân hàng
TP Hồ Chí Minh.

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COURSE OUTLINE
Chapter 1: An Introduction to Corporate finance

Chapter 2: Time value of money

Chapter 3: Risk and return

Chapter 4: Cost of capital

Chapter 5: Financial leverage and capital structure

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 CHAPTER 1
INTRODUCTION TO CORPORATE
FINANCE

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
KEY CONCEPTS AND SKILLS

1-7 Know Know the basic types of financial management decisions and the
role of the financial manager
Know Know the financial implications of the different forms of business
organization
Know Know the goal of financial management

Understand Understand the conflicts of interest that can arise between owners
and managers
Understand Understand the various types of financial markets

Understand Understand the various financial statements.

Compute Compute and, more importantly, interpret some financial ratios

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CHAPTER OUTLINE
• Part 1:
1. Corporate Finance and the Financial Manager
2. Forms of Business Organization
3. The Goal of Financial Management
4. The Agency Problem and Control of the Corporation
5. Financial Markets and the Corporation
• Part 2
Review: Some key financial indicators

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CORPORATE FINANCE
• Some important questions that are answered using finance:
• What long-term investments should the firm take on?
• Where will we get the long-term financing to pay for the investment?
• How will we manage the everyday financial activities of the firm?

1. đầu tư tiền vào đâu?

2. tiền đâu đầu tư?
3. làm tn để qli tcdn?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FINANCIAL MANAGER
• Financial managers try to answer some or all of these questions
• The top financial manager within a firm is usually the Chief Financial Officer
(CFO)
• Treasurer – oversees cash management, credit management, capital expenditures,
and financial planning
• Controller – oversees taxes, cost accounting, financial accounting and data processing

Video: Understanding Corporate Structure

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FINANCIAL MANAGEMENT DECISIONS
• Capital budgeting
• What long-term investments or projects should the business take on?

• Capital structure
• How should we pay for our assets?
• Should we use debt or equity?

• Working capital management

• How do we manage the day-to-day finances of the firm?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CAPITAL BUDGETING DECISION
• Capital budgeting decision (investment decision, capital expenditure-capex) is the
process of planning and managing a firm’s long-term investments.
• The financial manager tries to identify investment opportunities that the value of the
cash flow generated by that investment exceeds the cost of that investment.
• The types of investment opportunities that would typically be considered depend in
part on the nature of the firm’s business
• Evaluating the size, timing, and risk of future cash flows is the essence of capital
budgeting.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CAPITAL STRUCTURE DECISION
• Capital structure (or Financing decision) concerns ways in which the firm obtains and
manages the long-term financing it needs to support its long term investments. A firm’s
capital structure (or financial structure) is the specific mixture of long-term debt and
equity the firm uses to finance its operations.
• First, how much should the firm borrow? Second, what are the least expensive sources
of funds for the firm?
• Firms have a great deal of flexibility in choosing a financial structure. The question of
whether one structure is better than any other for a particular firm is the heart of the
capital structure issue.
• The financial manager has to decide exactly how and where to raise the money.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
WORKING CAPITAL MANAGEMENT

• Working capital include firm’s short-term assets and liabilities, such as inventory,
money owed to suppliers.
• Managing the firm’s working capital is a day-to-day activity that ensures that the firm
has sufficient resources to continue its operations and avoid costly interruptions
• Some questions of working capital management: How much cash and inventory should
we keep on hand? (2) Should we sell on credit? If so, what terms will we offer, and to
whom will we extend them? (3) How will we obtain any needed short-term financing?
Will we purchase on credit or will we borrow in the short term and pay cash? If we
borrow in the short term, how and where should we do it?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CONCEPT QUESTIONS
• What is the capital budgeting decision?
• What do you call the specific mixture of long-term debt and equity that a firm chooses
to use?
• Into what category of financial management does cash management fall?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 EXAMPLES OF RECENT INVESTMENT AND FINANCING DECISIONS BY
MAJOR PUBLIC CORPORATIONS.
Capital budgeting decision Capital structure decision
Intel (U.S.) Invests $7 billion in expanding semiconductor plant in Borrows $600 million from Chandler Industrial
Chandler, Arizona Development Authority.
Amazon (U.S.) Acquires self-driving start-up, Zoox, for over $1.2 Reinvests $33 billion that it generates from
billion operations
Amazon (U.S.) Announces construction of new plant to build the Announces plans to sell $2 billion of shares
electric Cybertruck
Shell (U.K./Holland Starts production at a deep-water development in the Cuts dividend to preserve cash
Gulf of Mexico
GlaxoSmithKline Spends $6 billion on research and development for Raises $1 billion by an issue 8-year bonds
(U.K.) new drugs.
Ørsted (Denmark) Completes a 230-MW wind farm in Nebraska Arranges a borrowing facility with 14 international
banks
Unilever Spends $8 billion on advertising and marketing Pays a dividend and completes $200 million
(U.K./Holland) program to buy back shares
Carnival Launches four new cruise ships Raises $770 million by sale of bonds; each bond can
Corporation be converted into about 19 shares
(U.S./U.K.)
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FORMS OF BUSINESS ORGANIZATION-1
• Three major forms of business
• Sole Proprietorship
• Partnership
• General
• Limited
• Corporation
• Joint stock company
• Limited Liability Company

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SOLE PROPRIETORSHIP
• Advantages • Disadvantages
• Easiest to start • Limited to life of owner
• Least regulated • Equity capital limited to owner’s
• Single owner keeps all the profits personal wealth
• Taxed once as personal income • Unlimited liability
• Difficult to sell ownership interest

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PARTNERSHIP
• Advantages • Disadvantages
• Two or more owners • Unlimited liability
• More capital available • General partnership
• Relatively easy to start • Limited partnership

• Income taxed once as • Partnership dissolves

personal income when one partner dies
or wishes to sell
• Difficult to transfer
ownership

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CORPORATION
• Advantages • Disadvantages
• Limited liability • Separation of ownership
• Unlimited life and management
• Separation of ownership • Double taxation (income
and management taxed at the corporate
• Transfer of ownership is rate and then dividends
easy taxed at the personal
rate)
• Easier to raise capital

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
GOAL OF FINANCIAL MANAGEMENT
• What should be the goal of a corporation?
• Maximize profit?
• Minimize costs?
• Maximize market share?
• Maximize the current value of the company’s stock?
• Does this mean we should do anything and everything to maximize owner
wealth?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
THE AGENCY PROBLEM
• Agency relationship
• Principal hires an agent to represent his/her interests
• Stockholders (principals) hire managers (agents) to run the company

• Agency problem
• Conflict of interest between principal and agent

• Management goals and agency costs

• the term agency costs refers to the costs of the conflict of interest between stockholders and
management. These costs can be indirect or direct.
• Direct agency costs come in two forms. The first type is a corporate expenditure that benefits
management but costs the stockholders. The second type of direct agency cost is an expense that arises
from the need to monitor management actions

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
MANAGING MANAGERS
• Managerial compensation
• Incentives can be used to align management and stockholder interests
• The incentives need to be structured carefully to make sure that they achieve their
goal
• Corporate control
• The threat of a takeover may result in better management
• Other stakeholders

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
WORK THE WEB EXAMPLE
• The Internet provides a wealth of information about individual companies
• One excellent site is cafef.vn
• Click on the web surfer to go to the site, choose a company and see what
information you can find!

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
QUICK QUIZ
• What are the three types of financial management decisions and what
questions are they designed to answer?
• What are the three major forms of business organization?
• What is the goal of financial management?
• What are agency problems and why do they exist within a corporation?
• What is the difference between a primary market and a secondary market?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
ETHICS ISSUES
• Is it ethical for tobacco companies to sell a product that is known to be addictive and a
danger to the health of the user? Is it relevant that the product is legal?
• Should boards of directors consider only price when faced with a buyout offer?
• Is it ethical to concentrate only on shareholder wealth, or should stakeholders as a whole be
considered?
• Should firms be penalized for attempting to improve returns by stifling competition (e.g.,
Microsoft)?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 REVIEW:KEY FINANICAL INDICATORS

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FINANCIAL STATEMENTS ANALYSIS
• Common-Size Balance Sheets
• Compute all accounts as a percent of total assets
• Common-Size Income Statements
• Compute all line items as a percent of sales
• Standardized statements make it easier to compare financial information,
particularly as the company grows.
• They are also useful for comparing companies of different sizes,
particularly within the same industry.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
3.2 RATIO ANALYSIS
• Ratios also allow for better comparison through time or between companies.
• As we look at each ratio, ask yourself:
• How is the ratio computed?
• What is the ratio trying to measure and why?
• What is the unit of measurement?
• What does the value indicate?
• How can we improve the company’s ratio?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CATEGORIES OF FINANCIAL RATIOS
• Short-term solvency or liquidity ratios
• Long-term solvency or financial leverage ratios
• Asset management or turnover ratios
• Profitability ratios
• Market value ratios

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
SHORT-TERM SOLVENCY OR LIQUIDITY RATIOS
• Short-term solvency ratios: provides information about a firm’s liquidity (liquidity
measures).
• Measure the firm’s ability to pay its bills over the short run without undue stress.
• These ratios focus on current assets and current liabilities
• Short-term creditors of interest.
• Book values and market values are likely to be similar
• Current assets and liabilities can change fairly rapidly

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 SOME TERMINOLOGIES
Net income− preferred stock dividend
• EPS = Earnings per Share=
Average of outstanding shares
• DPS=Dividend per share
Shareholder′ s equity−preferred stock
• BVPS= Book value per share=
Average of outstanding shares
• EBIT = Earnings Before Interest and Taxes
• EBITDA = Earnings Before Interest, Taxes, Depreciation and Amortization
• EBT: Earning before tax
• EAT: Earning after tax= EBT (1-t)=(EBIT-I)(1-t)
t: corporate income tax rate
I: interest payment
Example: Prufrock corporation has 33 millions outstanding stocks, calculate EPS, BVPS.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPUTING LIQUIDITY RATIOS
Prufrock corporation example:
• Current Ratio = CA / CL
• 708 / 540 = 1.31 times
• Quick Ratio = (CA – Inventory) / CL
• (708 - 422) / 540 = .53 times
• Cash Ratio = Cash / CL
• 98 / 540 = .18 times

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPUTING LONG-TERM LIQUIDITY RATIO (LEVERAGE RATIOS)
Prufrock corporation example:
• Total Debt Ratio = (TA – TE) / TA
• (3588 - 2591) / 3588 = 28%
• Debt/Equity = TD / TE
• (3588 – 2591) / 2591 = 38.5%
• Equity Multiplier = TA / TE = 1 + D/E
• 1 + .385 = 1.385

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
ASSET MANAGEMENT (TURNOVER) RATIOS
Prufrock corporation example:
• Inventory Turnover = Cost of Goods
Sold / Inventory
• 1344 / 422 = 3.2 times
• Receivables Turnover = Sales /
Accounts Receivable
• 2311 / 188 = 12.3 times
• Total Asset Turnover = Sales / Total
Assets
• 2311 / 3588 = .64 times
• It is not unusual for TAT < 1, especially
if a firm has a large amount of fixed
assets.

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPUTING PROFITABILITY MEASURES
• Profit Margin = Net Income / Sales
• 363 / 2311 = 15.7%
• Return on Assets (ROA) = Net Income /
Total Assets
• 363 / 3588 = 10.1%
• Return on Equity (ROE) = Net Income /
Total Equity
• 363 / 2591 = 14.0%
• EBITDA Margin = EBITDA / Sales
• 967 / 2311 = 41.8%

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPUTING MARKET VALUE MEASURES
Prufrock corporation example: 33 million
share outstanding
• Market Capitalization = $88 per share x 33
million shares = 2904 million
• PE Ratio = Price per share / Earnings per share
• 88 / 11 = 8 times
• Market-to-book ratio = market value per share /
book value per share
• 88 / (2591 / 33) = 1.12 times

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
USING FINANCIAL STATEMENTS
• Ratios are not very helpful by themselves: they need to be compared to something
• Time-Trend Analysis
• Used to see how the firm’s performance is changing through time

• Peer Group Analysis

• Compare to similar companies or within industries
• SIC and NAICS codes

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
POTENTIAL PROBLEMS
• There is no underlying theory, so there is no way to know which ratios are
most relevant.
• Benchmarking is difficult for diversified firms.
• Globalization and international competition makes comparison more
difficult because of differences in accounting regulations.
• Firms use varying accounting procedures.
• Firms have different fiscal years.
• Extraordinary, or one-time, events

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 End of Chapter

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 CHAPTER 2
TIME VALUE OF MONEY
CHAPTER ORGANISATION
2.1 Future Value and Compounding
2.2 Present Value and Discounting
2.3 More on Present and Future Values
2.4 Present and Future Values of Multiple Cash Flows
2.5 Valuing Equal Cash Flows: Annuities and Perpetuities
2.6 Comparing Rates: The Effect of Compounding Periods
2.7 Loan Types and Loan Amortization
2.8 Applications of time value of money: Bond valuation
2.9 Applications of time value of money: Stock valuation
2.10 Applications of time value of money: Project evaluation: NPV, IRR, MIRR, DPP.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 CHAPTER OBJECTIVES
Distinguish Distinguish between simple and compound interest.

Calculate Calculate the present value and future value of a single amount for both
one period and multiple periods.

Calculate Calculate the present value and future value of multiple cash flows.

Calculate Calculate the present value and future value of annuities.

Compare Compare nominal interest rates (NIR) and effective annual interest rates
(EAR).

Distinguish Distinguish between the different types of loans and calculate the present
value of each type of loan.

Calculate NPV, IRR, MIRR, DPP, stock and bond value

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TIME VALUE TERMINOLOGY
• Future value (FV) is the amount an investment is worth after one or more periods.
• Present value (PV) is the amount that corresponds to today’s value of a promised
future sum.
• The number of time periods between the present value and the future value is
represented by ‘t’.
• The rate of interest for discounting or compounding is
called ‘r’.
• All time value questions involve four values: PV, FV, r and t. Given three of them, it is
always possible to calculate the fourth.

57 Faculty of Finance
TIME VALUE TERMINOLOGY
• Compounding is the process of accumulating interest in an investment over time to
earn more interest.
• Interest on interest is earned on the reinvestment of previous interest payments.
• Discount rate is the interest rate that reduces a given future value to an equivalent
present value.
• Compound interest is calculated each period on the principal amount and on any
interest earned on the investment up to that point.
• Simple interest is the method of calculating interest in which, during the entire term of
the loan, interest is computed on the original sum borrowed.

58 Faculty of Finance
2.1 FUTURE VALUE OF A SINGLE CASH FLOW
• Suppose you invest $1,000 for one year at 5% per year. What is the future value in
one year?
• Interest = 1,000(.05) = 50
• Value in one year = principal + interest = 1,000 + 50 = 1,050
• Future Value (FV) = 1,000(1 + .05) = 1,050
• Suppose you leave the money in for another year. How much will you have two years
from now?
• FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50

59 Faculty of Finance
FUTURE VALUES: GENERAL FORMULA
• FV = PV(1 + r)t
• FV = future value
• PV = present value
• r = period interest rate, expressed as a decimal
• t = number of periods
• Future value interest factor = (1 + r)t

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EFFECTS OF COMPOUNDING
• Simple interest
• Compound interest
• Consider the previous example
• FV with simple interest = 1,000 + 50 + 50 = 1,100
• FV with compound interest = 1,102.50
• The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the
first interest payment

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FUTURE VALUES – EXAMPLE 2
• Suppose you invest the $1,000 from the previous example for 5 years. How much
would you have?
• 5 N; 5 I/Y; 1,000 PV
• CPT FV = -1,276.28
• The effect of compounding is small for a small number of periods, but increases as the
number of periods increases. (Simple interest would have a future value of $1,250,
for a difference of $26.28.)

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FUTURE VALUES – EXAMPLE 3
• Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much
would the investment be worth today?
• 200 N; 5.5 I/Y; -10 PV
• CPT FV = -447,189.84
• What is the effect of compounding?
• Simple interest = 10 + 200(10)(.055) = 120.00
• Compounding added $447,069.84 to the value of the investment

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FUTURE VALUE AS A GENERAL GROWTH FORMULA
• Suppose your company expects to increase unit sales of widgets by 15%
per year for the next 5 years. If you sell 3 million widgets in the current
year, how many widgets do you expect to sell in the fifth year?
• 5 N;15 I/Y; 3,000,000 PV
• CPT FV = -6,034,072 units (remember the sign convention)

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
QUICK QUIZ – PART I
• What is the difference between simple interest and compound interest?
• Suppose you have $500 to invest and you believe that you can earn 8%
per year over the next 15 years.
• How much would you have at the end of 15 years using compound interest?
• How much would you have using simple interest?

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FUTURE VALUES OF $100 AT 10%

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FUTURE VALUE OF $1 FOR DIFFERENT PERIODS AND RATES

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PRESENT VALUES
• How much do I have to invest today to have some amount in the future?
• FV = PV(1 + r)t
• Rearrange to solve for PV = FV / (1 + r)t
• When we talk about discounting, we mean finding the present value of some future
amount.
• When we talk about the “value” of something, we are talking about the present value
unless we specifically indicate that we want the future value.

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PRESENT VALUE – ONE PERIOD EXAMPLE
• Suppose you need $10,000 in one year for the down payment on a new car.
If you can earn 7% annually, how much do you need to invest today?
• PV = 10,000 / (1.07)1 = 9,345.79

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PRESENT VALUES – EXAMPLE 2
• You want to begin saving for your daughter’s college education and you
estimate that she will need $150,000 in 17 years. If you feel confident
that you can earn 8% per year, how much do you need to invest today?
• N = 17; I/Y = 8; FV = 150,000
• CPT PV = -40,540.34 (remember the sign convention)

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PRESENT VALUES – EXAMPLE 3
• Your parents set up a trust fund for you 10 years ago that is now
worth $19,671.51. If the fund earned 7% per year, how much did
your parents invest?
• N = 10; I/Y = 7; FV = 19,671.51
• CPT PV = -10,000

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PRESENT VALUE OF $1 FOR DIFFERENT PERIODS AND RATES

78 Faculty of Finance
PRESENT VALUE – IMPORTANT RELATIONSHIP I
• For a given interest rate – the longer the time period, the lower
the present value
• What is the present value of $500 to be received in 5 years? 10 years?
The discount rate is 10%
• 5 years: N = 5; I/Y = 10; FV = 500
CPT PV = -310.46
• 10 years: N = 10; I/Y = 10; FV = 500
CPT PV = -192.77

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
PRESENT VALUE – IMPORTANT RELATIONSHIP II
• For a given time period – the higher the interest rate, the smaller
the present value
• What is the present value of $500 received in 5 years if the interest rate
is 10%? 15%?
• Rate = 10%: N = 5; I/Y = 10; FV = 500
CPT PV = -310.46
• Rate = 15%; N = 5; I/Y = 15; FV = 500
CPT PV = -248.59

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
QUICK QUIZ – PART II
• What is the relationship between present value and future value?
• Suppose you need $15,000 in 3 years. If you can earn 6% annually, how
much do you need to invest today?
If you could invest the money at 8%, would you have to invest more or
less than at 6%? How much?

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DISCOUNT RATE
• Often we will want to know what the implied interest rate is on an
investment
• Rearrange the basic PV equation and solve for r
• FV = PV(1 + r)t
• r = (FV / PV)1/t – 1
• If you are using formulas, you will want to make use of both the yx and the
1/x keys

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2.3 DETERMINING THE DISCOUNT RATE
• You currently have $100 available for investment for a 21-year period. At what
interest rate must you invest this amount in order for it to be worth $500 at maturity?
• r can be solved in one of three ways:
• Use a financial calculator
• Take the nth root of both sides of the equation
• Use the future value tables to find a corresponding value. In this example, you
need to find the r for which the FVIF after 21 years is 5 (500/100).

83 Faculty of Finance
DETERMINING THE DISCOUNT RATE
• To determine the discount rate (r) in this example, a financial calculator is used.

Enter:
21 100 - 500
N I/Y PV FV
Solve for → 7.97

r = 7.97%

84 Faculty of Finance
DISCOUNT RATE – EXAMPLE 3
• Suppose you have a 1-year old son and you want to provide $75,000
in 17 years towards his college education. You currently have $5,000
to invest. What interest rate must you earn to have the $75,000 when
you need it?
• N = 17; PV = -5,000; FV = 75,000
• CPT I/Y = 17.27%

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QUICK QUIZ – PART III
• What are some situations in which you might want to know the implied
interest rate?
• You are offered the following investments:
• You can invest $500 today and receive $600 in 5 years. The investment is low
risk.
• You can invest the $500 in a bank account paying 4%.
• What is the implied interest rate for the first choice, and which investment should
you choose?

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QUICK QUIZ – PART III
• What are some situations in which you might want to know the
implied interest rate?
• You are offered the following investments:
• You can invest $500 today and receive $600 in 5 years. The investment is
low risk.
• You can invest the $500 in a bank account paying 4%.
• What is the implied interest rate for the first choice, and which investment
should you choose?

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FINDING THE NUMBER OF PERIODS
• Start with the basic equation and solve for t (remember your logs)
• FV = PV(1 + r)t
• t = ln(FV / PV) / ln(1 + r)
• You can use the financial keys on the calculator as well; just remember the sign
convention.

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FINDING THE NUMBER OF PERIODS
• You have been saving up to buy a new car. The total cost will be $10,000. You
currently have $8000. If you can earn 6% on your money, how long will you have to
wait?
• To determine the number of periods (t) in this example, a financial calculator is used.

Enter:
6 8000 - 10 000
N I/Y PV FV
Solve for → 3.83

t = 3.83 years

90 Faculty of Finance
NUMBER OF PERIODS – EXAMPLE 1
• You want to purchase a new car, and you are willing to pay
$20,000. If you can invest at 10% per year and you currently
have $15,000, how long will it be before you have enough
money to pay cash for the car?
• I/Y = 10; PV = -15,000; FV = 20,000
• CPT N = 3.02 years

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NUMBER OF PERIODS – EXAMPLE 2
• Suppose you want to buy a new house. You currently have $15,000, and
you figure you need to have a 10% down payment plus an additional 5%
of the loan amount for closing costs. Assume the type of house you want will
cost about $150,000 and you can earn 7.5% per year. How long will it be
before you have enough money for the down payment and closing costs?

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NUMBER OF PERIODS – EXAMPLE 2 CONTINUED
• How much do you need to have in the future?
• Down payment = .1(150,000) = 15,000
• Closing costs = .05(150,000 – 15,000) = 6,750
• Total needed = 15,000 + 6,750 = 21,750

• Compute the number of periods

• PV = -15,000; FV = 21,750; I/Y = 7.5
• CPT N = 5.14 years

• Using the formula

• t = ln(21,750 / 15,000) / ln(1.075) = 5.14 years

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
QUICK QUIZ – PART IV
• When might you want to compute the number of periods?
• Suppose you want to buy some new furniture for your family room. You currently have
$500, and the furniture you want costs $600. If you can earn 6%, how long will you
have to wait if you don’t add any additional money?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
SUMMARY OF TIME VALUE CALCULATIONS

95 Faculty of Finance
COMPREHENSIVE PROBLEM
• You have $10,000 to invest for five years.
• How much additional interest will you earn if the investment provides a 5%
annual return, when compared to a 4.5% annual return?
• How long will it take your $10,000 to double in value if it earns 5%
annually?
• What annual rate has been earned if $1,000 grows into $4,000 in 20
years?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
2.4 FUTURE VALUE OF MULTIPLE CASH FLOWS
• You deposit $1000 now, $1500 in one year, $2000 in two years and $2500 in three
years in an account paying 10 per cent interest per annum. How much do you have
in the account at the end of the third year?
• You can solve by either:
• compounding the accumulated balance forward one year at a time
• calculating the future value of each cash flow first and then totaling them.

97 Faculty of Finance
SOLUTIONS
• Solution 1
• End of year 1: ($1 000  1.10) + $1 500 = $2 600
• End of year 2: ($2 600  1.10) + $2 000 = $4 860
• End of year 3: ($4 860  1.10) + $2 500 = $7 846

• Solution 2
$1 000  (1.10)3 = $1 331
$1 500  (1.10)2 = $1 815
$2 000  (1.10)1 = $2 200
$2 500  1.00 = $2 500
Total = $7 846

98 Faculty of Finance
SOLUTIONS ON TIME LINES
Future value calculated by compounding forward one period at a time
0 1 2 3
Time
(years)
$0 $1100 $2860 $5346
1000 1500 2000 2500
x 1.1 x 1.1 x 1.1
$1000 $2600 $4860 $7846

Future value calculated by compounding each cash flow separately

0 1 2 3
Time
(years)

$1000 $1500 $2000 $2500

x 1.1
2200
x 1.12
1815
x 1.13
1331

Total future value $7846

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PRESENT VALUE OF MULTIPLE CASH FLOWS
• You will deposit $1500 in one year’s time, $2000 in two years time and $2500 in
three years time in an account paying 10 per cent interest per annum. What is the
present value of these cash flows?

• You can solve by either:

• discounting back one year at a time
• calculating the present value of each cash flow first and then totaling them.

100 Faculty of Finance

SOLUTIONS
• Solution 1
• End of year 2: ($2500  1.10–1) + $2000= $4273
• End of year 1: ($4273  1.10–1) + $1500= $5385
• Present value: ($5385  1.10–1) = $4895

• Solution 2
$2500  (1.10) –3 = $1878
$2000  (1.10) –2 = $1653
$1500  (1.10) –1 = $1364
Total = $4895

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2.5 ANNUITIES
• Annuities: A sequence of payments required to be made or received at equal
intervals of time (payments are usually equal in value)
• Some examples of annuities include insurance premiums, rental payments, dividends
on government bonds and instalments for loans or mortgages
• It is assumed that payments and interest periods coincide (Simple Ordinary Annuity)

• A perpetuity is an annuity in which the cash flows continue forever.

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PRESENT VALUE OF AN ANNUITY
C = equal cash flow

1 − 1/ (1 + r )t 
PV = C   

 r 
• The discounting term is called the present value interest factor for annuities (PVIFA).

103 Faculty of Finance

 • Example 1
You will receive $1000 at the end of each of the next ten years. The current
interest rate is 6 per cent per annum. What is the present value of this series of
cash flows?

PV = $1 000  

1 − 1/(1.06) 

10

 0.06 
= $1 000  7.3601
= $7 360.10
104 Faculty of Finance
 • Example 2
You borrow $10 000 to buy a car and agree to repay the loan by way of equal
monthly repayments over four years. The current interest rate is 12 per cent per
annum, compounded monthly. What is the amount of each monthly repayment?


1 − 1/ (1.01)48
$10 000 = C  

 0.01 
C = $263.33

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FINDING THE RATE FOR AN ANNUITY
• You have a loan of $5000 repayable by instalments of $745.15 at the end of each
year for 10 years. What rate is implicit in this 10 year annuity?
• To determine the discount rate (r) in this example, a financial calculator is used.

Enter:
10 5000 0 -745.15
N I/Y PV FV PMT
Solve for → 8.00

r = 8%

106 Faculty of Finance

FINDING THE NUMBER OF PAYMENTS FOR AN ANNUITY
• You have $2000 owing on your credit card. You can only afford to make the minimum payment of $40
per month. The interest rate on the credit card is 1 per cent per month. How long will it take you to pay
off the $2000.

• To determine the number of payments (t) in this example, a financial calculator is used.

Enter:
1 2 000 0 -40
N I/Y PV FV PMT
Solve for → 69.66

t = 69.66 months ÷ 12 = 5.81 years

107 Faculty of Finance

FUTURE VALUE OF AN ANNUITY
• The compounding term is called the future value interest factor for annuities (FVIFA).
Refer to Table A 4.

FV = C 
(1 + r ) − 1
t

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EXAMPLE—FUTURE VALUE OF AN ANNUITY
What is the future value of $1000 deposited at the
end of every year for 20 years if the interest rate is 6
per cent per annum?

FV = $1 000 
(1.06) 20

−1
0.06
= $1 000  36.7856
= $36 785.60

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ANNUITIES DUE
• An annuity for which the cash flows occur at the beginning of the period. Example: a
lease.
• Suppose an annuity due has five payments of $400 each, and the relevant discount
rate is 10 percent. The time line looks like this:

• Notice how the cash flows here are the same as those for a four-year ordinary
annuity, except that there is an extra $400 at Time 0. For practice, check to see that
the value of a four-year ordinary annuity at 10 percent is $1,267.95. If we add on
the extra $400, we get $1,667.95, which is the present value of this annuity due.
Annuity due value = Ordinary annuity value × (1 + r)
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PERPETUITIES
• The future value of a perpetuity cannot be calculated as the cash flows are infinite.

• The present value of a perpetuity is calculated as follows:

C
PV =
r

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GROWING ANNUITIES AND PERPETUITIES
• Annuities commonly have payments that grow over time. Suppose, for example, that
we are looking at a lottery payout over a 20-year period. The first payment, made
one year from now, will be $200,000. Every year thereafter, the payment will grow
by 5 percent, so the payment in the second year will be $200,000 × 1.05 =
$210,000. The payment in the third year will be $210,000 × 1.05 = $220,500, and
so on. What’s the present value if the appropriate discount rate is 11 percent?
• g is the growth rate

112 Faculty of Finance

2.6 COMPARING RATES
• The nominal interest rate (NIR) (stated interest rate, quoted interest rate) is the interest
rate expressed in terms of the interest payment made each period.
• The effective annual interest rate (EAR) is the interest rate expressed as if it was
compounded once per year.
• When interest is compounded more frequently than annually, the EAR will be greater
than the NIR.
• Annual percentage rate (APR) : The interest rate charged per period multiplied by
the number of periods per year.

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CALCULATION OF EAR

m
 NIR 
EAR = 1 +  − 1
 m 
m = number of times the interest is compounded

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COMPARING EARS
• Consider the following interest rates quoted by three banks:

• Bank A: 8.3%, compounded daily

• Bank B: 8.4%, compounded quarterly

• Bank C: 8.5%, compounded annually

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COMPARING EARS
365
 0.083 
EAR Bank A = 1 +  − 1 = 8.65%
 365 
4
 0.084 
EAR Bank B = 1 +  − 1 = 8.67%
 4 
1
 0.085 
EAR Bank C = 1 + − 1 = 8.50%
 1 

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COMPARING EARS
• Which is the best rate? For a saver, Bank B offers the best (highest) interest rate. For
a borrower, Banks A and C offer the best (lowest) interest rates.

• The highest NIR is not necessarily the best.

• Compounding during the year can lead to a significant difference between the NIR
and the EAR, especially for higher rates.

117 Faculty of Finance

COMPLETE THE TABLE BELOW:
Nominal annual Compounding Effective rate
rate periods
11.5% Daily
15% Monthly
Fortnightly 14.5%
Quarterly 14.8%
5% Semi annually
7% Quarterly
20% Daily
Semi annually 6%
Quarterly 8%
Daily 12%

118 Faculty of Finance

COMPLETE THE TABLE BELOW:
Nominal annual Compounding Effective rate
rate periods
11.5% Daily 12.19%
15% Monthly 16.08%
13.58% Fortnightly 14.5%
14.04% Quarterly 14.8%
5% Semi annually 5.06%
7% Quarterly 7.19%
20% Daily 22.13%
5.91% Semi annually 6%
7.77% Quarterly 8%
11.33% Daily 12%

119 Faculty of Finance

 2.7 APPLICATION OF TIME VALUE OF MONEY:
AMOTIZATION OF A LOAN

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
2.7 TYPES OF LOANS
• A pure discount loan is a loan where the borrower receives money today and repays
a single lump sum in the future.

• An interest-only loan requires the borrower to only pay interest each period and to
repay the entire principal at some point in the future.

• An amortised loan requires the borrower to repay parts of both the principal and
interest over time.

121 Faculty of Finance

AMORTIZATION OF A LOAN
A loan of $5,000 is negotiated for 5 years at 9% p.a.
• (a) Calculate the annually repayments.
• (b) How much principal and interest are paid with the 4th repayment? How much is
still owed after the 4th repayment?
• (c) How much principal and interest have been paid over the three years of the loan?
• (d) After the first year it is possible to increase the yearly repayment to $1,500. If
this is done how long will it now take to repay the loan and how much interest will be
saved?

122 Faculty of Finance

AMORTIZATION OF A LOAN

Year Beginning Total Interest Principal Ending

Balance Payment Paid Paid Balance

1 $5000.00 $1285.46 $450.00 $835.46 $4164.54

2 $4164.54 $1285.46 $374.81 $910.65 $3253.89

3 $3253.89 $1285.46 $292.85 $992.61 $2261.28

4 $2261.28 $1285.46 $203.52 $1081.94 $1179.33

5 $1179.33 $1285.46 $106.13 $1179.33 $0.00

Totals $6427.30 $1427.30 $5000.00

123 Faculty of Finance

SUMMARY 2.1-2.7
• For a given rate of return, the value at some point in the future of an investment
made today can be determined by calculating the future value of that investment.
• The current worth of a future cash flow or series of cash flows can be determined for
a given rate of return by calculating the present value of the cash flow(s) involved.
• It is possible to find any one of the four components
(PV, FV, r, t) given the other three.
• A series of constant cash flows that arrive or are paid at the end of each period is
called an ordinary annuity.
• For financial decisions, it is important that any rates are converted to effective rates
before being compared.

124 Faculty of Finance

2.8 APPLICATION OF TIME VALUE OF MONEY:
BOND VALUATION

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
BOND TERMINOLOGY
• Coupon: The stated interest payment made on a bond.
• Face value: The principal amount of a bond that is repaid at the end of the term.
Also called par value.
• Coupon rate: The annual coupon divided by the face value of a bond.
• Maturity: The specified date on which the principal amount of a bond is paid.
• Yield to maturity (YTM): The rate required in the market on a bond.

126 Faculty of Finance

BOND CHARACTERISTICS
• A bond is a type of fixed income security. Its promise is to deliver known future cash
flows.
• Investor (bondholder) lends money (principal amount) to issuer for a defined period of
time, at a variable or fixed interest rate
• In return, bondholder is promised
• Periodic coupon payments (most of the times paid semiannually); and/or
• The bond’s principal (maturity value/par value/face value) at maturity.

127 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
THE BOND PRICING FORMULA – 1
• Consider a bond paying coupons with frequency n.
• Cash flows: coupon C paid with frequency n up to year T, plus the principal M, paid at
T.
0 1 2 3 4 n

Purchase Coupon Coupon Coupon Coupon Coupon +

Price Face Value

Cash Outflows Cash Inflows

to the Investor to the Investor

• How much is the stream of cash flows worth today? To answer this question we need to
calculate the present value of the cash flows.
• The present value (purchase price) is the price we are willing to pay today in order to
receive the stream of cash flows.
128 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 THE BOND PRICING FORMULA-2
• Bond price is equal to present value of all the cash flows you receive if you hold to
maturity.
nT
𝑀𝐶
𝑃=෍ y s+ y nT
s=1 (1 + 𝑛) (1 + )
𝑛
• P: bond price;
• C: coupon payment (assumed constant);
• n: number of coupon payments per year;
• T: number of years to maturity;
• y: interest rate used to discount the cash flows; yield-to-maturity (YTM) or market
required yield;
• M: par value (or face value, or maturity value) of the bond.
129 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
THE BOND PRICING FOMULA-3
• Bond Price is equal to Present Value of all the cash flows you receive if you hold to
maturity

(2.2)

130 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
ZERO COUPON BONDS
• Make no periodic interest payments (coupon rate = 0%)
• The entire yield-to-maturity comes from the difference between the purchase price
and the par value
• Cannot sell for more than par value
• Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs)
• Treasury Bills and principal-only Treasury strips are good examples of zeroes

131 Faculty of Finance

THE BOND PRICING FOMULA-4
Three special cases of the bond pricing formula:

• A zero-coupon bond:

• An annuity (coupons only):

• A perpetuity bond (coupons only, infinite maturity):

132 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE
• Suppose the Xanth (pronounced “zanth”) Co. were to issue a bond with 10 years to
maturity. The Xanth bond has an annual coupon of $80. Similar bonds have a yield to
maturity of 8 percent. Based on our preceding discussion, the Xanth bond will pay $80
per year for the next 10 years in coupon interest. In 10 years, Xanth will pay $1,000 to
the owner of the bond. What would this bond sell for?

133
Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPUTING YIELD TO MATURITY
• Yield to Maturity (YTM) is the rate implied by the current bond price
• Finding the YTM requires trial and error if you do not have a financial
calculator and is similar to the process for finding r with an annuity
• If you have a financial calculator, enter N, PV, PMT, and FV, remembering
the sign convention (PMT and FV need to have the same sign, PV the
opposite sign)

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
YTM WITH ANNUAL COUPONS
• Consider a bond with a 10% annual coupon rate, 15 years to maturity and
a par value of $1,000. The current price is $928.09.
• Will the yield be more or less than 10%?
• N = 15; PV = -928.09; FV = 1,000; PMT = 100
• CPT I/Y = 11%

137 7-137
Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
YTM WITH SEMIANNUAL COUPONS
• Suppose a bond with a 10% coupon rate and semiannual coupons, has a
face value of $1,000, 20 years to maturity and is selling for $1,197.93.
• Is the YTM more or less than 10%?
• What is the semiannual coupon payment?
• How many periods are there?
• N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y = 4% (Is this the YTM?)
• YTM = 4%*2 = 8%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TABLE 7.1

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CURRENT YIELD VS. YIELD TO MATURITY
• Current Yield = annual coupon / price
• Yield to maturity = current yield + capital gains yield
• Example: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to
maturity, $1,197.93 price
• Current yield = 100 / 1,197.93 = .0835 = 8.35%
• Price in one year, assuming no change in YTM = 1,193.68
• Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = -.35%
• YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 GRAPHICAL RELATIONSHIP BETWEEN PRICE AND YIELD-TO-MATURITY (YTM)
1500

1400

1300

1200
Bond Price
1100

1000

900

800

700

600
0% 2% 4% 6% 8% 10% 12% 14%

YTM

Yield-to-maturity (YTM)

7-141 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 BOND PRICES: RELATIONSHIP BETWEEN COUPON AND YIELD

• If YTM = coupon rate, then par value = bond price

• If YTM > coupon rate, then par value > bond price
• Why? The discount provides yield above coupon rate
• Price below par value, called a discount bond
• If YTM < coupon rate, then par value < bond price
• Why? Higher coupon rate causes value above par
• Price above par value, called a premium bond

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 BOND CHARACTERISTICS AND REQUIRED RETURNS
• The coupon rate depends on the risk characteristics of the bond
when issued
• Which bonds will have the higher coupon, all else equal?
• Secured debt versus a debenture
• Subordinated debenture versus senior debt
• A bond with a sinking fund versus one without
• A callable bond versus a non-callable bond

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
INFLATION AND INTEREST RATES
• Real rate of interest – change in purchasing power
• Nominal rate of interest – quoted rate of interest, change in
actual number of dollars
• The ex ante nominal rate of interest includes our desired real rate
of return plus an adjustment for expected inflation

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
THE FISHER EFFECT
• The Fisher Effect defines the relationship between real rates, nominal rates,
and inflation
• (1 + R) = (1 + r)(1 + h), where
• R = nominal rate
• r = real rate
• h = expected inflation rate
• Approximation
• R=r+h

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE 7.5
• If we require a 10% real return and we expect inflation to be
8%, what is the nominal rate?
• R = (1.1)(1.08) – 1 = .188 = 18.8%
• Approximation: R = 10% + 8% = 18%
• Because the real return and expected inflation are relatively
high, there is significant difference between the actual Fisher
Effect and the approximation.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPREHENSIVE PROBLEM
• What is the price of a $1,000 par value bond with a 6% coupon rate paid
semiannually, if the bond is priced to yield 5% and it has 9 years to
maturity?
• What would be the price of the bond if the yield rose to 7%.
• What is the current yield on the bond if the YTM is 7%?

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
2.9 APPLICATION OF TIME VALUE OF MONEY:
STOCK VALUATION

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
STOCK CHARACTERISTICS
• Cash Flows for Stockholders
• If you buy a share of stock, you can receive cash in two ways
• The company pays dividends
• You sell your shares, either to another investor in the market or back to the
company
• As with bonds, the price of the stock is the present value of these expected cash
flows
• Preferred stock: receive a fix dividend over time.

149 Faculty of Finance

DIVIDEND AND CAPITAL GAIN
• Dividend:
• Common stockholders have the right to receive dividends if the board
of directors declares them.
• Dividends are usually paid in cash (cash dividends), but sometimes may
be paid in additional shares (stock dividends).
• Capital gains:
• Investors buy stock is to receive dividends; they may sell their stock for
more than they paid→ capital gain.
• When a stock is sold after having been held for 12 months or less, the
profit or loss is known as a short-term gain or loss. For stocks held
longer than 12 months, any gain or loss is long-term. Long-term gains
provide the greatest tax advantage

1 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
5
DIVIDEND CHARACTERISTICS
• Dividends are not a liability of the firm until a dividend has been declared by
the Board
• Consequently, a firm cannot go bankrupt for not declaring dividends
• Dividends and Taxes
• Dividend payments are not considered a business expense; therefore, they are not
tax deductible
• The taxation of dividends received by individuals depends on the holding period
• Dividends received by corporations have a minimum 70% exclusion from taxable
income

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
DIVIDEND
• Dividend payout ratio: The
percentage of earnings paid to
shareholders in dividends.Calculated
as:

• Dividend rate: The fixed or

adjustable rate paid on common Dividend per share
stock or preferred stock base on par =
value.Calculated as: Par value per share

1 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
5
COMMON STOCK-VALUE
• Face value (par value)
• Book value: The net asset value of a company, calculated by total assets minus
intangible assets (patents, goodwill) and liabilities. It is the total value of the company's
assets that shareholders would theoretically receive if a company were liquidated
• Market value: The current quoted price at which investors buy or sell a share of common
stock at a given time
• Intrinsic value: The actual value of a company or an asset based on an underlying
perception of its true value including all aspects of the business, in terms of both tangible
and intangible factors. This value may or may not be the same as the current market
value

1 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
5
FEATURES OF PREFERRED STOCK
• Dividends
• Stated dividend that must be paid before dividends can be paid to common
stockholders
• Dividends are not a liability of the firm, and preferred dividends can be
deferred indefinitely
• Most preferred dividends are cumulative – any missed preferred dividends
have to be paid before common dividends can be paid
• Preferred stock generally does not carry voting rights

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 The Dividend discount model (DDM)

Infinite holding period:

 Dt
V0 = 
t =1 (1 + r) t

(2)

Dt :dividend of period t
Vo: Present value of a stock
r: required rate of return on the stock

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
DDM -SINGLE HOLDING PERIOD
• Buy a stock and hold for one year
D1 P1 D1 + P1
V0 = 1
+ 1
= 1
(1 + r) (1 + r) (1 + r)

• P1 :the expected price per share at t=1

• D1:the expected dividend per share for year 1, assumed to be paid at the end of the year at t=1
• Example: suppose that you expect Carrefour SA (NYSE Euronext Paris: CA) to pay a €1.10
dividend next year. You expect the price of CA stock to be €53.55 in one year. The required
rate of return for CA stock is 9 percent. What is your estimate of the value of CA stock?
Discounting the expected dividend of €1.10 and the expected sales price of €53.55 at the
required return on equity of 9 percent, we obtain
D + P1 1.1 + 53.55
V0 = 1 1
= 1
= 50.14
1 (1 + r ) (1 + 0.09)
5 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 DDM-MULTIPLE HOLDING PERIODS
• Buy a stock and hold for n periods:

n Dt Pn
V0 =  t + (1 + r) n
t =1 (1 + r)

Example: For the next five years, the annual dividends of a stock are expected to be $2.00, $2.10,
$2.20, $3.50, and $3.75. In addition, the stock price is expected to be $40.00 in five years. If the
required return on equity is 10 percent, what is the value of this stock?
• The present values of the expected future cash flows can be written out as:

V0=

• Calculating and summing these present values gives a stock value of Po 1.818 +1.736 +1.653 +2.391
+2.328 +24.837 = $34.76.
• The five dividends have a total present value of $9.926 and the terminal stock value has a present
value of $24.837, for a total stock value of $34.76.
1
5 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
DIVIDEND CONSTANT GROWTH MODEL (GORDON MODEL)
• Dividends are expected to grow at a constant percent per period.
• P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
• P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …
• With a little algebra and some series work, this reduces to:

D 0 (1 + g) D1
P0 = =
R -g R -g

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DGM – EXAMPLE 1
• Suppose Big D, Inc., just paid a dividend of $0.50 per share. It is
expected to increase its dividend by 2% per year. If the market requires
a return of 15% on assets of this risk, how much should the stock be
selling for?
• P0 = .50(1+.02) / (.15 - .02) = $3.92

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DGM – EXAMPLE 2
• Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year. If the
dividend is expected to grow at 5% per year and the required return is 20%, what is
the price?
• P0 = 2 / (.2 - .05) = $13.33
• Why isn’t the $2 in the numerator multiplied by (1.05) in this example?

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 CONSTANT GROWTH MODEL (GORDON MODEL)
Example:
1. Suppose that an annual dividend of € 5 has just been paid (Do= € 5). The expected long - term
growth rate is 5% and the required return on equity is 8 percent.
Answer: The Gordon growth model value per share is Vo =Do(1 +g )/( r – g ) =(€ 5 *1.05)/(0.08 –
0.05) =€ 5.25/0.03= € 1752
2. A manufacturer of paper and plastic packaging has a sustainable increases in the level of earnings
with increases in dividends, payout ratio is 40 - 60 %. Most recent quarterly dividend was $0.26
.The forecasted dividend growth rate is 6.0 %per year, r= 10.1 %.
a) Calculate the Gordon growth model value for the above stock.
b) The current market price of stock is $30.18. Using your answer to question 1, judge whether the
stock is fairly valued, undervalued, or overvalued.

1
6 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
GORDON GROWTH MODEL- NO GROWTH (PREFERRED STOCK)
• If dividends are expected at regular intervals forever, then this is a
perpetuity and the present value of expected future dividends can be
found using the perpetuity formula
Po=D/r
• Stocks that have earnings and dividends that are expected to remain
constant → Preferred Stock
• Example: Suppose stock is expected to pay a $0.50 dividend every
quarter and the required return is 10% with quarterly compounding.
What is the price?
• P0 = .50 / (.1 / 4) = $20

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
QUICK QUIZ – PART I
• What is the value of a stock that is expected to pay a constant dividend of $2 per
year if the required return is 15%?
• What if the company starts increasing dividends by 3% per year, beginning with the
next dividend? The required return stays at 15%.

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USING THE GORDON GROWTH MODEL TO FIND R
• Start with the DGM:

D 0 (1 + g) D1
P0 = =
R -g R -g

D 0 (1 + g) D1
R= +g= +g
P0 P0

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FINDING THE REQUIRED RETURN - EXAMPLE
• Suppose a firm’s stock is selling for $10.50. It just paid a $1
dividend, and dividends are expected to grow at 5% per year.
What is the required return? divident payoutratio: tỉ lệ chi trả cổ tức = yearly divident pershare / earning
pershare or = dividends / net income
• R = [1(1.05)/10.50] + .05 = 15%
dividend rate = DPS/Face value dividend rate: tỉ lệ cổ tức = dividend pershare / par value pershare)
• What is the dividend yield? =dividend pershare / stock market price
lãi suất cổ tức
• 1(1.05) / 10.50 = 10%
• What is the capital gains lãiyield?
vốn
• g =5%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TABLE 8.1 - STOCK VALUATION SUMMARY

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COMPREHENSIVE PROBLEM

• XYZ stock currently sells for $50 per share. The next
expected annual dividend is $2, and the growth rate is 6%.
What is the expected rate of return on this stock?
• If the required rate of return on this stock were 12%, what
would the stock price be, and what would the dividend yield
be?

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 2.10 PROJECT EVALUATION-NPV, IRR, MIRR,
DPP

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
NET PRESENT VALUE (NPV)

• Net present value is the difference

chênh lệch
between an investment’s market value (in today’s
giá trị thị trường của một khoản đầu tư
dollars) and its cost (also in today’s dollars).
chi phí
Net: ròng ( đã trừ hết CP)
thước đo giá trị đc tạo ra bằng cách thực hiện một khảon đầu tư
• Net present value is a measure of how much value is created by undertaking an
investment. NPV > 0 tạo thêm tiền
npv = 0 huề vốn'
npv <0 lỗ
tỷ lệ chiết khấu
• Estimation of the future cash flows and the discount rate are important in the
calculation of the NPV.

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NET PRESENT VALUE
Steps in calculating NPV:

ước tính dòng tiền kỳ vọng trong tương lai

• The first step is to estimate the expected future cash flows.
ước tính lợi nhuận yêu cầu cho các dự án có mức độ rủi ro này
• The second step is to estimate the required return for projects of this risk level.
tìm PV và trừ đi khoản đầu tư
• The third step is to find the present value of the cash flows and subtract the initial
investment.

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NPV ILLUSTRATED

0 1 2
doanh thu
chi phí ban đầu
Initial outlay Revenues $1000 Revenues $2000
($1100) Expenses
chi phí 500 Expenses 1000
Cash flow $500 Cash flow $1000
dòng tiền

– $1100.00
1
$500 x
1.10
+454.55
1
$1000 x
1.102
+826.45

+$181.00 NPV

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NPV
NPV > 0 tạo thêm tiền
NPV < 0 lỗ
NPV = 0 huề vốn

đầu tư
dương từ chối âm
• An investment should be accepted if the NPV is positive and rejected if it is negative.

thước đo trực tiếp mức độ đầu tư đáp ứng mục tiêu quản lý tài chính nhằm gia tăng tài sản cho chủ sở hữu
• NPV is a direct measure of how well the investment meets the goal of financial
management—to increase owners’ wealth.

gia tăng giá trị cho cty

• A positive NPV means that the investment is expected to add value to the firm.

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pay back period: kỳ hoàn vốn

PAYBACK PERIOD
khoảng tgian để một khảon đầu tư tạo ra dòng tiền để thu hồi chi phí ban đầu

• The amount of time required for an investment to generate cash flows to recover its
initial cost.
• Steps of caculating payback period:
• Estimate the cash flows. ước tính dòng tiền
tích lũy các dòng tiền trong tương lai cho đến khi chúng bằng khaonr đầu tư ban đầu
• Accumulate the future cash flows until they equal the initial investment.
khoảng tgian để điều này diễn ra là kỳ hoàn vốn
• The length of time for this to happen is the payback period.
quy định
• An investment is acceptable if its calculated payback is less than some prescribed
number of years.

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PAYBACK PERIOD ILLUSTRATED
đầu tư ban đầu Initial investment = –$1000
Year Cash flow
1 $200
2 400
3 600

Accumulated dòng tiền lũy kế

Year Cash flow
1 $200
2 600
3 1200

Payback period = 2 2/3 years

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ADVANTAGES OF PAYBACK PERIOD

• Easy to understand.

• Adjusts for uncertainty of later cash flows.

• Biased towards liquidity.

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DISADVANTAGES OF PAYBACK PERIOD

• Time value of money and risk ignored.

• Arbitrary determination of acceptable payback period.

• Ignores cash flows beyond the cut-off date.

• Biased against long-term and new projects.

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DISCOUNTED PAYBACK PERIOD

• The length of time required for an investment’s discounted cash flows to equal its
initial cost.

• Takes into account the time value of money.

• More difficult to calculate.

• An investment is acceptable if its discounted payback is less than some prescribed

number of years.
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EXAMPLE—DISCOUNTED PAYBACK
Initial investment = —$1000
R = 10%
PV of
Year Cash flow Cash flow
1 $200 $182
2 400 331
3 700 526
4 300 205

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EXAMPLE—DISCOUNTED PAYBACK (CONTINUED )
Accumulated
Year discounted cash flow
1 $182
2 513
3 1039
4 1244

Discounted payback period is just under three years

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ORDINARY AND DISCOUNTED PAYBACK
Initial investment = –$300
R = 12.5%
Cash Flow Accumulated Cash Flow
Year Undiscounted Discounted Undiscounted Discounted

1 $ 100 $ 89 $ 100 $89

2 100 79 200 168
3 100 70 300 238
4 100 62 400 300
5 100 55 500 355

• Ordinary payback?
• Discounted payback?

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ADVANTAGES AND DISADVANTAGES OF DISCOUNTED PAYBACK
• Advantages • Disadvantages

- Includes time value of money - May reject positive NPV investments

- Easy to understand - Arbitrary determination of acceptable payback
period
- Does not accept negative estimated NPV investments
- Ignores cash flows beyond the cutoff date
- Biased towards liquidity
- Biased against long-term and new products

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ACCOUNTING RATE OF RETURN (ARR)
tỷ suất lợi nhuận kế toán

• Measure of an investment’s profitability.

thước đo khả năng sinh lời của một khaonr đầu tư

lợi nhuận ròng trbinh

average net profit
ARR =
average book value
gtri sổ sách trbinh

• A project is accepted if ARR > target average accounting return.

lợi nhuận kế toán trbinh mục tiêu

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EXAMPLE—ARR
Year
1 2 3
bán hàng Sales $440 $240 $160
chi phí Expenses 220 120 80
lợi nhuận gộpGross profit 220 120 80
khấu hao Depreciation 80 80 80
thu nhập chịu thuế
Taxable income 140 40 0
thuế Taxes (25%) 35 10 0
lợi nhuận ròng
Net profit $105 $30 $0

giả sử đầu tư ban đầu

Assume
' initial investment = $240

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EXAMPLE—ARR ( CONTINUED)

$105 + $30 + $0
Average net profit =
3
= $45
vốn đầu tư ban đầu
giá trị thanh lý
Initial investment + Salvage value
Average book value =
2
$240 + $0
=
2
= $120

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EXAMPLE—ARR ( CONTINUED)

Average net profit

ARR =
Average book value
$45
=
$120
= 37.5%

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DISADVANTAGES OF ARR

• The measure is not a ‘true’ reflection of return.

• Time value is ignored.

• Arbitrary determination of target average return.

• Uses profit and book value instead of cash flow and market value.

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ADVANTAGES OF ARR

• Easy to calculate and understand.

• Accounting information almost always available.

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INTERNAL RATE OF RETURN (IRR)
tỷ suất lợi nhuận nội bộ

• The discount rate that equates the present value of the future cash flows with the
initial cost.

• Generally found by trial and error.

• A project is accepted if its IRR is > the required rate of return.

• The IRR on an investment is the required return that results in a zero NPV when it is
used as the discount rate.
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EXAMPLE—IRR
Initial investment = –$200
Year Cash flow
1 $ 50
2 100
3 150

n Find the IRR such that NPV = 0

50 100 150
0 = –200 + + +
(1+IRR)1 (1+IRR)2 (1+IRR)3

50 100 150
200 = + +
(1+IRR)1 (1+IRR)2 (1+IRR)3

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EXAMPLE—IRR (CONTINUED )
Trial and Error
Discount rates NPV
0% $100
5% 68
10% 41
15% 18
20% –2

IRR is just under 20%—about 19.44%

0,19437

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NPV PROFILE
Net present value

120 Year Cash flow

0 – $275
100 1 100
2 100
80 3 100
4 100
60

40

20

– 20

– 40 Discount rate
2% 6% 10% 14% 18% 22%
IRR

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PROBLEMS WITH IRR
nhiều hơn 1 dòng tiền âm ----> nhiều tỷ lệ hoàn vốn

• More than one negative cash flow → multiple rates of return.

• Project is not independent → mutually exclusive investments. Highest IRR does not
indicate the best project.

Advantages of IRR
• Popular in practice
• Does not require a discount rate

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MULTIPLE RATES OF RETURN nhiều tỷ suất lợi nhuận

Assume you are considering a project for

which the cash flows are as follows:

Year Cash flows

0 –$252

1 1431
2 –3035
3 2850
4 –1000

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MULTIPLE RATES OF RETURN
n What’s the IRR? Find the rate at which
the computed NPV = 0:

at 25.00%: NPV = 0
at 33.33%: NPV = 0
at 42.86%: NPV = 0
at 66.67%: NPV = 0

n Two questions:
u 1. What’s going on here?
u 2. How many IRRs can there be?

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IRR AND NON-CONVENTIONAL CASH FLOWS
• When the cash flows change sign more than once, there is more than one IRR.
• When you solve for IRR you are solving for the root of an equation and when you
cross the x axis more than once, there will be more than one return that solves the
equation.
• If you have more than one IRR, you cannot use any of them to make your decision.

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MULTIPLE RATES OF RETURN
NPV
$0.06

$0.04

IRR = 25%
$0.02

$0.00

($0.02) IRR = 33.33% IRR = 66.67%

IRR = 42.86%
($0.04)

($0.06)

($0.08)

0.2 0.28 0.36 0.44 0.52 0.6 0.68

Discount rate

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THE MODIFIED INTERNAL RATE OF RETURN (MIRR)
tỷ suất lơij nhuận nội bộ được sửa đổi

• Controls for some problems with IRR lãi suất đi vay

• Calculate the net present value of all cash outflows using the borrowing rate.
tỷ lệ đầu tư
• Calculate the net future value of all cash inflows using the investing rate.
tương đương với giá trị này
• Find the rate of return that equates these values.
tái đầu tư
• Benefits: single answer and specific rates for borrowing and reinvestment
• Three methods:
pp chiết khấu
1.Discounting approach = Discount future outflows to present and add to CF0
pp tái đầu tư kết hợp từ đầu đến cuối
2. Reinvestment approach = Compound chi chiết
all CFs
khấu đến
except
hiện tại
the first one forward to end
pp kết hợp
3. Combination approach = Discount outflows to present; compound inflows to end
• MIRR will be unique number for each method
• Discount (finance) /compound (reinvestment) rate externally supplied
tỷ lệ chiết khấu / góp do bên ngoài cung cấp
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MIRR- EXAMPLE
Project cash tiền
flows:
ra tiền vào tiền ra

• Time 0: -$500 today; Time 1: + $1,000; Time 2: -$100

• Use combined method and RRR = 11%
• PV (outflows) = -$500 + -$100/(1.11)2 = -$581.16
• FV (inflow) = $1,000 x 1.11 = $1,110
• MIRR: N=2; PV=-581.16; FV=1,110; CPT I/Y = MIRR = 38.2

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MIRR VS IRR
• Different opinions about MIRR and IRR.
• MIRR avoids the multiple IRR problem.
• Managers like rate of return comparisons, and MIRR is better for this than IRR.
• Problem with MIRR: different ways to calculate with no evidence of the best method.
• Interpreting a MIRR is not obvious.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
IRR, NPV AND MUTUALLY-EXCLUSIVE PROJECTS
Net present value
Year
160 0 1 2 3 4
140 Project A: – $350 50 100 150 200
120
100 Project B: – $250 125 100 75 50
80
60
40
Crossover Point
20
0
– 20
– 40
– 60
– 80
– 100 Discount rate
0 2% 6% 10% 14% 18% 22% 26%

IRR A IRRB

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PROFITABILITY INDEX (PI)

• Expresses a project’s benefits relative to its initial cost.

PV of inflows
PI =
Initial cost
• Accept a project with a PI > 1.0.

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EXAMPLE—PI

Assume you have the following information on Project X:

Initial investment = –$1100 Required return = 10%

Annual cash revenues and expenses are as follows:

Year Revenues Expenses
1 $1000 $500
2 2000 1000

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EXAMPLE—PI (CONTINUED )
500 1 000
NPV = + − 1100
1.10 (1.10)2

= $181

181 + 1100
PI =
1100
= 1.1645 Net Present Value Index
= 181
1100
= 0.1645

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EXAMPLE—PI (CONTINUED )

Is this a good project? If so, why?

• This is a good project because the present value of the inflows exceeds the outlay.

• Each dollar invested generates $1.1645 in value or $0.1645 in NPV.

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ADVANTAGES AND DISADVANTAGES OF PI
Advantages Disadvantages

• Closely related to NPV, generally • May lead to incorrect decisions in

leading to identical decisions. comparisons of mutually exclusive
investments.

• Easy to understand.

• May be useful when available

investment funds are limited.

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CAPITAL BUDGETING IN PRACTICE
• We should consider several investment criteria when making decisions.

• NPV and IRR are the most commonly used primary investment criteria.

• Payback is a commonly used secondary investment criteria.

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 CHAPTER 3
RISK AND RETURN
CHAPTER OUTLINE
1.Dollar returns vs. Percentage returns
2.Historical average return and variance
3.Arithmetic vs. Geometric average returns
4.Expected Returns and Variances of a single asset
5.Portfolios, expected returns and variances of a portfolio of 2 assets
6.Diversification and Portfolio Risk
7.Risk: Systematic, Unsystematic Risk and Beta
8.The Security Market Line
9.The SML and the Cost of Capital: A Preview
*****Reading: RWJ 12edition: Chapter 12,13

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXPECTED LEARNING OUTCOMES
Know how to calculate the return on an investment
Understand the historical returns on various types of investments
Understand the historical risks on various types of investments
Know how to calculate expected returns, variance, covariance,correlation of a
single asset and a portfolio
Understand the impact of diversification
Understand the systematic risk principle
Understand the security market line
Understand the risk-return trade-off
Be able to use the Capital Asset Pricing Model

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
SIX FUNDAMENTAL PRINCIPLES OF FINANCE
P1: There Is No Such Thing As A Free Lunch
P2: Other Things Equal, Individuals :
􀂃 Prefer more money to less (non-satiation)
􀂃 Prefer money now to later (impatience)
􀂃 Prefer to avoid risk (risk aversion)
P3: All Agents Act To Further Their Own Self-Interest
P4: Financial Market Prices Shift to Equalize Supply and Demand
P5: Financial Markets Are Highly Adaptive and Competitive
P6: Risk-Sharing and Frictions Are Central to Financial Innovation
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
DOLLAR RETURNS : Lợi nhuận tuyệt đối

• Total dollar return = income from investment + capital gain (loss) due to
change in price
• Example 1:
bond: trái phiếu
▪ You bought a bond for $1000 one year ago. You have received two coupons of $30
each. You can sell the bond for $1025 today. What is your total dollar return?
• Income = 30 + 30 = 60
• Capital gain = 1025 – 1000 = 25
• Total dollar return = 60 + 25 = $85

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 PERCENTAGE RETURNS : lợi nhuận tương đối

• It is generally more intuitive to think in terms of percentage, rather than dollar, returns
• Dividend yield (or income yield) = income / beginning price
• Capital gains yield = (ending price – beginning price) / beginning price
• Total percentage return = dividend yield + capital gains yield
Example 1 (Cont.):
Dividend yield (income yield)=60/1000=6%
Capital gains yield= (1025-1000)/1000=2.5%
Total percentage return= 6%+2.5%=8.5%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE 2: CALCULATING RETURNS
• You bought a stock for $35, and you received dividends of $1.25. The stock
is now selling for $40.

▪ What is your dollar return?

• Dollar return = 1.25 + (40 – 35) = $6.25

▪ What is your percentage return?

• Dividend yield = 1.25 / 35 = 3.57%
• Capital gains yield = (40 – 35) / 35 = 14.29%
• Total percentage return = 3.57 + 14.29 = 17.86%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
FIGURE 12.4: A $1 INVESTMENT IN DIFFERENT TYPES OF PORTFOLIOS OVER 1925-2013

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 FIGURE A: YEAR-BY-YEAR TOTAL RETURNS ON FIGURE B: YEAR-BY-YEAR TOTAL RETURNS
SMALL-COMPANY STOCKS ON LONG-TERM GOVERNMENT BONDS

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
AVERAGE RETURN: ARITHMETIC VS. GEOMETRIC
• Arithmetic Mean Return (AM)
AM =  Ri / T
where  Ri = the sum of all the annual return, i=1,2….,T.
T = number of years
• Geometric Mean Return (GM)
Example: Year Beginning Value Ending Value Ri
1 100 115 ?
2 115 138 ?
3 138 110.4 ?

Arithmetic mean return=

Geometric mean return=
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
AVERAGE RETURN: ARITHMETIC VS. GEOMETRIC MEAN
• Arithmetic average – return earned in an average period over multiple periods
• Geometric average – average compound return per period over multiple periods
• The geometric average will be less than the arithmetic average unless all the returns are
equal
• Which is better?
▪ The arithmetic average is overly optimistic for long horizons
▪ The geometric average is overly pessimistic for short horizons
▪ So, the answer depends on the planning period under consideration
• 15 – 20 years or less: use the arithmetic
• 20 – 40 years or so: split the difference between them
• 40 + years: use the geometric
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
AVERAGE RETURNS
Investment Average Return
Large Stocks 12.1%
Small Stocks 16.9%
Long-term Corporate Bonds 6.3%

Long-term Government Bonds 5.9%

U.S. Treasury Bills 3.5%

Inflation 3.0%
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
RISK PREMIUMS

• The “extra” return earned for taking on risk

treasury bills: tín phiếu kho bạc

• Treasury bills are considered to be risk-free

risk premium: phần bù rủi ro

• The risk premium is the return over and above the risk-free rate

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TABLE 12.3: AVERAGE ANNUAL RETURNS AND RISK PREMIUMS
Investment Average Return Risk Premium

Large Stocks 12.1% 8.6%

Small Stocks 16.9% 13.4%

Long-term Corporate Bonds 6.3% 2.8%

Long-term Government Bonds 5.9% 2.4%

U.S. Treasury Bills 3.5% 0.0%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
VARIANCE AND STANDARD DEVIATION OVER A PERIOD
• Variance and standard deviation measure the volatility of asset returns
• The greater the volatility, the greater the uncertainty
• Historical variance = sum of squared deviations from the mean / (number of observations
– 1)

where R1, R2,…RT is return at time 1, 2, …,T; 𝑅 is the average return over the whole period.

• Standard deviation = square root of the variance= 𝑉𝑎𝑟(𝑅)

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE: VARIANCE AND STANDARD DEVIATION OVER A PERIOD
Year Actual Average Deviation from the Mean Squared Deviation
Return Return
1 .15 .105 .045 .002025

2 .09 .105 -.015 .000225

3 .06 .105 -.045 .002025

4 .12 .105 .015 .000225

Totals .42 .00 .0045

Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873

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EXPECTED RETURNS OF A SINGLE ASSET OVER SCENARIOS
• Expected returns are based on the probabilities of possible outcomes
• In this context, “expected” means average if the process is repeated
many times
• Expected return is equal to the sum of the potential returns 𝑅𝑖 multiplied
with the corresponding probability of the returns 𝑃𝑖
𝑛

Expected Return = ෍(Probability of Return) × (Possible Return)

𝑖=1

n index: chỉ số chung của thị trường chứng khoán

E ( R ) =  pi Ri
recossion: suy thoái
or brom: mở rộng'

i =1
223 Faculty of Finance
EXAMPLE: EXPECTED RETURNS OF A SINGLE ASSET
• Suppose you have predicted the following returns for stocks C and T in
three possible states of the economy. What are the expected returns?

State Probability C T
Boom 0.3 15 25
Normal 0.5 10 20
Recession ??? 2 1

• RC = .3(15) + .5(10) + .2(2) = 9.9%

• RT = .3(25) + .5(20) + .2(1) = 17.7%

224 Faculty of Finance

VARIANCE AND STANDARD DEVIATION OF A SINGLE ASSET
• Variance and standard deviation measure the volatility of returns
• Using unequal probabilities for the entire range of possibilities
• Weighted average of squared deviations
𝑛

Variance 𝜎 2 = ෍ Probability × Possible Return − Expected Return 2

𝑖=1
n
Or σ 2 =  pi ( Ri − E ( R )) 2
i =1

Standard deviation is the square root of the variance

225 Faculty of Finance

 EXAMPLE: EXPECTED RETURN AND VARIANCE OF A SINGLE ASSET
Price return [Ri-E(Ri)]^2 [Ri-E(Ri)]*[Rj-E(Rj]
time index GMD MBB Index GMD MBB index GMD MBB Index-GMD Index-MBB
1 710 16,450 13,786
2 783 18,000 13,743 10.3% 9.4% -0.3% 0.13% 0.08% 0.48% 0.01% -0.36%
3 854 19,400 14,906 9.2% 7.8% 8.5% 0.07% 0.01% 0.03% -0.03% -0.03%
4 791 17,800 13,484 -7.4% -8.2% -9.5% 1.98% 2.21% 2.61% 2.44% 2.70%
5 889 23,800 15,337 12.4% 33.7% 13.7% 0.33% 7.34% 0.51% 1.42% 0.24%
6 950 23,450 18,628 6.9% -1.5% 21.5% 0.00% 0.65% 2.20% -0.03% 0.03%
7 1,020 29,500 20,808 7.4% 25.8% 11.7% 0.01% 3.68% 0.26% 0.12% 0.02%
8 1,194 35,750 26,750 17.1% 21.2% 28.6% 1.10% 2.12% 4.81% 1.26% 1.98%
9 1,169 32,700 27,350 -2.1% -8.5% 2.2% 0.77% 2.30% 0.19% 1.55% 0.65%
10 1,239 33,500 30,200 6.0% 2.4% 10.4% 0.00% 0.17% 0.14% 0.04% 0.00%
Mean of return 6.6% 9.1% 9.6%
Variance of return 0.55% 2.25% 1.30%
Covariance 0.85% 0.65%
Correlation 0.76 0.77
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PORTFOLIOS
▪ A portfolio is simply a specific combination of securities, usually defined
by portfolio weights that sum to 1:

• 𝜔𝑖 is the weight of security i; 𝑁𝑖 is the number of security i; 𝑃𝑖 is the price

of security i.

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EXAMPLE: PORTFOLIO WEIGHTS
• Suppose you have $15,000 to invest and you have purchased securities
in the following amounts. What are your portfolio weights in each
security?
• $2000 of DCLK
• $3000 of KO
• $4000 of INTC
• $6000 of KEI
•DCLK: 2/15 = .133
•KO: 3/15 = .2
•INTC: 4/15 = .267
•KEI: 6/15 = .4
228 Faculty of Finance
 PORTFOLIO EXPECTED RETURNS AND VARIANCE
• The expected return of a portfolio is the weighted average of the expected returns of the
respective assets in the portfolio
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛𝑠 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜: 𝐸 𝑅𝑝𝑜𝑟𝑡 = 𝑤𝑖 𝐸 𝑅𝑖 + 𝑤𝑗 𝐸 𝑅𝑗

𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜: 𝑉𝑎𝑟 𝑅𝑝𝑜𝑟𝑡 = 𝑤𝑖2 𝜎𝑖2 + 𝑤𝑗2 𝜎𝑗2 + 2𝑤𝑖 𝑤𝑗 𝐶𝑜𝑣𝑖𝑗

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑡𝑢𝑟𝑛𝑠 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 (stdev): 𝜎𝑝𝑜𝑟𝑡 = 𝑉𝑎𝑟 𝑅𝑃

Where:
• 𝜔𝑖 is the weight of security i
• 𝐸 𝑅𝑖 : expected return of security i
• 𝐶𝑜𝑣𝑖𝑗 : Covariance of security i and j

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 PORTFOLIO EXPECTED RETURNS AND VARIANCE-COVARIANCE OF RETURNS
• A measure of the degree to which two variables “move together” relative to their
individual mean values over time
• For two assets, i and j, the covariance of rates of return is defined as :
𝑛 𝑛
1 1
𝐶𝑜𝑣𝑖𝑗 = ෍ 𝑅𝑖𝑡 − 𝐸 𝑅𝑖 𝑅𝑗𝑡 − 𝐸 𝑅𝑗 𝐶𝑜𝑣𝑖𝑗 = ෍ 𝑅𝑖𝑡 − 𝐸 𝑅𝑖 𝑅𝑗𝑡 − 𝐸 𝑅𝑗
𝑛 𝑛−1
𝑡=1 𝑡=1
• The covariance of a variable with itself:
𝑛 𝑛 2
𝑅𝑖𝑡 − 𝐸 𝑅𝑖 𝑅𝑖𝑡 − 𝐸 𝑅𝑖 𝑅𝑖𝑡 − 𝐸 𝑅𝑖
𝐶𝑜𝑣𝑖𝑖 = ෍ =෍ = 𝜎2
𝑛 𝑛
𝑡=1 𝑡=1

• Note: when applying to sample data, we divide the values by (n – 1) rather than
by n to avoid statistical bias.

230 Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
PORTFOLIO EXPECTED RETURNS AND VARIANCE-CORRELATION
• The correlation coefficient is obtained by standardizing (dividing) the covariance
by the product of the individual standard deviations
Where:
𝐶𝑜𝑣𝑖𝑗
𝜌𝑖𝑗 = ρij = correlation coefficient of returns
𝜎𝑖 𝜎𝑗 σi = standard deviation of Ri
σj = standard deviation of Rj
Note: when sample data is used, σ is divided by (n – 1) to avoid statistical bias.
• The coefficient can vary only in the range +1 to −1
• A value of +1 would indicate perfect positive correlation. This means that returns for
the two assets move together in a positively and completely linear manner
• A value of −1 would indicate perfect negative correlation. This means that the returns
for two assets move together in a completely linear manner, but in opposite directions
231
Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 EXAMPLE: COVARIANCE, CORRELATION BETWEEN TWO RISKY ASSETS
Price return [Ri-E(Ri)]^2 [Ri-E(Ri)]*[Rj-E(Rj]
time index GMD MBB index GMD MBB index GMD MBB Index-GMD Index-MBB
1 710 16,450 13,786
2 783 18,000 13,743 10.3% 9.4% -0.3% 0.13% 0.08% 0.48% 0.01% -0.36%
3 854 19,400 14,906 9.2% 7.8% 8.5% 0.07% 0.01% 0.03% -0.03% -0.03%
4 791 17,800 13,484 -7.4% -8.2% -9.5% 1.98% 2.21% 2.61% 2.44% 2.70%
5 889 23,800 15,337 12.4% 33.7% 13.7% 0.33% 7.34% 0.51% 1.42% 0.24%
6 950 23,450 18,628 6.9% -1.5% 21.5% 0.00% 0.65% 2.20% -0.03% 0.03%
7 1,020 29,500 20,808 7.4% 25.8% 11.7% 0.01% 3.68% 0.26% 0.12% 0.02%
8 1,194 35,750 26,750 17.1% 21.2% 28.6% 1.10% 2.12% 4.81% 1.26% 1.98%
9 1,169 32,700 27,350 -2.1% -8.5% 2.2% 0.77% 2.30% 0.19% 1.55% 0.65%
10 1,239 33,500 30,200 6.0% 2.4% 10.4% 0.00% 0.17% 0.14% 0.04% 0.00%
Mean of return 6.6% 9.1% 9.6%
Variance of return 0.55% 2.25% 1.30%
Covariance 0.85% 0.65%
Correlation 0.76 0.77
232 Faculty of Finance
 EXAMPLE: COVARIANCE, CORRELATION BETWEEN TWO RISKY ASSETS
Price return [Ri-E(Ri)]^2 [Ri-E(Ri)]*[Rj-E(Rj]
time index GMD MBB index GMD MBB index GMD MBB Index-GMD Index-MBB
1 710 16,450 13,786
2 783 18,000 13,743 10.3% 9.4% -0.3% 0.13% 0.08% 0.48% 0.01% -0.36%
3 854 19,400 14,906 9.2% 7.8% 8.5% 0.07% 0.01% 0.03% -0.03% -0.03%
4 791 17,800 13,484 -7.4% -8.2% -9.5% 1.98% 2.21% 2.61% 2.44% 2.70%
5 889 23,800 15,337 12.4% 33.7% 13.7% 0.33% 7.34% 0.51% 1.42% 0.24%
6 950 23,450 18,628 6.9% -1.5% 21.5% 0.00% 0.65% 2.20% -0.03% 0.03%
7 1,020 29,500 20,808 7.4% 25.8% 11.7% 0.01% 3.68% 0.26% 0.12% 0.02%
8 1,194 35,750 26,750 17.1% 21.2% 28.6% 1.10% 2.12% 4.81% 1.26% 1.98%
9 1,169 32,700 27,350 -2.1% -8.5% 2.2% 0.77% 2.30% 0.19% 1.55% 0.65%
10 1,239 33,500 30,200 6.0% 2.4% 10.4% 0.00% 0.17% 0.14% 0.04% 0.00%
Mean of return 6.6% 9.1% 9.6%
Variance of return 0.55% 2.25% 1.30%
Covariance 0.85% 0.65%
Correlation 0.76 0.77
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 PORTFOLIO OF TWO RISKY ASSETS -EXAMPLE
• Example: From 2018-2021, Gemadept had an average monthly return of 9.1%
and a std dev of 15%. Military bank had an average return of 9.6% and a std
dev of 11.41%. Their correlation is 0.51.How would a portfolio of the two
stocks perform, given the weight in the following table?

w_GMD w_MBB E[RP] var(RP) stdev(RP)

0 1 1.08% 0.3881% 6.23%
0.25 0.75 1.25% 0.3616% 6.01%
0.5 0.5 1.42% 0.4459% 6.68%
0.75 0.25 1.58% 0.6409% 8.01%
1 0 1.75% 0.9467% 9.73%

Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
PORTFOLIO OF TWO RISKY ASSETS -MEAN/STANDARD DEVIATION TRADE-OFF

Mean/SD Trade-Off for Portfolios of GMD and MBB

1.90% GMD
Expected return (E[Rp])

1.70% Efficient frontier 1.75%

1.50% 1.58%
1.42% stdev(RP)
1.30% 1.25%
1.10% 1.08%
0.90% MBB
0.70%
0.50%
4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00%
Standard deviation (stdev (Rp))

Faculty of Finance
PORTFOLIO DIVERSIFICATION
• Portfolio diversification is the investment in several different asset classes or sectors
• Diversification is not just holding a lot of assets
• For example, if you own 50 Internet stocks, you are not diversified
• However, if you own 50 stocks that span 20 different industries, then you are
diversified
The Principle of Diversification:
• Diversification can substantially reduce the variability of returns without an equivalent
reduction in expected returns
• This reduction in risk arises because worse than expected returns from one asset are
offset by better than expected returns from another
• However, there is a minimum level of risk that cannot be diversified away and that is
the systematic portion

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TABLE 13.7

237 Faculty of Finance

FIGURE 13.1- THE POWER OF DIVERSIFICATION

238 Faculty of Finance

SYSTEMATIC RISK VS. UNSYSTEMATIC RISK
Systematic Risk Unsystematic risk
• Risk factors that affect a large number of • Risk factors that affect a limited number of
assets assets
• Also known as non-diversifiable risk or • Also known as unique risk and asset-specific
market risk risk, idiosyncratic risk, diversifiable risk
• Includes such things as changes in GDP, • Includes such things as labor strikes, part
inflation, interest rates, etc. shortages, etc.
• There is a reward for bearing risk • The risk that can be eliminated by
• There is not a reward for bearing risk combining assets into a portfolio
unnecessarily • If we hold only one asset, or assets
• The expected return on a risky asset in the same industry, then we are
depends only on that asset’s systematic risk exposing ourselves to risk that we
since unsystematic risk can be diversified could diversify away
away

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TOTAL RISK
• Total risk = systematic risk + unsystematic risk
• The standard deviation of returns is a measure of total risk
• For well-diversified portfolios, unsystematic risk is very small
• Consequently, the total risk for a diversified portfolio is essentially
equivalent to the systematic risk

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MEASURING SYSTEMATIC RISK
• How do we measure systematic risk?
• We use the beta coefficient
• What does beta tell us?
• A beta of 1 implies the asset has the same systematic risk as the overall market
• A beta < 1 implies the asset has less systematic risk than the overall market
• A beta > 1 implies the asset has more systematic risk than the overall market

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WHAT WE HAVE LEARNED SO FAR….
▪ Portfolio risk depends primarily on covariances
– Not stocks’ individual volatilities
▪ Diversification reduces risk
– But risk common to all firms cannot be diversified away
• Everyone has a portfolio on the same efficient frontier
• Hold the tangency portfolio M: Suppose all investors hold the same portfolio M; what must M
be?
→M is the market portfolio
▪ Hold the tangency portfolio M
– The tangency portfolio has the highest expected return for a given level of risk (i.e., the
highest Sharpe ratio)

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 PORTFOLIO: EFFICIENT FRONTIER, TANGENCY PORTFOLIO
2.4%

1.8% Military bank

Tangency
Expected Return

portfolio M
Vinamilk
1.2%
Gemadept

0.6%

T-Bill

0.0%
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
Standard Deviation of Return

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TABLE 13.8

Insert Table 13.8 here

244 Faculty of Finance

TOTAL VS. SYSTEMATIC RISK
• Consider the following information:
Standard Deviation Beta
Security C 20% 1.25
Security K 30% 0.95

• Which security has more total risk?

• Which security has more systematic risk?
• Which security should have the higher expected return?

245 Faculty of Finance

WORK THE WEB EXAMPLE
• Many sites provide betas for companies
• International stock market: Yahoo Finance provides beta, plus a lot of
other information under its Key Statistics link
• Vietnam stock market: cophieu68.vn, cafef.vn

246 Faculty of Finance

EXAMPLE: PORTFOLIO BETAS
• Consider the previous example with the following four securities
Security Weight Beta
DCLK .133 2.685
KO .2 0.195
INTC .267 2.161
KEI .4 2.434
• What is the portfolio beta?
• .133(2.685) + .2(.195) + .267(2.161) + .4(2.434) = 1.947

247 Faculty of Finance

BETA AND THE RISK PREMIUM
• Remember that the risk premium = expected return – risk-free rate
• The higher the beta, the greater the risk premium should be
• Can we define the relationship between the risk premium and beta so
that we can estimate the expected return?
• YES!

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EXAMPLE: PORTFOLIO EXPECTED RETURNS AND BETAS
30%

25%

Expected Return
20%
E(RA)
15%

10%

5%

0%R
f
0 0.5 1 1.5 2 2.5 3
Beta
A

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REWARD-TO-RISK RATIO: DEFINITION AND EXAMPLE
• The reward-to-risk ratio is the slope of the line illustrated in the previous example

• Slope = (E(RA) – Rf) / (A – 0)

• Reward-to-risk ratio for previous example =
(20 – 8) / (1.6 – 0) = 7.5

• What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above
the line)?
• What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below
the line)?

250 Faculty of Finance

MARKET EQUILIBRIUM
• In equilibrium, all assets and portfolios must have the same reward-to-risk
ratio, and they all must equal the reward-to-risk ratio for the market

E ( RA ) − R f E ( RM − R f )
=
A M

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SECURITY MARKET LINE
• The security market line (SML) is the representation of market equilibrium
• The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / M
• But since the beta for the market is ALWAYS equal to one, the slope can
be rewritten
• Slope = E(RM) – Rf = market risk premium

252 Faculty of Finance

THE CAPITAL ASSET PRICING MODEL (CAPM)
• The capital asset pricing model defines the relationship between risk and
return
• E(RA) = Rf + A(E(RM) – Rf)
• If we know an asset’s systematic risk, we can use the CAPM to determine
its expected return
• This is true whether we are talking about financial assets or physical
assets

253 Faculty of Finance

FACTORS AFFECTING EXPECTED RETURN
• Pure time value of money: measured by the risk-free rate
• Reward for bearing systematic risk: measured by the market risk premium
• Amount of systematic risk: measured by beta

254 Faculty of Finance

EXAMPLE - CAPM
• Consider the betas for each of the assets given earlier. If the risk-free rate is 4.15%
and the market risk premium is 8.5%, what is the expected return for each?

Security Beta Expected Return

DCLK 2.685 4.15 + 2.685(8.5) = 26.97%
KO 0.195 4.15 + 0.195(8.5) = 5.81%
INTC 2.161 4.15 + 2.161(8.5) = 22.52%
KEI 2.434 4.15 + 2.434(8.5) = 24.84%

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FIGURE 13.4

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QUICK QUIZ
• How do you compute the expected return and standard deviation for an individual
asset? For a portfolio?
• What is the difference between systematic and unsystematic risk?
• What type of risk is relevant for determining the expected return?
• Consider an asset with a beta of 1.2, a risk-free rate of 5%, and a market return of
13%.
• What is the reward-to-risk ratio in equilibrium?
• What is the expected return on the asset?

257 Faculty of Finance

COMPREHENSIVE PROBLEM
• The risk free rate is 4%, and the required return on the market is 12%.
What is the required return on an asset with a beta of 1.5?
• What is the reward/risk ratio?
• What is the required return on a portfolio consisting of 40% of the asset
above and the rest in an asset with an average amount of systematic
risk?

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END OF CHAPTER

259 Faculty of Finance

 CHAPTER 4
COST OF CAPITAL
KEY CONCEPTS AND SKILLS
• Know how to determine a firm’s cost of equity capital
• Know how to determine a firm’s cost of debt chi phí vốn

• Know how to determine a firm’s overall cost of capital

• Understand pitfalls of overall cost of capital and how to manage them

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 LEARNING OBJECTIVES
Determine Determine a firm’s cost of equity capital.

Determine Determine a firm’s cost of debt.

Determine Determine a firm’s overall cost of capital and how to use it to

value a company.

Explain Explain how to correctly include flotation costs in capital

budgeting projects.

Describe Describe some of the pitfalls associated with a firm’s overall

cost of capital and what to do about them.
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CHAPTER OUTLINE chi phí của dn là suất sinh lời yêu cầu of nhà đầu tư
nợ rẻ hơn vốn chủ sở hữu vì nhà đầu tư yêu cầu sức sinh lời cho nợ ít hơn chủ sỡ hữu ( nguồn
gốc là ở rủi ro
1. The Cost of Capital: Some Preliminaries
dòng thu nhập càng chắc chắn thì càng ít rủi ro
2. The Cost of Equity nợ an toàn hơn vốn chủ sở hữu

3. The Costs of Debt and Preferred Stock

4. The Cost of retained earnings.
5. The Weighted Average Cost of Capital
6. Divisional and Project Costs of Capital
7. Flotation Costs and the Weighted Average Cost of Capital

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1. WHY COST OF CAPITAL IS IMPORTANT
• We know that the return earned on assets depends on the risk of those
assets
• The return to an investor is the same as the cost to the company
• Our cost of capital provides us with an indication of how the market
views the risk of our assets
• Knowing our cost of capital can also help us determine our required
return for capital budgeting projects

định giá cổ phiếu chỉ dùng equity

định giá dn dùng nợ và vốn chủ sở hữu
dòng tiền nào r theo đó
dòng tieenf càng rủi ro r cangf cao
định giá cái nào thì dùng cái đó
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REQUIRED RETURN
• The required return is the same as the appropriate discount rate and is
based on the risk of the cash flows
• We need to know the required return for an investment before we can
compute the NPV and make a decision about whether or not to take the
investment
• We need to earn at least the required return to compensate our investors
for the financing they have provided

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 2. COST OF EQUITY
• The cost of equity is the return required by equity investors given the risk of the cash
flows from the firm
• Business risk: The equity risk that comes from the nature of the firm’s operating activities
phân biệt
• vềFinancial
btap lms nhà risk: The equity risk that comes from the financial policy (the capital structure)
of the firm
• There are two major methods for determining the cost of equity
• Dividend growth model
• SML, or CAPM

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THE DIVIDEND GROWTH MODEL APPROACH
• Start with the dividend growth model formula and rearrange to solve for RE

D1
P0 =
giả định doanh nghiệp tăng trưởng đều mãi mãi RE − g
D1
RE = +g
P0

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DIVIDEND GROWTH MODEL EXAMPLE
• Suppose that your company is expected to pay a dividend of $1.50 per
share next year. There has been a steady growth in dividends of 5.1%
per year and the market expects that to continue. The current price is
$25. What is the cost of equity?

1.50
RE = + .051 = .111 = 11.1%
25

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EXAMPLE: ESTIMATING THE DIVIDEND GROWTH RATE
• One method for estimating the growth rate is to use the historical
average
• Year Dividend Percent Change
• 2005 1.23 -
• 2006 1.30
• 2007 1.36 (1.30 – 1.23) / 1.23 = 5.7%
• 2008 1.43 (1.36 – 1.30) / 1.30 = 4.6%
• 2009 1.50 (1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%
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ADVANTAGES AND DISADVANTAGES OF DIVIDEND GROWTH MODEL
• Advantage – easy to understand and use
• Disadvantages
• Only applicable to companies currently paying dividends
• Not applicable if dividends aren’t growing at a reasonably constant rate
• Extremely sensitive to the estimated growth rate – an increase in g of 1% increases
the cost of equity by 1%
• Does not explicitly consider risk

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THE SML APPROACH
• Use the following information to compute our cost of equity
• Risk-free rate, Rf
• Market risk premium, E(RM) – Rf
• Systematic risk of asset, 

rủi ro hệ thống cổ phiếu e

RE = R f +  E ( E ( RM ) − R f )

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EXAMPLE - SML
• Suppose your company has an equity beta of .58, and the current risk-
free rate is 6.1%. If the expected market risk premium is 8.6%, what is
your cost of equity capital?
• RE = 6.1 + .58(8.6) = 11.1%
• Since we came up with similar numbers using both the dividend growth
model and the SML approach, we should feel good about our estimate

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ADVANTAGES AND DISADVANTAGES OF SML
• Advantages
• Explicitly adjusts for systematic risk
• Applicable to all companies, as long as we can estimate beta
• Disadvantages
• Have to estimate the expected market risk premium, which does vary over time
• Have to estimate beta, which also varies over time
• We are using the past to predict the future, which is not always reliable

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EXAMPLE – COST OF EQUITY
• Suppose our company has a beta of 1.5. The market risk premium is expected to be
9%, and the current risk-free rate is 6%. We have used analysts’ estimates to
determine that the market believes our dividends will grow at 6% per year and our
last dividend was $2. Our stock is currently selling for $15.65. What is our cost of
equity?

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3. COST OF DEBT
• The cost of debt is the required return on our company’s debt
• We usually focus on the cost of long-term debt or bonds
• The required return is best estimated by computing the yield-to-maturity on the
existing debt
• We may also use estimates of current rates based on the bond rating we expect
when we issue new debt
• The cost of debt is NOT the coupon rate

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EXAMPLE: COST OF DEBT
• Suppose we have a bond issue currently outstanding that has 25 years
left to maturity. The coupon rate is 9%, and coupons are paid
semiannually. The bond is currently selling for $908.72 per $1,000 bond.
What is the cost of debt?
• N = 50; PMT = 45; FV = 1000; PV = -908.72; CPT I/Y = 5%; YTM = 5(2) = 10%

 1 
1 -
 (1 + r) t  FV
Bond Value = C  +
 r  (1 + r) t

 

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COST OF PREFERRED STOCK
• Reminders
• Preferred stock generally pays a constant dividend each period
• Dividends are expected to be paid every period forever
• Preferred stock is a perpetuity, so we take the perpetuity formula,
rearrange and solve for RP
• RP = D / P 0

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE: COST OF PREFERRED STOCK
• Your company has preferred stock that has an annual dividend of $3. If the current price
is $25, what is the cost of preferred stock?
• RP = 3 / 25 = 12%

một trong những quyết định trả cổ tức bằng tiền mặt nahf đầu tư sẽ bị đnahs thuế thu nhập cá nhân, còn giữu lại để tái đầu tư phải hiệu quả hơn
viẹc tự đi đầu tư

trả cổ tức bằng cổ phiếu ko có chi phí phát hành

chi phí phát hành là một con số rất lớn

phát hành cổ phiếu tốn chi phí phát hành rất nhiều để trả cho đơn vị bảo lãnh phát hành là ngân hàng, công ty
chứng khoán

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COST OF RETAINED EARNINGS (1) DỊCH LẠI ĐỂ HỈU
lợi nhuận giữu lại
• New common equity is raised in two ways: (1) by retaining some of the current year’s
earnings and (2) by issuing new common stock.
• Retained earnings refers to that part of the current year’s earnings not paid as dividends
(hence, available for reinvestment in the business this year)
• Cost of Retained Earnings (rs) The rate of return required by stockholders on a firm’s
common stock.
• Cost of New Common Stock (re) The cost of external equity; based on the cost of retained
earnings, but increased for flotation costs necessary to issue new common stock
• The firm needs to earn at least as much on any earnings retained as the stockholders could
earn on alternative investments of comparable risk.
• If the firm cannot invest retained earnings to earn at least rs , it should pay those funds to
its stockholders and let them invest directly in stocks or other assets that will provide that
return
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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COST OF RETAINED EARNINGS (2)- MEASURES
• CAPM APPROACH
• BOND-YIELD-PLUS-RISK-PREMIUM APPROACH
• DIVIDEND-YIELD-PLUS-GROWTH-RATE, OR DISCOUNTED CASH FLOW (DCF),
APPROACH

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COST OF RETAINED EARNINGS (2)- MEASURES-CAPM APPROACH
• Step 1: Estimate the risk-free rate, rRF. We generally use the 10-year Treasury bond rate
as the measure of the risk-free rate, but some analysts use the short-term Treasury bill
rate.
• Step 2: Estimate the stock’s beta coefficient, bi , and use it as an index of the stock’s risk.
• Step 3: Estimate the market risk premium. Recall that the market risk premium is the
difference between the return that investors require on an average stock and the risk-
free rate.
• Step 4: Substitute the preceding values in the CAPM equation to estimate the required
rate of return :

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COST OF RETAINED EARNINGS (2)- MEASURES-CAPM APPROACH
• Example: Assume that in today’s market, rRF 5 5.6%, the market risk premium is RPM
55.0%, and Allied’s beta is 1.48. Using the CAPM approach, Allied’s cost of equity is
estimated to be 13.0%:

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COST OF RETAINED EARNINGS (3)- MEASURES
BOND-YIELD-PLUS-RISK-PREMIUM APPROACH
• This measure is usually used when reliable inputs for the CAPM approach are not
available
• Empirical studies suggest that the risk premium on a firm’s stock over its own bonds
generally ranges from 3 to 5 percentage points (evidence from Roger G. Ibbotson for
US stock market) ít rủi ro phải tìm chứ ko lấy 3 5 %
YTM
rs=bond yield + risk premium
Example: Allied’s bonds yield 10%, its cost of equity might be estimated as follows
rs= Bond yield + Risk premium= 10.0% + 4.0% =14.0%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
COST OF RETAINED EARNINGS (2)- MEASURES-DIVIDEND-YIELD-PLUS-GROWTH-RATE, OR DISCOUNTED CASH FLOW (DCF), APPROACH

• According to DCF model, assume P0 is the current stock price, Dt is the dividend expected to
be paid at the end of Year t,rs is the required rate of return. Current stock price is→

If dividends are expected to grow at a constant rate, the above equation reduces to:

solve for rs :
→investors expect to receive a dividend yield, D1/P0, plus a capital gain, g, for a total
expected return of rs

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
4. THE WEIGHTED AVERAGE COST OF CAPITAL
• We can use the individual costs of capital that we have computed to get
our “average” cost of capital for the firm.
• This “average” is the required return on the firm’s assets, based on the
market’s perception of the risk of those assets
• The weights are determined by how much of each type of financing is
used

W D, chi phí sử dụng R D

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CAPITAL STRUCTURE WEIGHTS
• Notation
• E = market value of equity = # of outstanding shares times price per share
• D = market value of debt = # of outstanding bonds times bond price
• V = market value of the firm = D + E
• Weights
• wE = E/V = percent financed with equity
• wD = D/V = percent financed with debt

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EXAMPLE: CAPITAL STRUCTURE WEIGHTS
• Suppose you have a market value of equity equal to $500 million and a market
value of debt equal to $475 million.
• What are the capital structure weights?
• V = 500 million + 475 million = 975 million
• wE = E/V = 500 / 975 = .5128 = 51.28%
• wD = D/V = 475 / 975 = .4872 = 48.72%

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TAXES AND THE WACC
• We are concerned with after-tax cash flows, so we also need to consider the effect of
taxes on the various costs of capital
• Interest expense reduces our tax liability
• This reduction in taxes reduces our cost of debt
• After-tax cost of debt = RD(1-TC)

• Dividends are not tax deductible, so there is no tax impact on the cost of equity
• WACC = wERE + wDRD(1-TC)

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXTENDED EXAMPLE – WACC - I
• Equity Information • Debt Information
• 50 million shares • $1 billion in outstanding debt
(face value) 1 TỶ CỔ HIẾU NHÂN LÊN RA
• $80 per share PV
• Current quote = 110 GIÁ 1 CỔ PHIẾU
• Beta = 1.15
• Coupon rate = 9%,
• Market risk premium = 9% semiannual coupons
• Risk-free rate = 5% • 15 years to maturity

• Tax rate = 40%

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EXTENDED EXAMPLE – WACC - II
• What is the cost of equity?
• RE = 5 + 1.15(9) = 15.35%
• What is the cost of debt? YTM = RD

• N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268

• RD = 3.927(2) = 7.854%
NỬA NĂM 1 LẦN
• What is the after-tax cost of debt?
• RD(1-TC) = 7.854(1-.4) = 4.712%

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EXTENDED EXAMPLE – WACC - III
• What are the capital structure weights?
• E = 50 million (80) = 4 billion
• D = 1 billion (1.10) = 1.1 billion
• V = 4 + 1.1 = 5.1 billion
• wE = E/V = 4 / 5.1 = .7843
• wD = D/V = 1.1 / 5.1 = .2157
• What is the WACC?
• WACC = .7843(15.35%) + .2157(4.712%) = 13.06%

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EASTMAN CHEMICAL I
• Click on the web surfer to go to Yahoo Finance to get information on Eastman
Chemical (EMN)
• Under Profile and Key Statistics, you can find the following information:
• # of shares outstanding
• Book value per share
• Price per share
• Beta

• Under analysts estimates, you can find analysts estimates of earnings growth (use as
a proxy for dividend growth)
• The Bonds section at Yahoo Finance can provide the T-bill rate
• Use this information, along with the CAPM and DGM to estimate the cost of equity

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EASTMAN CHEMICAL II
• Go to FINRA to get market information on Eastman Chemical’s bond issues
• Enter Eastman Ch to find the bond information
• Note that you may not be able to find information on all bond issues due to the
illiquidity of the bond market
• Go to the SEC site to get book valve information from the firm’s most recent 10Q

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EASTMAN CHEMICAL III
• Find the weighted average cost of the debt
• Use market values if you were able to get the information
• Use the book values if market information was not available
• They are often very close
• Compute the WACC
• Use market value weights if available

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
EXAMPLE: WORK THE WEB
• Find estimates of WACC at www.valuepro.net
• Look at the assumptions
• How do the assumptions impact the estimate of WACC?

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TABLE 14.1 COST OF EQUITY

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TABLE 14.1 COST OF DEBT

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
TABLE 14.1 WACC

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
5. DIVISIONAL AND PROJECT COSTS OF CAPITAL
• Using the WACC as our discount rate is only appropriate for projects that
have the same risk as the firm’s current operations
• If we are looking at a project that does NOT have the same risk as the firm,
then we need to determine the appropriate discount rate for that project
• Divisions also often require separate discount rates

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
USING WACC FOR ALL PROJECTS - EXAMPLE
• What would happen if we use the WACC for all projects regardless of
risk?
• Assume the WACC = 15%
Project Required Return IRR
A 20% 17%
B 15% 18%
C 10% 12%

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THE PURE PLAY APPROACH
• Find one or more companies that specialize in the product or service that
we are considering
• Compute the beta for each company
• Take an average
• Use that beta along with the CAPM to find the appropriate return for a
project of that risk
• Often difficult to find pure play companies

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SUBJECTIVE APPROACH
• Consider the project’s risk relative to the firm overall
• If the project has more risk than the firm, use a discount rate greater than the WACC
• If the project has less risk than the firm, use a discount rate less than the WACC
• You may still accept projects that you shouldn’t and reject projects you should accept, but
your error rate should be lower than not considering differential risk at all

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 SUBJECTIVE APPROACH - EXAMPLE
Risk Level Discount Rate

Very Low Risk WACC – 8%

Low Risk WACC – 3%

Same Risk as Firm WACC

High Risk WACC + 5%

Very High Risk WACC + 10%

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
6. FLOTATION COSTS
• The required return depends on the risk, not how the money is raised
• However, the cost of issuing new securities should not just be ignored
either
• Basic Approach
• Compute the weighted average flotation cost
• Use the target weights because the firm will issue securities in these percentages
over the long term

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NPV AND FLOTATION COSTS - EXAMPLE
• Your company is considering a project that will cost $1 million. The project will generate after-tax cash
flows of $250,000 per year for 7 years. The WACC is 15%, and the firm’s target D/E ratio is .6 The
flotation cost for equity is 5%, and the flotation cost for debt is 3%. What is the NPV for the project
after adjusting for flotation costs?
• fA = (.375)(3%) + (.625)(5%) = 4.25%
• PV of future cash flows = 1,040,105
• NPV = 1,040,105 - 1,000,000/(1-.0425) = -4,281

• The project would have a positive NPV of 40,105 without considering flotation costs
• Once we consider the cost of issuing new securities, the NPV becomes negative

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QUICK QUIZ
• What are the two approaches for computing the cost of equity?
• How do you compute the cost of debt and the after-tax cost of debt?
• How do you compute the capital structure weights required for the WACC?
• What is the WACC?
• What happens if we use the WACC for the discount rate for all projects?
• What are two methods that can be used to compute the appropriate discount rate
when WACC isn’t appropriate?
• How should we factor flotation costs into our analysis?

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ETHICS ISSUES

• How could a project manager adjust the cost of capital

(i.e., appropriate discount rate) to increase the likelihood
of having his/her project accepted?
• Is this ethical or financially sound?

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COMPREHENSIVE PROBLEM
• A corporation has 10,000 bonds outstanding with a 6% annual coupon rate, 8 years
to maturity, a $1,000 face value, and a $1,100 market price.
• The company’s 100,000 shares of preferred stock pay a $3 annual dividend, and
sell for $30 per share.
• The company’s 500,000 shares of common stock sell for $25 per share and have a
beta of 1.5. The risk free rate is 4%, and the market return is 12%.
• Assuming a 40% tax rate, what is the company’s WACC?

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 End of Chapter

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
 CHAPTER 5: CAPITAL
STRUCTURE THEORIES
cấu trucs vốn
cc

sử dụng nợ ntn là tốt

thay đổi ctruc vốn là thay đổi phần trăm nợ và vốn mà ko làm thay đổi tổng tsan

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
KEY CONCEPTS AND SKILLS

Understand the effect of financial leverage on cash flows and the

Understand cost of equity

Understand the impact of taxes and bankruptcy on capital structure

Understand choice

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CHAPTER OUTLINE
vay nợ nhiều hay vay nợ ít ảnh hưởng đến rủi ro của cổ đông tăng lên

The Capital Structure Question

The Effect of Financial Leverage tác động của đòn bẫy tài chính

Capital Structure and the Cost of Equity Capital

M&M Propositions I and II with Corporate Taxes lý thuyết M&M

Bankruptcy Costs
Optimal Capital Structure
The Pie Again
The Pecking-Order Theory
Observed Capital Structures

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CAPITAL RESTRUCTURING tái cơ cấu vốn

tăng nợ thfi phải giảm vốn

%D+%E=1
• We are going to look at how changes in capital structure affect the value of the firm,
all else equal
• Capital restructuring involves changing the amount of leverage a firm has without
changing the firm’s assets
đòn bẫy phát hành
• The firm can increase leverage by issuing debt and repurchasing outstanding shares
• The firm can decrease leverage by issuing new shares and retiring outstanding debt

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CHOOSING A CAPITAL STRUCTURE
• What is the primary goal of financial managers?
• Maximize stockholder wealth
• We want to choose the capital structure that will maximize stockholder
wealth
• We can maximize stockholder wealth by maximizing the value of the firm
or minimizing the WACC

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THE EFFECT OF LEVERAGE
• How does leverage affect the EPS and ROE of a firm?
• When we increase the amount of debt financing, we increase the fixed interest
expense
• If we have a really good year, then we pay our fixed cost and we have more left
over for our stockholders
• If we have a really bad year, we still have to pay our fixed costs and we have less
left over for our stockholders
• Leverage amplifies the variation in both EPS and ROE

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EXAMPLE: FINANCIAL LEVERAGE, EPS AND ROE – PART I
• We will ignore the effect of taxes at this stage
• What happens to EPS and ROE when we issue debt and buy back shares
of stock?
HIỆN HỮU CỦA DN KẾ HOẠCH / DJW KIÊNS THAY ĐỎI

TĂNG NỢ= PHÁT HÀNH TRÁI PHIẾU ĐỂ MUA LẠI

CỔ PHIẾU

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CAPITAL STRUCTURE SCENARIOS FOR THE TRANS AM CORPORATION
dãi biến động của ROE và EPScủa có debt và no debt đều như nhau
thay đổi tùy thuộc vào dự báo của nền kte

ROE no debt cao hơn có Debt

= EBIT - I
= NET INCOME / EQUITY

= NETINCOME/NO OF SHARES

317 Faculty of Finance biến động nhiều rủi ro nhiều

EXAMPLE: FINANCIAL LEVERAGE, EPS AND ROE – PART II
• Variability in ROE
• Current: ROE ranges from 6.25% to 1.75%
• Proposed: ROE ranges from 2.5% to 27.5%
• Variability in EPS
• Current: EPS ranges from $1.25 to $3.75
• Proposed: EPS ranges from $0.50 to $5.50
• The variability in both ROE and EPS increases when financial leverage is
increased

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BREAK-EVEN EBIT giao điểm hòa vốn

• Find EBIT where EPS is the same under both the current and proposed
capital structures
• If we expect EBIT to be greater than the break-even point, then leverage
may be beneficial to our stockholders
• If we expect EBIT to be less than the break-even point, then leverage is
detrimental to our stockholders

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EXAMPLE: BREAK-EVEN EBIT

EBIT EBIT − 400,000

=
400,000 200,000
400,000
EBIT = EBIT − 250,000
200,000
EBIT = 2(EBIT − 250,000)
EBIT = $800,000
800,000
EPS = = $2.00
400,000

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 Financial Leverage: EPS and EBIT for the Trans Am Corporation

$6.00

$5.00

Break-even Point:
$4.00 EPS = $2; EBIT = $800,000
EPS

Current
$3.00
Proposed

$2.00

$1.00

$0.00
$500,000 $1,000,000 $1,500,000
800000
EBIT

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CONCLUSIONS
• 1. The effect of financial leverage depends on the company’s EBIT. When EBIT is
relatively high, leverage is beneficial.
• 2. Under the expected scenario, leverage increases the returns to shareholders, as
measured by both ROE and EPS.
• 3. Shareholders are exposed to more risk under the proposed capital structure
because the EPS and ROE are much more sensitive to changes in EBIT in this case.
lợi nhuận kỳ vọng
• 4. Because of the impact that financial leverage has on both the expected return to
cổ đông
stockholders and the riskiness of the stock, capital structure is an important
consideration. cơ cấu vốn

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EXAMPLE: HOMEMADE LEVERAGE AND ROE
• Current Capital Structure • Proposed Capital Structure
• Investor borrows $500 and uses $500 of • Investor buys $250 worth of stock (25
her own to buy 100 shares of stock shares) and $250 worth of bonds paying
10%.
• Payoffs:
• Recession: 100(0.60) - .1(500) = $10 • Payoffs:
• Expected: 100(1.30) - .1(500) = $80 • Recession: 25(.20) + .1(250) = $30
• Expansion: 100(2.00) - .1(500) = $150 • Expected: 25(1.60) + .1(250) = $65
• Expansion: 25(3.00) + .1(250) = $100
• Mirrors the payoffs from purchasing 50
shares of the firm under the proposed • Mirrors the payoffs from purchasing 50
capital structure shares under the current capital structure

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CAPITAL STRUCTURE THEORY
• Modigliani and Miller (M&M)Theory of Capital Structure
• Proposition I – firm value giá trị of dn

• Proposition II – WACC
• The value of the firm is determined by the cash flows to the firm and the
risk of the assets
• Changing firm value
• Change the risk of the cash flows
• Change the cash flows

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CAPITAL STRUCTURE THEORY UNDER THREE SPECIAL CASES
• Case I – Assumptions giá sử mtruong ko có thuế

• No corporate or personal taxes

• No bankruptcy costs
xem xét việc sd nợ để xem ảnh hưởng đến WACC
• Case II – Assumptions ntn

• Corporate taxes, but no personal taxes

• No bankruptcy costs
• Case III – Assumptions
• Corporate taxes, but no personal taxes
• Bankruptcy costs

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CASE I – PROPOSITIONS I AND II
• Proposition I
• The value of the firm is NOT affected
by changes in the capital structure CP

• The cash flows of the firm do not TP

change; therefore, value doesn’t

change

• Proposition II
• The WACC of the firm is NOT
affected by capital structure

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Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking
CASE I - EQUATIONS
khi vay nợ D/V tăng E/V giảm xuống --> WACC ko đổi
THUẾ g như vậy --> gtri dn ko đổi
• Without tax: WACC = RA = (E/V)RE + (D/V)RD
->RE = RA + (RA – RD)(D/E)
-> M&Mtỷ Proposition II, which tells us that the cost of equity depends on three things:
sâuts lợi nhuận yêu cầu trên tài sản của cty
The required rate of return on the firm’s assets, RA; the firm’s cost of debt, RD; and the
ty lệ nợ trên vốn chủ sỡ hữ của cty
firm’s debt-equity ratio, D/E.
RA is the “cost” of the firm’s business risk, i.e., the risk of the firm’s assets
• (RA – RD)(D/E) is the “cost” of the firm’s financial risk, i.e., the additional return
required by stockholders to compensate for the risk of leverage
lợi nhuận bổ sung mà các cổ đông yc để bù đắp cho rr đòn bẫy

khi ko có nợ rr vốn csh cao hơn rr nợ

khi có nợ rr vốn csh thấp hơn rr nợ

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FIGURE 16.3

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CASE I - EXAMPLE
D/E=1.5
D+E= 1 V=2
--> %E= 40% D+E=2 --> D= 2-E
• Data %D=60%

• Required return on assets = 16%; cost of debt = 10%; percent of debt = 45%
• What is the cost of equity?
• RE = 16 + (16 - 10)(.45/.55) = 20.91%
• Suppose instead that the cost of equity is 25%, what is the debt-to-equity ratio?
• 25 = 16 + (16 - 10)(D/E)
• D/E = (25 - 16) / (16 - 10) = 1.5
• Based on this information, what is the percent of equity in the firm?
• E/V = 1 / 2.5 = 40%

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THE CAPM, THE SML AND PROPOSITION II
• How does financial leverage affect systematic risk?
• CAPM: RA = Rf + A(RM – Rf)
• Where A is the firm’s asset beta and measures the systematic risk of the firm’s assets

• Proposition II
• Replace RA with the CAPM and assume that the debt is riskless (RD = Rf)
• RE = Rf + A(1+D/E)(RM – Rf)

RE= Rg + betaA ( 1+ D/E)(Rm-Rg)

RE= Rg + betaE(Rm-Rg)

--> betaE= betaA(1+D/E) financial risk

business risk
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BUSINESS RISK AND FINANCIAL RISK
• RE = Rf + A(1+D/E)(RM – Rf)
• CAPM: RE = Rf + E(RM – Rf)
• E = A(1 + D/E)
• Therefore, the systematic risk of the stock depends on:
• Systematic risk of the assets, A, (Business risk)
• Level of leverage, D/E, (Financial risk)

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CASE II – M&M PROPOSITIONS I AND II WITH CORPORATE TAXES-CASH FLOW

• Interest is tax deductible

• Therefore, when a firm adds debt, it reduces taxes, all else equal
• The reduction in taxes increases the cash flow of the firm
• How should an increase in cash flows affect the value of the firm?

có thuế sẽ có lá tránh thuế từ lãi vay

lãi vay sẽ đc khấu trừ thuế

dn tiêu tiền ròi nộp thuế

cá nhân đóng thuế ròi tiêu tiền

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 tốt hơn vì ko phải trả lãi vay nhưng
CASE II - EXAMPLE phải trả tax nhìu hơn --> dòng tiền
dành cho dn sẽ thấp hơn levered firm
ko nợ có nợ
sd đòn bẫy
Unlevered Firm Levered Firm

EBIT 5,000 5,000

Interest lãi 0 500
Taxable Income thu nhập chịu thuế 5,000 4,500

= EBIT * %tax
5000 * 34%
Taxes (34%) 1,700 34% của 4,500 1,530
= texable income - taxes
Net Income thu nhập ròng 5000 - 1700 3,300 4500 - 1530 2,970
dòng tiền of toàn bộ dn = netincome + lãi vay
CFFA cast flow firm asset 3,300 2970 + 500
3,470
tax shield ( lá tránh thuế )= 1800-1530=170
500 * 34%
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INTEREST TAX SHIELD tiết kiệm thuế từ lãi vay
170 170 170
= 170/RD= I * TC/RD= RD*D*TC/RD= D*TC
• Annual interest tax shield
• Tax rate times interest payment
• 6,250 in 8% debt = 500 in interest expense
• Annual tax shield = .34(500) = 170
• Present value of annual interest tax shield
• Assume perpetual debt for simplicity
• PV = 170 / .08 = 2,125
• PV = D(RD)(TC) / RD = DTC = 6,250(.34) = 2,125

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CASE II- WITH CORPORATE TAXES– M&M PROPOSITION I
• The value of the firm increases by the present value of the annual interest
tax shield
• Value of a levered firm = value of an unlevered firm + PV of interest tax shield
• Value of equity = Value of the firm – Value of debt
• Assuming perpetual cash flows
• VU = EBIT(1-T) / RU GTRI CỦA DN KO VAY NỢ= CF/RU= EBIT ( 1-TC)/RU
• VL = VU + DTC gtri của dn có nợ sẽ tăng lên CFFA without Debt

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EXAMPLE: CASE II – PROPOSITION I
• Data
• EBIT = 25 million; Tax rate = 35%; Debt = $75 million; Cost of debt = 9%;
Unlevered cost of capital = 12%
• VU = 25(1-.35) / .12 = $135.42 million
• VL = 135.42 + 75(.35) = $161.67 million
• E = 161.67 – 75 = $86.67 million

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FIGURE 16.4

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CASE II – PROPOSITION II
• The WACC decreases as D/E increases because of the government
subsidy on interest payments
ko có thuế sẽ ko nhân cho 1 - tc và sẽ nhỏ hơn có thuế
• RA = (E/V)RE + (D/V)(RD)(1-TC)
WACC giảm khi D/A giảm
• RE = RU + (RU – RD)(D/E)(1-TC)
• Example
• RE = 12 + (12-9)(75/86.67)(1-.35) = 13.69%
• RA = (86.67/161.67)(13.69) + (75/161.67)(9)(1-.35)
RA = 10.05%

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EXAMPLE: CASE II –
PROPOSITION II
• Suppose that the firm changes its capital structure so that the debt-to-
equity ratio becomes 1.
• What will happen to the cost of equity under the new capital structure?
• RE = 12 + (12 - 9)(1)(1-.35) = 13.95%
• What will happen to the weighted average cost of capital?
• RA = .5(13.95) + .5(9)(1-.35) = 9.9%

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FIGURE 16.5

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M&M SUMMARY

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M&M SUMMARY

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 COMPREHENSIVE EXAMPLE
• You are given the following information for the Format Co.: EBIT = $126.58; TC = .21; D = $500; RU
= .20 The cost of debt capital is 10 percent. What is the value of Format’s equity? What is the cost of
equity capital for Format? What is the WACC?
Value of the firm if it has no debt: Based on M&M Proposition II with taxes, the cost
of equity is:

From M&M Proposition I with taxes, we know that the value of the
firm with debt
Finally, the WACC is

Because the firm is worth $605 total and the debt is worth $500, the
equity is worth $105:

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CASE III
• Now we add bankruptcy costs
• As the D/E ratio increases, the probability of bankruptcy increases
• This increased probability will increase the expected bankruptcy costs
• At some point, the additional value of the interest tax shield will be offset by the
increase in expected bankruptcy cost
• At this point, the value of the firm will start to decrease, and the WACC will start to
increase as more debt is added

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BANKRUPTCY COSTS
• Direct costs
• Legal and administrative costs
• Ultimately cause bondholders to incur additional losses
• Disincentive to debt financing
• Financial distress
• Significant problems in meeting debt obligations
• Firms that experience financial distress do not necessarily file for bankruptcy

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MORE BANKRUPTCY COSTS
• Indirect bankruptcy costs
• Larger than direct costs, but more difficult to measure and estimate
• Stockholders want to avoid a formal bankruptcy filing
• Bondholders want to keep existing assets intact so they can at least receive that money
• Assets lose value as management spends time worrying about avoiding bankruptcy instead of
running the business
• The firm may also lose sales, experience interrupted operations and lose valuable employees

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OPTIMAL CAPITAL STRUCTURE
• THE STATIC THEORY OF CAPITAL STRUCTURE: The theory that a firm borrows up to
the point where the tax benefit from an extra dollar in debt is exactly equal to the
cost that comes from the increased probability of financial distress.

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FIGURE 16.6: THE STATIC THEORY OF CAPITAL STRUCTURE: THE OPTIMAL
CAPITAL STRUCTURE AND THE VALUE OF THE FIRM

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FIGURE 16.7: THE STATIC THEORY OF CAPITAL STRUCTURE: THE OPTIMAL CAPITAL
STRUCTURE AND THE COST OF CAPITAL

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CONCLUSIONS
• Case I – no taxes or bankruptcy costs
• No optimal capital structure
• Case II – corporate taxes but no bankruptcy costs
• Optimal capital structure is almost 100% debt
• Each additional dollar of debt increases the cash flow of the firm
• Case III – corporate taxes and bankruptcy costs
• Optimal capital structure is part debt and part equity
• Occurs where the benefit from an additional dollar of debt is just offset by the
increase in expected bankruptcy costs

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• Figure 17.8:
The Capital Structure Question

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MANAGERIAL RECOMMENDATIONS
• The tax benefit is only important if the firm has a large tax liability
• Risk of financial distress
• The greater the risk of financial distress, the less debt will be optimal for the firm
• The cost of financial distress varies across firms and industries, and as a manager
you need to understand the cost for your industry

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FIGURE 16.9: THE EXTENDED PIE MODE

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THE VALUE OF THE FIRM
• Value of the firm = marketed claims + nonmarketed claims
• Marketed claims are the claims of stockholders and bondholders
• Nonmarketed claims are the claims of the government and other potential stakeholders

• The overall value of the firm is unaffected by changes in capital structure

• The division of value between marketed claims and nonmarketed claims may be
impacted by capital structure decisions

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THE PECKING-ORDER THEORY
• Theory stating that firms prefer to issue debt rather than equity if
internal financing is insufficient.
• Rule 1
• Use internal financing first
• Rule 2
• Issue debt next, new equity last

• The pecking-order theory is at odds with the tradeoff theory:

• There is no target D/E ratio
• Profitable firms use less debt
• Companies like financial slack

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OBSERVED CAPITAL STRUCTURE
• Capital structure does differ by industry
• Differences according to Cost of Capital 2008 Yearbook by Ibbotson
Associates, Inc.
• Lowest levels of debt
• Computers with 5.61% debt
• Drugs with 7.25% debt
• Highest levels of debt
• Cable television with 162.03% debt
• Airlines with 129.40% debt

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WORK THE WEB EXAMPLE
• You can find information about a company’s capital structure relative to its industry,
sector and the S&P 500 at Reuters
• Click on the web surfer to go to the site
• Choose a company and get a quote
• Choose Ratio Comparisons

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QUICK QUIZ
• Explain the effect of leverage on EPS and ROE
• What is the break-even EBIT, and how do we compute it?
• How do we determine the optimal capital structure?
• What is the optimal capital structure in the three cases that were discussed in this
chapter?
• What is the difference between liquidation and reorganization?

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ETHICS ISSUES
• Suppose managers of a firm know that the company is approaching financial distress.
• Should the managers borrow from creditors and issue a large one-time dividend to shareholders?
• How might creditors control this potential transfer of wealth?

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COMPREHENSIVE PROBLEM
• Assuming perpetual cash flows in Case II - Proposition I, what is the value of the
equity for a firm with EBIT = $50 million, Tax rate = 40%, Debt = $100 million, cost
of debt = 9%, and unlevered cost of capital = 12%?

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END OF CHAPTER

362
Dr. Duong Thị Thuy An Faculty of Finance Ho Chi Minh University of Banking