FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
FINA2010 Financial Management
Revision handbook
Contents:
Pages
Chapter 1 Introduction to Corporate Finance
2-4
Chapter 5 Introduction to Valuation: The Time Value of Money
5-7
Chapter 6 Discounted Cash Flow Valuation
8-13
Chapter 7 Interest rate and Bond Valuation
14-21
Chapter 8 Stock Valuation
22-25
Chapter 9 Net Present Value and Other Investments Criteria
26-32
Chapter 10 Making Capital Investment Decisions
33-38
Chapter 14 Cost of Capital
39-43
Chapter 16 Financial Leverage and Capital Structure Policy
44-48
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FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
Chapter 1 Introduction to Corporate Finance
1.1 Corporate Finance and the Financial Manager
Financial Managers need to
Definition
make decision of …
Capital budgeting
Process of planning and managing a
firm’s long-term investments in
fixed assets.
Capital structure
Mix of debt (borrowing) and equity
(ownership interest) to finance
operations
Working capital
Manage short-term assets and
management
liabilities
Chief Financial Officer (CFO)
or Vice-President of Finance
Subordinate 1: Controller
Subordinate 2: Treasurer
Concerns
The size, the type of fixed assets,
timing and riskiness of future cash
flows
Financing cost (interest), the size,
timing, source and optimal mix
The size of inventory, credit
policy and source
Coordinates the activities of the treasurer and the controller
Oversees cost and financial accounting, taxes, and
information systems.
Oversees cash management, credit management, financial planning,
and capital expenditures.
1.2 Forms of Business Organization
Characteristics
Sole
Proprietorship
Owned by one person
Partnership
Multiple owners, but not incorporated.
General
partnership
Limited
partnership
Share in gains or losses;
Unlimited liability
General partners:
Run business; unlimited liability.
Corporation
Limited partner:
Not run business;
Limited liability according to contribution
to the partnership
Composed of one or more owners;
Distinct legal person, which has many
rights, duties and privileges,
Setup doc.: articles and a set of bylaws
(Articles: include company’s name,
intended life, business purpose, maximum
shares issued)
(By-laws: rules to regulate company itself,
such as election methods of directors.)
Advantages
Disadvantages
Ease of start-up,
Lower regulation,
Owner keeps all profits,
Taxed once as personal income
More equity capital available
than a sole proprietorship,
Relatively easy to start,
Income taxed once at personal
tax rate.
Limited life,
Limited equity capital,
Unlimited liability (personally responsible),
Low liquidity
Unlimited liability for general partners,
Dissolution when partner dies or wishes to
sell,
Difficult to transfer ownership,
Low liquidity.
Limited liability,
Unlimited life,
Separation of ownership and
management,
High liquidity,
Ease of raising capital.
Agency costs (from separation of ownership
and management),
Double taxation (although a reduction by
new tax law).
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FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
1.3 The Goal of Financial Management
Corporation: maximization of (market) value for owners (equity-holders)
Methods: Maximizing current stock price (incorporate expectations about the future of the company and
trade-off between short-run profits and long-run profits), Realizing profits from management’s vision and
strategies, etc.
Sarbanes-Oxley Act
Aim
Intended results
Unintended results
Require a) the assessment of internal control structure and financial reporting in
annual report; b) the signature of corporate officers (declare no false and omit
presentation; being responsible to internal control and accurate presentation, e.g.
disclose deficiencies; c) the approval from auditor’s evaluation
Protect investors from corporate abuses (e.g. personal loans from a company to
its officers)
More detailed and accurate financial reporting;
Increased management awareness of internal controls;
Increased responsibility for corporate officers;
Identification of internal control weaknesses
Delisting from the exchanges (Going dark)
1.4 The Agency Problem and Control of the Corporation
Agency relationships
Agency problem
Direct costs
Indirect costs
Corporate Control
Proxy fight
Takeover
Stakeholders
The relationship between stockholders and management. This occurs when one
party (principal) hires another (agent) to represent their interests.
Possible conflicts of interest between the principals and agents. In other words,
management goals (such as focusing on profits instead of equity, the
independence of decision-making power and perks) may be different from
shareholders’ goals.
Corporate expenditures to benefit (e.g. incentive-based compensation) and
monitor (e.g. extra auditor fees) management. Bonus and stock options (for
management to have ownership) and job promotion are structured incentives.
Sub-optimal decisions (reject too risky projects that may fails to protect job
security)
E.g. Proxy fight and Takeover
This is to trigger replacing existing management by unhappy stockholders. Proxy
is the authority to vote someone else’s stock.
It may result in better management since existing management fears they will be
replaced.
Any person or entity, other than a stockholder or creditor, who potentially has a
claim on the cash flows of a firm.
1.5 Financial markets and the Corporation
Primary market
Secondary market
The market in which securities are sold by the company.
E.g. Public and private placements of securities (such as IPO), SEC registration,
and underwriters.
The market where securities that have already been issued are traded between
investors.
E.g. Stock exchanges (NYSE, HKEx) and Over-the-counter (OTC) market
(NASDAQ)
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Dr Haynes Yung
Concept check:
1. What are the area(s) of capital budgeting?
I. the identification of investment opportunities that have a positive net value
II. the mix of long-term debt and equity used to finance a firm's operations.
III. planning and manage a firm’s long-term investments in fixed assets
IV. the daily control of a firm's short-term assets and short-term liabilities
V. the assessment of prospective project that have a positive net value
A. I, III, IV
B. I, III, V
C. II, III, IV
D. I, III, IV, V
2. Which one of the following grants someone the right to vote on behalf of a shareholder?
A. employment contract
B. articles of corporation
C. proxy
D. stock agreement
E. personal authorization letter
3. Which one of the following parties has ultimate control of a corporation?
A. liquidators
B. shareholders
C. board of directors
D. chief executive officer
E. debtholders
Solution:
1. B
2. C
3. B
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FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
Chapter 5 Introduction to Valuation: The Time Value of Money
Future value (FV)
Interest rate (r)
Compounding
Interest on
interest
Compound
interest
Simple interest
Present value
(PV)
Discounting
Discount rate
Discounted cash
flow (DCF)
valuation
The amount of money an investment will grow to over some period of time at
some given interest rate.
The “exchange rate” between earlier money and later money, which also called
Implicit rate of return, Discount rate, Cost of capital, Opportunity cost of capital,
Required return.
This process of leaving your money and any accumulated interest in an investment
for more than one period, thereby reinvesting the interest.
Interest earned on the reinvestment of previous interest payments.
E.g. invested $200 two years ago, r=10%.
=>$20 interest from $220 in 1st year.
He reinvested the $20.
=>$22 interest on his $220 in 2nd year.
The extra $2 he earned in 2nd year is “interest on interest”.
Interest earned on both the initial principal and the interest reinvested from prior
periods.
Interest earned only on the original principal amount invested, without investing
interest.
The current value of future cash flows discounted at the appropriate discount rate.
Calculate the present value of future cash flows.
The rate used to calculate the present value of future cash flows.
Calculating the present value of a future cash flow to determine its value today.
Calculation:
FV = PV(1 + r)t & PV = FV / (1 + r)t
Rearrange (r and t):
FV = PV(1 + r)t
where FV = future value
PV = present value
r = period interest rate
t = number of periods
Future value interest factor (FVIT) = (1 + r)t
E.g. FVIF(10%,4) = 1.14 = 1.464
Present value interest factor (PVIT) =
1
(1+𝑟)𝑡
𝐹𝑉 1
r = ( )𝑡 − 1
𝑃𝑉
E.g. PV=$100, FV=$150, 6 periods (r=7%)
𝑙𝑛(
𝐹𝑉
)
𝑃𝑉
t = 𝑙𝑛(1+𝑟)
E.g. PV=$100, FV=$150, 7% (t=6)
E.g. PVIF(10%,4) = 1 / 1.14 = .683
Rule of 72 can estimate how long it takes to double a sum of money
Time to double money = 72 / (interest rate per year)
E.g. If r = 9% p.a., 8 years to double the money
Time to double money = 72 / 9% = 8 years
If 8 years to double the money, r= 9% p.a.
Interest rate per year = 72 / 8 years = 9%
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FINA2010 Financial Management (2018-2019)
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Self-test:
(a) 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?
(b) Suppose you had a relative who deposited $100 at 5.5% interest 200 years ago. How much would the
investment be worth today? (i) using simple interest (ii) using compounded interest.
(c) How long will it take your $10,000 to double in value if it earns 5% annually?
(d) What is the annual implied rate of interest if $1,000 grows into $4,000 in 20 years?
Concept Check:
1. Today, you deposit $4,000 into a retirement savings account. The account will compound interest at
3% annually. You decide not to withdraw any principal or interest until you retire in fifty years. Which
one of the following statements is correct?
A. The total amount of interest you will earn will equal $4,000  0.03  50.
B. The interest amount you earn will triple in value every year.
C. The interest you earn ten years from now will equal the interest you earn twenty years from now.
D. The future value of this amount is equal to $4,000  (1 + 50)0.03.
E. The present value of this investment is equal to $4,000.
2. Your best friend will give you $5,000 when you graduate. He expects you to graduate three years from
now. What is the change of the present value of this gift if you join a 2-year exchange program and delay
your graduation by two years?
A. becomes negative
B. increases
C. cannot be determined from the information provided
D. decreases
3. You invested $1,000 in an account that pays 2% simple interest. How much more could you have
earned over a 40-year period if the interest had compounded annually?
A. $406.04
B. $407.04
C. $408.04
D. $704.40
E. $804.40
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FINA2010 Financial Management (2018-2019)
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4. A year ago, you deposited $10,000 into a retirement savings account at a fixed rate of 1.5%. Today,
you could earn a fixed rate of 2% on a similar type account. However, your rate is fixed and cannot be
adjusted. How much less could you have deposited last year if you could have earned a fixed rate of 2%
and still have the same amount as you currently will when you retire 49 years from today?
A. $2,022.01 less
B. $2,139.91 less
C. $2,178.44 less
D. $2,231.73 less
E. $2,294.03 less
5. You decide to buy a new apartment in the future. One choice is $5 million standard flat in a new town.
Another choice is $10 million luxury house in Central Business District. You have $200,000 today that
can be invested at your bank. The bank pays 5% annual interest on its accounts. How many years less
would you take to save enough money to afford buying the cheaper flat, rather than the luxury house?
Assume the price of both apartments remains constant.
A. 14.21 years less
B. 14.41 years less
C. 14.61 years less
D. 14.81 years less
E. 15.01 years less
Solution:
Self-test
(a) PV = 19,671.51 / (1.07)10 = 9,999.998 = 10,000
(b) (i) 100 + 200(100)(0.055) = 1200
(ii) 100(1.055)200 = 4,471,898
(c) 14.2 years
(d) 7.18%
Concept Check
1. E
2. D
3. C [($1000*1.02^40)-($1000+$1000*0.02*40) = $408.0397]
4. C [$10000-(($10000*1.015^50)*(1/(1.02^50))) = $2178.4374]
5. A [$5,000,000 = $200,000*(1 + 0.05)t; t = 65.9739 years
$10,000,000 = $200,000*(1 + 0.05)t; t = 80.1806 years
Answer = 14.2067]
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FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
Chapter 6 Discounted Cash Flow Valuation
Annuity
Ordinary
annuity
Annuity due
Perpetuity
Growing
annuity
Effective
Annual Rate
(EAR)
Annual
Percentage
Rate (APR)
EAR vs APR
Pure discount
loan
Interest-Only
Loan
Amortized
loan
Equal payments occurred at regular intervals over a stated time period
The annuity which the first payment occurs at the end of the period
The annuity which the first payment occurs at the beginning of the period
Infinite series of equal payments paid at equal time intervals
Also called “consols” in Britain
E.g. Preferred stock (preference stock)
A growing stream of cash flows with a fixed maturity
The actual rate paid (or received) after accounting for compounding that occurs during the
year.
// The interest rate expressed as if it were compounded once per year.
Annual rate that is quoted by law or a lender.
// The interest rate charged per period multiplied by the number of periods per year.
// The interest rate expressed in terms of the interest payment made each period. It is also
called “stated interest rate” or “quoted interest rate”.
APR is a stated rate and is computed as (r x n), where r is the rate per period and n is the
number of periods per year. EAR considers compounding and is computed as (1 + r)n - 1.
EAR is higher than APR as long as the account is compounded more than once a year and
the interest rate is greater than zero. The EAR is the equivalent rate based on annual
compounding. EAR has greater importance because it is the actual cost of a loan.
The borrower receives money today and repays a single lump sum at a point of time in the
future. (Receive principal at once + Repay principal at once)
E.g. 1-year, 10% T-bill  T0: +$1000 (Inflow); T1: -$1100 (Outflow)
The borrower to pay interest each period and to repay the entire principal (the original
loan amount) at some point in the future. If there is only one period, a pure discount loan
and an interest-only loan is the same.
(Receive principal at once + Repay principal at once + Repay interest in many times)
E.g. 3-year, 7% corporate bonds
 T0: +$1000 (Inflow); T1: -$70 (Outflow); T2: -$70 (Outflow); T3: -$1070 (Outflow)
The process of providing for a loan to be paid off by making regular payments, including
both interest and principal amounts. The amounts of principal and interest need not be
fixed in each increments.
(Receive principal at once + Repay principal and interest in many times)
E.g. 4-year (Medium-term), 30% business loans (fixed principal + varied interest)
 T0: +1000 (inflow); T1: -$550 (250+300) (Outflow); T2: -$475 (250+225) (Outflow);
T3: -$400 (250+150) (Outflow); T4: -$325 (250+75) (Outflow) [Total interest: $750]
Note:
 Cash flows occur at the end of each period are implicitly assumed, i.e. ordinary annuity.
 If you are looking at monthly periods, you need a monthly rate. If you have an APR based on
monthly compounding, you have to use monthly periods, or adjust the interest rate appropriately if
you have payments other than monthly.
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Formula:
Ordinary
annuity
1

1  (1  r ) t
PV  C 
r







Eg. $4,000 annual saving for 50 years;
4% p.a.; what is the value today?
(Answer: $85,928.74)
Eg. $4,000 saving a year; 4% p.a.;
what is the value at the end of 50
years? (Answer: $610,668.3)
 (1  r ) t  1
FV  C 

r


Annuity due
1

1  (1  r ) t
PV  C 
r




 (1  r )


E.g. $1m is saved five years from now.
An annuity is to set aside on the first
day of each month starting today.
Saving rate is 3% p.a. What is the
amount to save each month? (Answer:
$15,430.12)
 (1  r ) t  1
FV  C 
 (1  r )
r


Perpetuity
Growing
annuity
𝑃𝑉 =
𝐶
𝑟
C
C  (1  g )
C  (1  g )t 1
PV 


(1  r )
(1  r ) 2
(1  r )t
t
C   (1  g )  

PV 
1  
r  g   (1  r )  


EAR
E.g. The first payment is $1,000,
receive payments for 10 years,
expected growth rate is 3%, discount
rate is 5%. What is the present value?
(Answer: $8747.6)
m
 APR 
EAR  1 
1
m 

where m is the number of compounding periods
per year
APR
APR  m (1  EAR)

1
m
- 1

E.g. EAR=30%, compounded
quarterly, what is APR? (Answer:
27.12%)
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FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
Self-test:
1. A mortgage requires you to pay $70,000 at the end of each of the next 8 years. The interest rate is 8%.
(a) What is the present value of these payments?
(b) Calculate for each year the loan balance that remains outstanding, the interest payment on the loan,
and the reduction in the loan balance.
2. You estimate that by the time you retire in 35 years, you will have accumulated savings of $2 million.
If the interest rate is 8% and you live 15 years after retirement, what annual level of expenditure will
those savings support? Unfortunately, inflation will eat into the value of your retirement income. Assume
a 4% inflation rate and work out a spending program for your retirement that will allow you to increase
your expenditure in line with inflation.
3. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated
retirement at age 65. She wants to be able to withdraw $105,000 from her savings account on each
birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your
friend intends to invest her money in the local credit union, which offers 7% interest per year. She wants
to make equal annual payments on each birthday into the account established at the credit union for her
retirement fund.
(a) If she starts making these deposits on her 36th birthday and continues to make deposits until she is
65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able
to make the desired withdrawals at retirement?
(b) Suppose your friend has just inherited a large sum of money. Rather than making equal annual
payments, she has decided to make one lump sum payment on her 35th birthday to cover her
retirement needs. What amount does she have to deposit?
(c) Suppose your friend’s employer will contribute $1,500 to the account every year as part of the
company’s profit-sharing plan. In addition, your friend expects a $150,000 distribution from a
family trust fund on her 55th birthday, which she will also put into the retirement account. What
amount must she deposit annually now to be able to make the desired withdrawals at retirement?
Concept Check:
1. Here are two annuities which provide monthly payments of $800 for seven years and pay 3% interest
per quarter. Annuity A and annuity B will pay you on the first day and the last day of each month
respectively. Which one of the following statements is correct?
A. These two annuities have equal present values as of today and equal future values at the end of year
seven.
B. Annuity B has a greater future value than annuity A.
C. Annuity A has a greater present value than annuity B.
D. Annuity A is an ordinary annuity.
E. Annuity B is an annuity due.
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Dr Haynes Yung
2. Mary and Peter receive $480 on the first day and the last day of each month respectively. Both two
annuities will last for next three years. If discount rate is equal to 9.5%, what is the difference of the
present values between them?
A. $110.54
B. $112.06
C. $114.32
D. $116.08
E. $118.63
3. A project considered by the Chinese Press has an initial cash outflow of $500,000. The project will
offer cash inflows of $5,000 monthly for 120 months. What is the return rate?
A. 3.62%
B. 3.74%
C. 3.86%
D. 3.89%
E. 3.94%
4. The cash flows of Wi-Fi project are to pay $70,000 today, to receive $30,000 one year from today, a
payment of $60,000 three years from today and the final receipt of $160,000 four years from today. What
is the present value if the discount rate is 10%?
A. $20,169
B. $20,440
C. $20,752
D. $21,476
E. $21,861
5. What is APR on a bank loan if a stated rate is 5% per quarter?
A. 5%
B. 20%
C. 40%
D. 60%
E. 80%
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FINA2010 Financial Management (2018-2019)
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Solution:
Self-test
1. (a)
 1

1
PV  $70,000  

 $402,264.7 3
8 
 0.08 0.08  (1.08) 
(b)
Beginning-ofYear Balance
($)
402,264.73
364,445.91
323,601.58
279,489.71
231,848.88
180,396.79
124,828.54
64,814.82
Year
1
2
3
4
5
6
7
8
2.
Year-End
Interest on
Balance ($)
32,181.18
29,155.67
25,888.13
22,359.18
18,547.91
14,431.74
9,986.28
5,185.19
Total
Year-End
Payment ($)
70,000.00
70,000.00
70,000.00
70,000.00
70,000.00
70,000.00
70,000.00
70,000.00
Amortization
of Loan ($)
37,818.82
40,844.33
44,111.87
47,640.82
51,452.09
55,568.26
60,013.72
64,814.81
End-of-Year
Balance ($)
364,445.91
323,601.58
279,489.71
231,848.88
180,396.79
124,828.54
64,814.82
0.01
This is an annuity problem with the present value of the annuity equal to $2 million (as of
your retirement date), and the interest rate equal to 8% with 15 time periods. Thus, your
annual level of expenditure (C) is determined as follows:
1

1
PV  C   
t 
 r r  (1  r) 
 1

1
$2,000,000  C  

15 
 0.08 0.08  (1.08) 
C  $233,659
With an inflation rate of 4% per year, we will still accumulate $2 million as of our retirement
date. However, because we want to spend a constant amount per year in real terms (R, constant
for all t), the nominal amount (Ct) must increase each year. For each year t: R = Ct /(1 + inflation
rate)t
Therefore:
PV [all Ct ] = PV [all R  (1 + inflation rate)t] = $2,000,000
 (1  0.04)1 (1  0.04) 2
(1  0.04)15 
R 


.
.
.

  $2,000,000
1
2
(1 0.08)15 
 (1 0.08) (1  0.08)
R  [0.9630 + 0.9273 + . . . + 0.5677] = $2,000,000
R  11.2390 = $2,000,000
R = $177,952
Alternatively, consider that the real rate is
(1  0 .08)
 1  .03846. Then, redoing the steps
(1 0.04)
above using the real rate gives a real cash flow equal to:
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C  $2,000,000


1
1

  $177,952

 0.03846 0.03846  (1.03846) 15 
Thus C1 = ($177,952  1.04) = $185,070, C2 = $192,473, etc.
3. PVA = $105,000{[1 – (1/1.07)20] / 0.07} = $1,112,371.50
This amount is the same for all three parts of this question.
(a) If your friend makes equal annual deposits into the account, this is an annuity with the FVA equal to
the amount needed in retirement. The required savings each year will be:
FVA = $1,112,371.50 = C[(1.0730 – 1) / 0.07]
C = $11,776.01
(b) Here we need to find a lump sum savings amount. Using the FV for a lump sum equation, we get:
FV = $1,112,371.50 = PV(1.07)30
PV = $146,129.04
(c) In this problem, we have a lump sum savings in addition to an annual deposit. Since we already know
the value needed at retirement, we can subtract the value of the lump sum savings at retirement to find out
how much your friend is short.
FV of trust fund deposit = $150,000(1.07)10 = $295,072.70
So, the amount your friend still needs at retirement is:
FV = $1,112,371.50 – 295,072.70 = $817,298.80
Using the FVA equation, and solving for the payment, we get:
$817,298.80 = C[(1.07 30 – 1) / 0.07]
C = $8,652.25
This is the total annual contribution, but your friend’s employer will contribute $1,500 per year you’re
your friend must contribute:
Friend's contribution = $8,652.25 – 1,500 = $7,152.25
Concept Check
1. C
2. E [PV of Mary’s annuity = $480*(1-(1/(1+(0.095/12))^36))/(0.095/12)*(1+0.095/12) = $15,103.199
PV of Peter’s annuity = $480*(1-(1/(1+(0.095/12))^36))/(0.095/12) = $14,984.571
Difference = $15,103.199 - $14,984.571 = $118.628]
3. B [$500,000 = $5,000*(1-(1/(1+(r/12))^120))/(r/12); r = 3.7368%]
4. D [-$70,000 + $30,000/1.1 - $60,000/1.1^3 + $160,000/1.1^4 = $21,475.992]
5. B [5%*4 = 20%]
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Chapter 7 Interest rate and Bond Valuation
Bond
Coupon
Face value
Coupon rate
Maturity
Level coupon
bond
Yield to
maturity (YTM)
Current yield
Current yield vs
YTM
Par value bond
Discount bond
Premium bond
Interest rate
risk
Price risk
Reinvestment
rate risk
Long-term IOUs, usually interest-only loans.
The stated, regular interest payment made on a bond.
The principal amount of a bond that is repaid at the end of the term. Also called
par value.
The annual coupon divided by the face value of a bond, quoted as a % of face value.
The specified date on which the face value of a bond is paid, usually in years.
The bond which coupon is constant and paid every year
The rate required in the market on a bond, called bond “yield” for short. Also, it is
the rate implied by the current bond price as it makes the discounted cash flows
from a bond equal to the bond’s market price.
A bond’s annual coupon divided by its market price
Yield to maturity = current yield + capital gains yield
E.g.: 10% coupon bond, with semiannual coupons, face value of $1,000, 20 years to
maturity, bond price of $1,197.93
Explanation:
Current yield = 100 / 1,197.93 = 0.0835 = 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 = -0.0035 = -0.35%
YTM = 8.35 - 0.35 = 8%
In other words, buying a premium bond and holding it to maturity ensures capital
losses over the life of the bond; however, the higher-than-market coupon will
exactly offset the losses. The opposite is true for discount bonds.
A bond sells for its par value.
A bond sells for the price below par value.
If YTM > coupon rate, then par value > bond price
Why? The discount provides yield above coupon rate.
A bond that sells for the price above par value.
If YTM < coupon rate, then par value < bond price
Why? Higher coupon rate causes value above par.
The risk that arises for bond owners from fluctuating interest rates. How much
interest rate risk a bond has depends on how sensitive its price to interest rate
changes is. Price risk and reinvestment risk are two kinds of interest rate risk.
Change in price due to changes in interest rates.
Longer term bonds & lower coupon rate bonds have more price risk.
Uncertainty concerning rates at which cash flows can be reinvested.
Shorter term bonds & higher coupon rate bonds have more reinvestment risk.
Bond pricing
Bonds of similar risk (and maturity) will be priced to yield about the same return,
theorems
regardless of the coupon rate.
Debt vs Equity
Debt
Equity
(Characteristics)  Not an ownership interest
 Ownership interest
 Creditors do not have voting rights  Common stockholders vote for the
board of directors and other issues
 Interest is considered a cost of
 Dividends are not considered a cost
doing business and is tax
deductible
of doing business and are not tax
deductible
 Creditors have legal recourse if
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interest or principal payments are
missed
Excess debt can lead to financial
distress and bankruptcy
Bond indenture
Terms of a
bond

Dividends are not a liability of the
firm, and stockholders have no legal

recourse if dividends are not paid
 An all equity firm cannot go
bankrupt merely due to debt since it
has no debt
Written legal agreement between issuer and creditors (bondholders) detailing terms
of borrowing. (Also, deed of trust.) The indenture includes the following provisions:
(1) The basic terms of the bonds
(2) The total face amount of bonds issued
(3) A description of property used as security (if applicable)
(4) Sinking fund provisions
(5) Call provisions
(6) Details of protective covenants
Include face value, par value, and form
Registered Forms
Bearer Forms
The registrar of the company records
Bond is issued without record of the
ownership of each bond; payment is
owner’s name; payment is made to
made directly to the owner of record.
whomever holds the bond (physical
possession).
Sinking fund
provisions
Call provisions
Protective
covenants
Issuer makes periodic payments to retire part of the outstanding bond (Early
redemption). For a sinking fund, it is an account managed by a trustee.
It allows bond issuer to retire (repurchase) part or all of the bond at call price.
It limits on carrying out certain activities of the bond issuers (borrower) during the
term of the loan, usually to protect the interests of bondholders (lender), e.g. limit on
the amount of debt, amount of dividend, etc.
Security
There are four kinds of securities.
(1) Collateral – secured by financial securities
(2) Mortgage – secured by real property, normally land or buildings
(3) Debentures – Unsecured debt with 10 or more years to maturity (in US); Secured
debt (in UK)
E.g. 20-year, 10% unsecured bonds at par  debenture
(4) Notes – unsecured debt with original maturity less than 10 years
E.g. 7.5%, $1 million in unsecured, non-callable debt, matures 8 years from now.
Order of precedence of claims (payments).
Subordinated debenture – of lower priority than senior debt
Seniority
High Grade
Medium Grade
Investment
Grade
Low Grade
Moody’s Aaa, S&P and Fitch AAA – capacity to pay is extremely strong
Moody’s Aa and S&P AA – capacity to pay is very strong.
Moody’s A, S&P and Fitch A – capacity to pay is strong, but more susceptible
to changes in circumstances
Moody’s Baa, S&P and Fitch BBB – capacity to pay is adequate, adverse
conditions will have more impact on the firm’s ability to pay.
Rating of Baa or BBB and above
Moody’s Ba and B, S&P and Fitch BB and B - considered possible that the
capacity to pay will degenerate.
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Very Low
Grade
Moody’s C (and below) and S&P and Fitch C (and below) – income bonds with
no interest being paid, or in default with principal and interest in arrears.
Government
Bonds
Long-term debt instruments issued by a governmental entity.
Treasury Securities
Municipal Securities
Federal government debt which are
Debt of state and local
exempt from state taxation
governments
 T-bills – pure discount bonds with
 Varying degrees of default risk,
original maturity of one year or less
rated similar to corporate debt
 T-notes – coupon debt with original
 Interest received is tax-exempt
maturity between one and ten years
at the federal level
 T-bonds – coupon debt with original
maturity greater than ten years
Zeroes are pure discount loans (only one repayment at maturity), deep discount
bonds. Bonds are offered at deep discounts because there are no periodic coupon
payments. The entire yield-to-maturity comes from the difference between the
purchase price and the par value, so it has a higher price risk than a comparable
coupon bond.
 Coupon payments of floaters adjust periodically according to an index.
 Floaters have less price risk and maintain a fixed real return.
 Coupons may have a “collar” – the rate cannot go above a specified “ceiling”
or below a specified “floor”.
 Examples – adjustable rate mortgages and inflation-linked Treasuries (ibond
in H.K.). In US, I-bonds are an inflation-indexed savings bond designed for
the individual investor, e.g. “TIPS” (Treasury Inflation-Protected Securities).
They pay an interest rate equal to a fixed rate plus the inflation rate. The
fixed rate is fixed for the 30-year possible life of the bond, and the inflation
rate is adjusted every six months. Interest is added to the bond value each
month but compounded semiannually.
It is issued by property and casualty companies to help fund excessive claims.
Pay interest and principal as usual unless claims reach a certain threshold for a
single disaster. At that point, bondholders may lose all remaining payments.
Also, it demands a higher required return.
Coupon is paid if corporate income is sufficient. If earnings are not enough to
cover the interest payment, it is not owed. Also, it demands a higher required
return.
Bonds can be converted into a fixed number of shares of common stock at the
bondholders discretion.
Shareholders can redeem for par at their discretion.
Most transactions are OTC (over-the-counter) transactions with dealers
connected electronically. OTC market is not transparent. Daily bond trading
volume (in dollars) exceeds stock trading volume, but trading in individual
issues tends to be very thin.
Zero-coupon
bonds
Floating-rate
bonds
Disaster bonds
(e.g. CAT
Bonds)
Income bonds
Convertible
bonds
Put bonds
Bond market
Treasury
quotation
Bid price
- The price a dealer is willing to pay for a security. (You sell.)
Ask price
- The price a dealer is willing to take for a security. (You buy.)
Bid–ask spread- Difference between the bid and the ask prices. (Dealer’s profits)
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Maturity
2021 Nov 15
Clean price
Dirty price
Coupon
8.000
Bid
136:29
Asked
136:32
Chg
+5
Asked yield
4.36
 Treasury bonds all make semiannual payments and have a face value of
$1,000, so this bond will pay $40 per six months.
 For historical reasons, Treasury prices are quoted in 32nds. Because prices
are quoted in 32nds, the smallest possible price change is 1/32. This change is
called the “tick” size. Thus, the bid price (136:29), actually means 136 29/32,
or 136.906% of face value. With a $1,000 face value, this price represents
$1,369.06. The bid-ask spread is 3/32, or $93.75.
 The next number quoted is the change in the asked price from the previous
day, measured in ticks (in 32nds), so this issue’s asked price rose by 5/32 of
1%, or 0.15625%, of face value from the previous day.
 Asked yield is the yield to maturity, based on the asked price.
 Notice that this is a premium bond, and its yield to maturity (4.36%) is less
than its coupon rate (8%).
Also called Quoted price. Bonds are quoted without accrued interest.
Price actually paid (total purchase cost) = Quoted price + Accrued interest
Accrued interest is computed by taking a pro rata share of the coupon payment.
E.g. a T-bond with a 4% semiannual yield and a clean price of $1,282.50:
Number of days since last coupon
= 61
Number of days in the coupon period = 184
Accrued interest
= (61/184)(0.04*1000) = $13.26
Dirty price
= $1,282.50 + $13.26 = $1,295.76
Fisher Effect
It is a theoretical relationship between real rates, nominal rates, and inflation.
Exact relationship: (1 + R) = (1 + r)(1 + h)
I.e.
r = [(1 + R) / (1 + h)] – 1
Approximate relationship: R = r + h
where R = nominal rate (rates that have not been adjusted for inflation)
r = real rate (rates that have been adjusted for inflation)
h = expected inflation rate
Term Structure
The relationship between time to maturity and yields, all else equal.
of Interest Rates I.e. Relationship between nominal interest rates on default-free, pure discount
bonds and maturity (Pure time value of money).
Treasury yield
A plot of the yields on treasury notes and bonds relative to maturity, based on
curve
coupon bond yields.
Normal – upward-sloping; long-term yields are higher than short-term yields
Inverted – downward-sloping; long-term yields are lower than short-term yields
The slope primarily depends on the combined effects of inflation premium and
the interest rate risk premium.
Factors
(1) Real rate of interest – the compensation investors demand for forgoing
Affecting Bond
the use of their money after adjusting for the effects of inflation
Yields
(2) Expected future inflation (premium) – portion of the nominal rate that is
compensation for expected inflation
(3) Interest rate risk (premium) – reward for bearing interest rate risk
[Remember: Anything else that affects the risk of the cash flows to the
bondholders will affect the required returns.]
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(4) Default risk (premium) – portion of a nominal rate that represents
compensation for the possibility of default [Remember: bond ratings!]
(5) Taxability (premium) – portion of a nominal rate that represents
compensation for unfavorable tax status [Remember: municipal versus
taxable!]
(6) Liquidity (premium) – portion of a nominal rate that represents
compensation for lack of an active market wherein a bond can be sold for
its actual value. [Remember: bonds that have more frequent trading will
generally have lower required returns]
Value of a bond (market price): The present value of the expected cash flows (the coupons and the face
value) discounted at the market rate of interest.
0
1
cF
cF
In formula, we know bond value =
2
…
t-1
t
cF
cF + F
…
𝐶𝑥
1
1−
(1+𝑟)𝑡
+
𝐹
𝑟
(1+𝑟)𝑡
= Present value of the coupons + Present value of the face amount
where (1) face value (F) paid at maturity, (2) coupon (C) [coupon rate (c) multiplied by face value (F)]
paid per period, (3) t periods to maturity, and (4) a yield of r per period
Suppose Sammy, Co. issues $1,000 par bonds with 20 years to maturity. The annual coupon is $110.
Similar bonds have a yield to maturity of 11%.
Bond value = 110[1 – 1/(1.11)20] / 0.11 + 1,000 / (1.11)20 = 875.97 + 124.03 = $1,000
or N = 20; I/Y = 11; PMT = 110; FV = 1,000; CPT PV = -1,000
Since the coupon rate and the yield are the same, the price should equal face value. ( Par value bond)
Suppose the YTM on bonds is 13% instead of
11%.
Suppose the YTM on bonds is 9% instead of
11%.
Bond price
= 110[1 – 1/(1.13)20] / 0.13 + 1,000/(1.13)20
= $859.50 ( Discount bond)
Bond value
= 110[1 – 1/(1.09)20] / 0.09 + 1,000/(1.09)20
= $1,182.57 ( Premium bond)
The difference is $140.50, which is equal to the
present value of the difference between bonds with
coupon rates of 13% ($130)
Note:
 If not stated specifically, face value of bond is $1,000 and coupon payments will be paid twice a year.
 The expected cash flows don’t change during the life of the bond. However, the bond price will
change as interest rates change and as the bond approaches maturity.
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Self-test:
Which bonds will have the higher yield, all else equal?
(a) Secured debt versus a debenture
(b) Subordinated debenture versus senior debt
(c) A bond with a sinking fund versus one without
(d) A callable bond versus a non-callable bond
Concept Check:
1. CU Entertainment has 20-year bonds outstanding. These coupons are sent directly to each of the
individual bondholders. These direct payments of the bond indicate that they are defined as being issued:
A. at par.
B. in street form.
C. as debentures.
D. in registered form.
E. in bearer form.
2. Which of the following are characteristics of a discount bond?
I. coupon rate < yield-to-maturity
II. coupon rate > yield-to-maturity
III. coupon rate < current yield
IV. coupon rate > current yield
V. market price < face price
VI. market price > face value
A. I, III and V only
B. I, IV and V only
C. I, IV and VI only
D. II, III and V only
E. II, IV and VI only
3. A 4-year bond pays interest semiannually on April 1 and October 1. Assume today is February 1. What
will the difference be between the clean and dirty prices today?
A. no difference
B. one month's interest
C. two month's interest
D. three month's interest
E. four month's interest
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4. Which of the following statements is incorrect?
I. The term structure of time to maturity and yields are always inversely related.
II. The real rate of return has significant impact on the slope of the term structure of interest rates.
III. Higher expected future inflation rates tend to increase the slope of the term structure of interest rates.
IV. The term structure of interest rates includes interest rate risk premium only.
A. I only
B. I, II only
C. I, IV only
D. II, III, and IV only
E. I, II, and IV only
5. High-Fiber Foods has a 8% semiannual coupon bond outstanding issued at par. The current price and
yield to maturity are $1,077.8 and 7.25% respectively. How long does this bond take to mature?
A. 15.87 years
B. 19.58 years
C. 24.62 years
D. 37.41 years
E. 39.17 years
6. The bonds of Mcpeters cabinets provides a 7.2% coupon and is issued at par. The bonds are currently
quoted at 103.44. What is the current yield on these bonds?
A. 2.69%
B. 3.33%
C. 6.66%
D. 6.96%
E. 7.20%
7. Virginia wants to raise $20 million to establish a start-up company. She plans to sell 30-year, zerocoupon par value bonds. Yield to maturity of this bond is 12%. What is the minimum number of bonds
she has to sell to raise $20 million?
A. 114,870
B. 127,395
C. 612,211
D. 655,723
E. 659,754
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Solution:
Self-test
(a) Debenture has higher yield. Secured debt is less risky because the income from the security is used to
pay it off first. In other words, a secured debt offers additional protection in bankruptcy, it should
have a lower required return (lower yield) than a debenture.
(b) Subordinated debenture has higher yield because it will be paid after the senior debt.
(c) Bond without sinking fund has higher yield. Company has to come up with substantial cash at
maturity to retire debt and this is riskier than systematic retirement of debt through time.
(d) Callable bond has higher yield. bondholders bear the risk of the bond being called early, usually
when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at
lower rates.
Concept Check
1. D
2. A [Discount bond: Yield to maturity > Current yield > Coupon rate
Premium bond: Yield to maturity < Current yield < Coupon rate]
3. E [4 months are counted from Oct 1 to Feb 1.]
4. E
5. B [$1077.8 = $40*(1-(1/(1+(7.25%/2))^(t*2)))/(7.25%/2)+1000/((1+7.25%/2)^(t*2)); t =19.58 years]
6. D [Current yield = (0.072*$1,000) / (1.0344*$1,000) = 6.9606%]
7. E [$20,000,000/(1,000/(1+0.06)^60) = 659,753.817]
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Chapter 8 Stock Valuation
Dividend growth
model
Dividend yield
A model that determines the current price of a stock as its dividend next period
divided by the sum of the discount rate less the dividend growth rate.
A stock’s expected cash dividend divided by its current price.
Capital gains
yield
The dividend growth rate, or the rate at which the value of an investment grows.
Common stock
Cumulative
voting
Equity without priority for dividends or in bankruptcy.
A procedure in which a shareholder may cast all votes for one member of the board
of directors. The directors are all elected at once. Total votes that each shareholder
may cast equal the number of shares times the number of directors to be elected. In
general, if N directors are to be elected, it takes [1 / (N+1)]% of the stock + 1 share to
assure a deciding vote for one directorship.
A procedure in which a shareholder may cast all votes for each member of the board
of directors. The directors are elected one at a time, and every share gets one vote.
A grant of authority by a shareholder allowing another individual to vote his or her
shares. A proxy fight is a struggle between management and outsiders for control of
the board, waged by soliciting shareholders’ proxies.
Payments by a corporation to shareholders, made in either cash or stock. Payment of
dividends is at the discretion of the board. A firm cannot default on an undeclared
dividend, nor can it be forced to file for bankruptcy because of nonpayment of
dividends. Dividends are not tax deductible for the paying firm.
Stock with dividend priority over common stock, normally with a fixed
dividend rate, generally without voting rights. Preferred dividends can be deferred
indefinitely and are mostly cumulative (any missed preferred dividends have to be
paid before common dividends can be paid.) Preferred stock represents equity in the
firm, but has many features of debt, including a stated yield, preference in terms of
cash flows and liquidation, and some issues are callable and/or convertible into
common shares.
Straight
(majority) voting
Proxy
Dividends
Preferred stock
Primary market
Secondary
market
Dealer
Broker
Specialist
NYSE
NASDAQ
The market in which new securities are originally sold to investors.
The market in which previously issued securities are traded among investors.
An agent who buys and sells securities from inventory.
An agent who arranges security transactions among investors.
A NYSE member acting as a dealer in a small number of securities on the exchange
floor; often called a market maker.
Specialists manage the order flow by keeping the limit order book. The limit order
book lists the trades that investors have given to their brokers that include desired
trading prices. The specialist is also a dealer that holds an inventory in their assigned
stock.
It is a computer network and has no physical location where trading takes place and
has a multiple market maker system rather than a specialist system.
Note:
 Why is common share more difficult to value in practice than a bond? First, the promised cash flows
are known in advance. Second, the life of the investment is essentially forever because common stock
has no maturity. Third, there is no way to easily observe the rate of return that the market requires.
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Formula:
General case
P0 
D3
D1
D2


 ......
1
2
(1  R)
(1  R)
(1  R) 3
where Dt is dividends paid at time t and R is required return.
Zero growth case
(Perpetuity)
P0 
D
R
(Constant) Dividend
1rowth Model
P0 
D3
D t 1
D1
D2


 ...... 
1
2
3
(1  R)
(1  R)
(1  R)
(1  R) t
D 0 (1  g )1 D1 (1  g ) 2 D 2 (1  g ) 3
D 0 (1  g ) t
P0 


 ..... 
(1  R) 1
(1  R) 2
(1  R) 3
(1  R) t
Now multiply both sides by (1  R)/(1  g) :
(1  R)
(1  g )1 (1  g ) 2
(1  g ) t 1
P0  D0 [1 


......

]
(1  g)
(1  R) 1 (1  R) 2
(1  R) t -1
Subtract t he second equation from the third and you get :
[
(1  R) - (1  g)
(1  g ) t
]P0  D0 [1 
]
(1  g)
(1  R) t
(1  g ) t
] goes to one as t approaches infinity.
(1  R) t
D (1  g)
D1
Assume R  g, P0  0

(R - g)
(R - g)
D t 1
so
Pt 
(R - g)
D (1  g)
D
and Required return R  0
g  1 g
P0
P0
D
where 1 is dividend yield, g is capital gains yield
P0
The term [1 
Non-constant growth
case
D3
Dt
Pt
D1
D2


 ... 

1
2
3
t
(1  R)
(1  R)
(1  R)
(1  R)
(1  R) t
D (1  g )
where Pt  t
(R - g)
P0 
Market multiple (Peer Using (a) P/E
P=
benchmark P/E
x EPS (earning per share
comparison)
(b) Price-sales  P = benchmark Price-sales x Sales per share
()
Note:
 “Why do we assume that R > g?”  First, R may be less than g in the short-run, eg. non-constant
growth problem. Second, in equilibrium, high returns on investment will attract capital, which, in the
absence of technological change, will ensure that in succeeding periods, higher returns cannot be
earned without taking greater risk. But, taking greater risk will increase R, so g cannot be increased
without raising R.
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Concept Check:
1. Robertson Co. has a dividend-paying stock with a -9.3% total return this year. Which one of the
following must be true?
A. The required rate of return for this stock increased over the year.
B. The dividend must be constant.
C. The firm is experiencing non-constant growth.
D. The dividend yield must be zero.
E. The stock has a negative capital gains yield.
2. Which one of the following occurs in the primary market?
A. a purchase of 200 shares of M&M stock from a current shareholder
B. a purchase of newly issued stock from HSBC
C. Tencent's purchase of Google stock
D. gift of 300 shares of common stock to Red Cross
E. gift of 600 shares of common stock by a grandfather to his grandson
3. Dragon Boat Theatres has paid annual dividends of $0.26, $0.43, and $0.59 a share over the past three
years, respectively. Now, the firm decides to maintain a constant dividend since its business development
has leveled off. Provide that the lack of expected future growth, this stock will be purchased if you can
only earn at least a 19% rate of return. What is the maximum amount you should pay for one share of this
stock today?
A. $2.26
B. $2.28
C. $3.09
D. $3.11
E. $3.15
4. The stock of HK & CHINA Logistics sells for $13.86 a share. When the annual dividend is distributed,
it is expected to pay $1.66 per share next year. The company has a policy of raising its dividends by 5%
annually and expects to continue. What is this stock’s market rate of return?
A. 11.59%
B. 11.98%
C. 16.98%
D. 18.98%
E. 20.86%
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5. Hang Lung, Inc. common stock yielded a 28.08% rate of return last year. Annual dividend was $0.13 a
share, or a dividend yield of 0.91%. What was the rate of price increase this year?
A. 27.17%
B. 27.33%
C. 27.56%
D. 27.71%
E. 28.11%
6. Annual dividend of HK Airlines was paid at $1.29 a share last month. The company expects to pay
$1.33, $1.45, and $1.62 a share over the next 3 years, respectively. After that, the dividend will be
constant at $1.91 per share per year. What is the market price of this stock if the market rate of return is
12.5%?
A. $12.78
B. $13.61
C. $14.20
D. $19.33
E. $20.59
7. Madonna holds Microsoft Corporation preferred stock with a constant 4.3% return. The stock is priced
at $62.30 a share currently. What is dividend per share (DPS)?
A. $2.00
B. $2.25
C. $2.53
D. $2.68
E. $2.91
Solution:
1.
2.
3.
4.
5.
6.
7.
E
B
D [$0.59 / 0.19 = $3.105]
C [$1.66 / $13.86 + 0.05 = 16.9769%]
A [28.08% - 0.91% = 27.17%]
C [$1.33/1.125 + $1.45/(1.125^2) + ($1.62+$1.91/0.125)/1.125^3 = $14.1973]
D [$62.3*4.3% = $2.6789]
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Chapter 9 Net Present Value and Other Investments Criteria
Good investment criterias:
1. Concern Time Value of Money [discounting]
2. Concern Risk of future cashflow [self determined discount rate!]
3. Provide information on values created for the company [returns calculations involved]
Payback period
Discounted cash flow
(DCF) valuation
Discounted payback
period
Average accounting
return (AAR)
Net present value
(NPV)
Internal rate of return
(IRR)
The length of time must wait to recoup the money it has invested in a project.
Advantages
Disadvantages
1. Easy to understand.
1. Ignores the time value of money.
2. Adjusts for uncertainty of later
2. Requires an arbitrary cutoff point.
cash flows.
3. Ignores cash flows beyond cutoff date.
3. Biased toward liquidity.
4. Biased against long-term projects, such
as R&D, and new projects.
5. Ignores the risk of cash flows.
Rule: an investment is accepted if its calculated payback period is no more than
some pre-specified number of years.
The process of estimating the today’s value of an investment by discounting its future
cash flows.
The length of time required for an investment’s discounted cash flows to equal its
initial cost.
Advantages
Disadvantages
1. Includes time value of money.
1. May reject positive NPV investments.
2. Easy to understand.
2. Requires an arbitrary cutoff point.
3. Does not accept negative
3. Ignores cash flows beyond cutoff date.
estimated NPV investments.
4. Biased against long-term projects, such
4. Biased toward liquidity.
as research and development, and new
5. Includes the risk of cash flows.
projects.
Rule: an investment is accepted if its discounted payback is no more than some
pre-specified number of years.
An investment’s accounting profit divided by its average accounting value.
Textbook’s Definition: AAR = average net income / average book value.
Advantages
Disadvantages
1. Easy to calculate.
1. Not a true rate of return; time value of money is
2. Needed information will
ignored. (Same value of money in all periods)
usually be available.
2. Uses an arbitrary benchmark cutoff rate.
3. Based on accounting (book) values, not cash
flows and market values. Thus, it cannot compare
with the returns in capital markets.
4. Ignores the risk of cash flow.
Rule: an investment is accepted if its AAR exceeds a target return.
The difference between an investment’s market value and its cost. NPV rule accounts
for the time value of money, risk of cash flows (through choosing discount rate) and
provides a clear indication of increase in value for the firm (A positive NPV increase
the owners’ wealth.), so it should be the primary decision rule for capital budgeting.
Rule: an investment is accepted if NPV is positive and rejected if it is negative.
The rate makes the present value of the future cash flows equal to the initial cost or
investment. In other words, the discount rate makes the NPV = zero. The IRR rule
accounts for time value (through finding the rate of return that equates all of the cash
flows on a time value basis), the risk of the cash flows (through comparing it with
required return, which is determined by the risk of the project), provides an indication
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Net present value
profile
NPV vs IRR
Non-conventional
cash flows and
multiple rates of
return
Mutually exclusive
investment decisions
Modified internal rate
of return (MIRR)
Profitability index (PI)
(benefit–cost ratio)
of value (value is increased if return actually earned exceeds required return.), so IRR
rule is considered as our primary decision criteria.
Advantages
Disadvantages
1. Closely related to NPV, often
1. May result in multiple answers or not
leading to identical decisions.
deal with nonconventional cash flows.
2. Easy to understand and
2. May lead to incorrect decisions in
communicate.
comparisons of mutually exclusive projects.
Rule: an investment is accepted if the IRR exceeds the required return. It should
be rejected otherwise.
A graphical representation of the relationship between an investment’s NPVs and
various discount rates. Note that the NPV profile is also a form of sensitivity analysis.
If a project’s cash flows are conventional (costs are paid early and benefits are
received over the life), and if the project is independent, NPV and IRR will give the
same decision. Since IRR has some problems (non-conventional cash flows and
mutually exclusive projects) that the NPV does not have, we finally choose NPV as
our ultimate decision rule. When the decision result of NPV rule and IRR rule are
different, it may check with any non-conventional cash flows and NPV profile.
If cash flows change sign more than once, then you will have multiple IRRs. If there
are 5 sign changes, there are 5 IRRs, 3 IRRs, or 1 IRR. If there are 2 sign changes,
there are either 2 IRRs or no IRRs.
Possible reasons:
1. Net cost to shutting down a project: Collecting natural resources (After the
resource has been harvested, there is generally a cost associated with restoring
the environment.)
2. “Financing” project: there is a positive cash flow followed by a series of
negative cash flows.
A situation in which taking one investment prevents the taking of another.
Initial investments are substantially different (issue of scale)
The MIRR is a modification to the IRR. A project’s cash flows are modified by (1)
discounting the negative cash flows back to the present (Discounting approach); (2)
compounding cash flows to the end of the project’s life (Reinvestment approach); or
(3) combining (1) and (2) (Combination approach). An IRR is then computed on the
modified cash flows.
Advantages
Disadvantages
1. Single answer (don’t suffer
1. Not clear how to interpret MIRR. (A rate
from multiple rate of return.)
of return on a modified set of cash flows,
2. Specific rates for borrowing and not the project’s actual cash flows.)
reinvestment.
2. No clear reason to say which method is
better than any other.
3. Not truly “internal” because they depend
on externally supplied discounting or
compounding rates.
The present value of an investment’s future cash flows divided by its initial cost
(Only if the initial investment is the only cash outflow) OR PV inflow / PV outflow.
It measures the benefit per unit cost, based on the time value of money.
Advantages
Disadvantages
1. Closely related to NPV, generally leading 1. May lead to incorrect decisions
to identical decisions.
in comparisons of mutually
2. Easy to understand and communicate.
exclusive investments.
3. May be useful when available investment
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funds are limited. (Case of limited capital)
Rule: an investment is accepted if the PI exceeds 1 (ie. positive NPV). It should
be rejected otherwise.
Note:
 NPV and IRR are the most commonly used primary investment criteria. Payback is a commonly used
secondary investment criteria because short paybacks allow firms to have funds sooner to invest in
other projects without going to the capital markets. Even though payback and AAR should not be
used to make the final decision, we should consider the project very carefully if they suggest
rejection. There may be more risk than we have considered or we may want to pay additional
attention to our cash flow estimations. Sensitivity and scenario analysis can be used to help us
evaluate our cash flows.
 Why are smaller firms more likely to use payback as a primary decision criterion?
1) small firms don’t have direct access to the capital markets and therefore find it more difficult to
estimate discount rates based on funds cost;
2) the AAR is the project-level equivalent to the ROA measure used for analyzing firm
profitability; and
3) some small firm decision-makers may be less aware of DCF approaches than their large firm
counterparts.
 When managers are judged and rewarded primarily on the basis of periodic accounting figures, there
is an incentive to evaluate projects with methods such as payback or average accounting return. On
the other hand, when compensation is tied to firm value, it makes more sense to use NPV as the
primary decision tool.
Self-test:
1. Given cash revenues of Huge textile is $20,000 per year, assuming everything goes as expected. Cash
costs (including taxes) will be $14,000 per year. We will wind down Huge textile in 8 years. The plant,
property, and equipment will be worth $2,000 as salvage at that time. The project costs $30,000 to launch.
15% discount rate on new projects is adopted. Is this a good investment? If there are 1,000 shares of stock
outstanding, what will be the effect on the price per share of taking this investment. Given that the goal of
financial management is to increase share value, what decision should a financial manager make and why?
2. How can we determine just what this crossover point is? The crossover rate, by definition, is the
discount rate that makes the NPVs of two projects equal. Suppose we have 2 mutually exclusive projects:
Year
Project A
Project B
0
-$400
-$500
1
250
320
2
280
340
What is the crossover rate?
3. The details of two mutually exclusive projects, project A and B, are as follow.
Project A
Project B
CF at T0
- $500
- $400
CF at T1
$325
$325
CF at T2
$325
$200
IRR
19.43%
22.17%
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NPV
$64.05
$60.74
(a) The required return for both projects is 10%. Which project should you accept and why?
(b) If you have only $450 cash in hand now, which project should you accept and why?
4. Yoyo Inc. considers two mutually exclusive projects with launching new product and the relevant
discount rate is 15%.
Project A (CU-100)
Project B (CU-200)
Initial investment: $550,000 at time 0.
Initial investment: $350,000 at time 0.
Next five years (Year 1-5) of sales will
Cash flow ay Year 1 is $100,000. In each subsequent
generate cash flow of $185,000 per year.
year (Year 2-5) cash flow will grow at 10% per year.
Introduction of new product at Year 6 will
Introduction of new product at Year 6 will terminate
terminate further cash flows from this project.
further cash flows from this project.
Calculate the following investment criteria. And what implications from each of investment criteria are?
(a) Payback period
(b) IRR
(c) PI
(d) NPV
Concept Check:
1. Which one of the following will increase the net present value of a project?
A. increasing the required rate of return
B. making all cash inflows occurs at an earlier time period
C. decreasing all the values of the project's discounted cash inflows
D. decreasing the amount of the final cash inflow
E. decreasing the project's initial cost at time 0
2. If the NPV of a project is 0, then:
A. an increase in the project's initial cost will result in a positive NPV of the project.
B. the total of the cash inflows must equal to cash outflows of the project.
C. any delay of projected cash inflows will result in a negative NPV of the project.
D. the return of the project is exactly the same as the discount rate.
E. the project's PI must also be 0.
3. The consequences of applying the discounted payback decision rule to all projects are:
I. some positive NPV projects are rejected.
II. some projects are accepted, otherwise which would be rejected under the payback rule.
III. a firm becomes more short-term focused.
IV. the less liquid projects are rejected in favor of the most liquid projects.
V. projects are incorrectly accepted due to ignoring the time value of money.
A. I only
B. I, II and III
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C. I, III and IV
D. I, IV and V
E. I, II, IV and V.
4. Which of the following statements incorrectly applies to AAR?
I. It needs a cutoff rate as a benchmark.
II. It considers the time value of money.
III. It is the primary decision rule to analyze independent projects.
IV. It considers the risk of cash flow.
V. It is easily obtainable information for computation.
A. I, II and III
B. I, III and IV
C. II, III and IV
D. II, III and V
5. Which one of the following statements related to the internal rate of return (IRR) is incorrect?
I. A project with an IRR equal to the required return would reduce the value of a firm if accepted.
II. Both the timing and the amount of a project's cash flows affect the value of the project's IRR.
III. It is best used when comparing mutually exclusive projects.
IV. It is tedious to compute without the use of either a financial calculator or a computer.
A. I and II
B. I and III
C. II and III
D. II and IV
6. Hugo Communications has a project with the following cash flows. Should this project be accepted
using discounting approach to the MIRR calculation if the discount rate is 17%? Why or why not?
Year
Cash flow
0
-$300,650
1
153,720
2
290,470
3
-35,130
A. Yes; The MIRR is 15.88%.
B. Yes; The MIRR is 18.32%.
C. Yes; The MIRR is 21.66%.
D. No; The MIRR is 16.27%.
E. No; The MIRR is 21.66%.
7. Should this project be accepted using profitability index rule if discount rate is 11%? Why or why not?
Year
Cash flow
0
-$300,650
1
153,720
2
0
3
230,470
A. Yes; The PI is 0.94.
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B. Yes; The PI is 1.01.
C. Yes; The PI is 1.02.
D. No; The PI is 0.94.
E. No; The PI is 1.01.
8. The initial cost of the project is $529,000. And, expected annual net incomes are shown as follow.
Three-year straight-line depreciation method is used. What is AAR if the required discount rate is 20.5%?
Year
Annual net income
1
$34,600
2
64,800
3
83,900
A. 19.88%
B. 20.31%
C. 21.67%
D. 22.92%
E. 23.10%
Solution:
Self-test
1.
Year
Initial cost
Inflows
Outflows
Salvage
Net CF
0
-30
-30
1
2
3
4
5
6
7
8
+20
-14
+20
-14
+20
-14
+20
-14
+20
-14
+20
-14
+20
-14
+6
+6
+6
+6
+6
+6
+6
+20
-14
+2
+6
1
)
8
$2000
NPV  $30000  {$ 6000[ 1.15 ] 
}
0.15
1.15 8
NPV  $30000  $(26,924  654)
1- (
NPV  $2,422
Therefore, this is not a good investment. Taking it would decrease the total stock value by $2,422. With
1,000 shares outstanding, there is a loss of value of $2,422/1,000 = $2.42 per share. Thus, a financial
manager should reject this project since it decreases the share value.
Note: Salvage value ($2,000) in calculating NPV is the cash inflow in the final year of the project.
2. To find the crossover rate, first consider moving out of investment A and into investment B.The
method is to invest an extra $100 (=$500- 400). For this $100 investment, you’ll get an extra $70 (=$320250) in 1st year and an extra $60 (=$340- 280) in 2nd year. Based on our discussion, the NPV of the
switch, NPV(B-A), is equal to -$100 + [70/(1+R)] + [60/(1+R)2]
Then, we find IRR by setting the NPV equal to zero: NPV(B-A) = 0 = -$100 + [70/(1+R)] + [60/(1+R)2]
And, IRR is exactly 20%. It means we are indifferent between the two investments at a 20% discount rate
because the NPV of the difference in their cash flows is zero. Since two investments have the same value,
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so this 20% is the crossover rate. Let’s check to see that the NPV at 20% is $2.78 for both investments. In
general, you can find the crossover rate by taking the difference in the cash flows and calculating the IRR
using the difference. It doesn’t make any difference which one you subtract from which. To see this, find
the IRR for (A-B); you’ll see it’s the same number.
3. (a) Project A. It is because NPV ($64.05) is higher. As long as we do not have limited capital, we
should choose project A. Students will often argue that you should choose B because then you
can invest the additional $100 in another good project, say C. The point is that if we do not
have limited capital, we can invest in A and C and still be better off.
(b) Project B. In simply, there is not enough money for initial cost of Project A.
4.
(a) Payback period for CU-100 = 2 + ($180,000/$185,000) = 2.97 years
Payback period for CU-200 = 3 + ($19,000/$133,100) = 3.14 years
Since the CU-100 has a shorter payback period than the CU-200, the company should choose
the CU-100. Remember the payback period does not necessarily rank projects correctly.
(b) Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we
find that:
CU-100:
0 = –$550,000 + $185,000({1 – [1/(1 + IRR)5 ]} / IRR)
IRRCU-100 = 20.27%
CU-200:
0 = –$350,000 + $100,000 / (1 + IRR) + $110,000 / (1 + IRR)2 + $121,000 / (1 + IRR)3
+ $133,100 / (1 + IRR)4 + $146,410 / (1 + IRR)5
IRRCU-200 = 20.34%
IRR criterion implies accepting the CU-200.
(c) PICU-100 = ($185,000{[1 – (1/1.15)5 ] / .15 }) / $550,000
= 1.128
PICU-200 = [$100,000 / 1.15 + $110,000 / 1.152 + $121,000 / 1.153 + $133,100 / 1.154
+ $146,410 / 1.155] / $350,000
= 1.139
PI criterion implies accepting the CU-200.
(d) NPVCU-100 = –$550,000 + $185,000{[1 – (1/1.15)5 ] / .15 }
NPVCU-200 = –$350,000 + $100,000 / 1.15 + $110,000 / 1.152 + $121,000 / 1.153
+ $133,100 / 1.154 + $146,410 / 1.155
NPV criterion implies accepting the CU-100.
Concept Check
1. E
2. D
3. C
4. C
5. B
32
= $70,148.69
= $48,583.79
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Dr Haynes Yung
6. C [IRR=0=-$300,650+(-$35,130/1.17)+$153,720/(1+IRR)+$290,470/(1+IRR)^2; IRR = 21.6638%]
7. C [PI = ($153,720/1.11 + $230,470/1.11^3) / $300,650 = 1.0211]
8. E [AAR = (($34,600+$64,800+$83,900)/3) / (0.5*($529,000+$0)) = 23.1002%]
Chapter 10 Making Capital Investment Decisions
Relevant cash
flows
Incremental cash
flows
Stand-Alone
Principle
Sunk Costs
Opportunity Costs
Erosion (or
Cannibalism)
Net Working
Capital
Financing Costs
Pro forma financial
statements
Accelerated cost
recovery system
(ACRS)
Book value vs
market value
Depreciation tax
shield
Equivalent annual
cost (EAC) or
Equivalent annual
annuity (EAA)
Cash flows that occur (or don’t occur) because a project is undertaken. Cash
flows that will occur whether or not we accept a project aren’t relevant.
Any and all changes in the firm’s future cash flows that are a direct consequence
of taking the project.
The assumption for project to be analyzed based on the project's incremental cash
flows. In other words, viewing projects as “mini-firms” with their own assets,
revenues and costs to evaluate separately from other activities of the firm.
A cash flow already paid or accrued. These costs should not be included in the
incremental cash flows of a project. From an emotional standpoint, it does not
matter what investment has already been made. We need to make our decision
based on future cash flows, even if it means abandoning a project that has already
had a substantial investment.
Any cash flows lost or forgone by taking one course of action rather than another.
Applies to any asset or resource that has value if sold, or leased, rather than used.
New project revenues gained at the expense of existing products/services.
Incremental investments in cash, inventories and receivables that need to be
included in cash flows of new projects if they are not offset by changes in
payables. Later, as projects end, this investment is often recovered.
We generally don’t include the cash flows associated with interest payments or
principal on debt, dividends, or other financing costs in computing cash flows.
Financing costs are part of the division of cash flows of a project and reflected in
the discount rate used to discount the project cash flows.
Financial statements projecting future years’ operations.
A depreciation method under U.S. tax law allowing for the accelerated write-off
of property under various lifetime classifications.
Net fixed assets is different from the market value of the assets since the arbitrary
methods used to compute depreciation rarely match changes in economic value.
The tax saving that results from the depreciation deduction, calculated as
depreciation expense multiplied by the relevant tax rate.
The present value of a project’s costs/regular cash flow calculated on an annual
basis. The primary purpose is to compute the annual cost of each machine on a
comparable basis so that the least expensive machine can be identified given that
the machines generally have differing lives and costs. The assumption is that
whichever machine is acquired, it will be replaced at the end of its useful life.
EAC considers required rate of return, operating costs, need for replacement and
aftertax salvage value.
Rule: A project is accepted when its EAC is smaller than that of an alternate
project.
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Calculation:
Project cash flow
(Cash flow from
assets)
= Project operating cash flow (OCF)
- Project change in net working capital (NWC)
- Project capital spending
Operating cash flow
(OCF)
= Earnings before interest and taxes (EBIT)
[Bottom-up approach]
+ Depreciation
- Taxes
= Net income + Depreciation
Note: Assume there is no interest expense.
In simple case, where EBIT
= Sales – Costs – Depreciation
= Unit price*unit sales – Variable costs – Fixed costs – Depreciation
In simple case, where Taxes
= EBIT*tax rate
= Sales – Costs – Taxes
Depreciation
(example)
[Top-down approach]
= (Sales-Costs)*(1-tax rate) + Depreciation*tax rate
[Tax shield approach]
Consider the purchase of a 5-year, $50,000 machine with a 34% marginal tax
rate. Assume a 0 salvage value at the end of year 5 and an appropriate discount
rate of 10%.
Straight-line method:
Tax deductible depreciation (each year) = $50,000 / 5 = $10,000.
Tax shield (each year) = $10,000(0.34) = $3,400.
Present value of tax shield is $12,888.68.
Given MACRS depreciation rates, they have the following tax shields:
Year 1: 50,000(0.2)(0.34) = $3,400
Year 2: 50,000(0.32)(0.34) = $5,440
Year 3: 50,000(0.192)(0.34) = $3,264
Year 4: 50,000(0.1152)(0.34) = $1,958.40
Year 5: 50,000(0.1152)(0.34) + (0 - 0.34(0 – 2,880)) = $2,937.60
(Because the salvage is expected to be 0 in year 5, you need to compute the tax
benefit received when the asset is disposed of at the end of year 5 to be
consistent with the assumptions used in the straight-line calculation.)
Present value of the tax shield is $13,200.70.
where after-tax salvage
= salvage value – tax rate*(salvage value – book value)
= (0 - 0.34(0 – 2,880))
= $979.2
If the asset is fully depreciated, after-tax salvage = salvage value*(1-tax rate).
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Net capital spending
= purchase price of new asset - selling price of existing asset + costs of site
preparation, setup, and startup +/- increase (decrease) in tax liability due to sale
of old asset at other than book value
Example: Replacement problem (in ppt)
Original Machine
Initial cost = 100,000
Annual depreciation = 9000
Purchased 5 years ago
Book Value = 55,000
Salvage today = 65,000
Salvage in 5 years = 10,000
New Machine
Initial cost = 150,000
5-year life
Straight-line dep = 30,000
Salvage in 5 years = 17,000
Cost savings = 50,000/year
If required return and tax rate are 10% and 40% respectively. The old machine will be sold when the new
machine is purchased. The incremental CF is the change from the old to the new situation. What are the
cash flow consequences of selling the old machine today instead of in 5 years?
Buy new machine
Sell old machine
= $65,000 – 0.4($65,000 – $55,000)
Net capital spending =$(150,000 – 61,000)
= $150,000 (outflow)
= $61,000 (inflow)
= $89,000(outflow)
EBIT = Cost saving – incremental depreciation (new-old)
= $50,000 – $(30,000 – 9,000)
= $50,000 – $21,000
= $29,000
OCF = EBIT – Taxes + Depreciation OR Cost Saving*(1-tax rate) + Depreciation*tax rate
= $(29,000 – 11,600 + 21,000) OR $50,000(1-0.4) + $21,000(0.4)
= $38,400
Net Salvage Value on new machine = $17,000 - 0.4($17,000 -$0)
= $10,200
Net Salvage Value on old machine = $10,000 - 0.4($10,000 – $10,000) = $10,000
This is an opportunity cost because we no longer receive this at Year 5 (we lose the $10,000 cash because
we sell the machine today)
Incremental terminal CF
= $200
Year
Net capital
spending
OCF
Salvage (new)
Salvage (old)
NWC
Net CF
0
-89,000
0
-89,000
1
2
3
4
5
+38,400
+38,400
+38,400
+38,400
+38,400
+38,400
+38,400
+38,400
+38,400
+10,200
-10,000
0
+38,600
Self-test:
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A dishwasher, which helps cost-saving, costs $640,000. This machine will be utilized in 5-year project
but is classified as 3-year MACRS taxable asset. Initial net working capital investment is $55,000,
relevant discount rate is 12% and relevant tax rate is 35%. Estimates salvage value is $60,000 in Year 5.
What level of pre-tax cost savings does CU Canteen require for this project to be profitable?
Concept Check:
1. Which of the following should be included in the analysis of a new product?
I.
II.
III.
IV.
reduction in sales for a current product once the new product is introduced
market value of a machine owned by the firm which will be used to produce the new product
money already spent for research and development of the new product
increase in accounts receivable needed to finance sales of the new product
A. I and III only
B. I, II and III
C. I, II, and IV
D. II, III, and IV
E. All of the above
2. When Michael considers the purchase of a new machine, he evaluates two machines which have
different initial and ongoing costs and different lives. Whichever machine is purchased will be replaced at
the end of its useful life. You should select the machine which has the:
A. lowest annual operating cost.
B. highest annual operating cost.
C. highest equivalent annual cost.
D. lowest equivalent annual cost.
E. longest life.
3. Which of the following are correct?
I.
II.
III.
IV.
V.
Net working capital is the only expenditure where at least a partial recovery can be made at the end of
a project.
Ignore any tax effects, increase in inventory is a project cash inflow.
Net working capital requirements can create a cash inflow at the beginning of a project.
The operating cash flow of a cost cutting project can be positive even though there are no sales.
Pro forma statements should include all the relevant incremental cash flows and all project-related
fixed asset acquisitions and disposals, be compiled on a stand-alone basis and exclude interest
expense in general.
A. I and III.
B. III and IV.
C. I, III and IV.
D. IV and V.
E. III, IV and V.
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4. HK Financial Inc. bought an apartment for $800,000 ten years ago. 8 years ago, repairs expenses of the
building cost $399,000. Annual taxes are $29,000. Its current book value and current market value are
$301,000 and $1,334,000 respectively. If the company decides to use this apartment for a new project,
what value, if any, should be included in the initial cash flow of the project?
A. $301,000
B. $800,000
C. $1,199,000
D. $1,228,000
E. $1,334,000
5. Morgan Jewelry owned a MACRS 6-year machine at a cost of $400,000. Which one of the following
will be correct calculation of book value at the end of year 3?
A. $400,000  (0.20 + 0.32 + 0.192)
B. $400,000 / (1 + 0.20 + 0.32 + 0.192)
C. [$400,000  (1 - 0.20)]  (1 - 0.32)  (1 - 0.192)
D. $400,000 / [(1 + 0.20)  (1 + 0.32)  (1 + 0.192)]
E. $400,000  (1 - 0.20 - 0.32 - 0.192)
6. Eagle Co. considers a project which will decrease accounts payable by $16,000 and require additional
inventory of $477,000. Accounts receivable are currently $711,000. The increase of account receivables
is expected to rise about 7% if this project is accepted. What is the project's initial cash flow for net
working capital?
A. -$542,770
B. -$542,700
C. -$477,000
D. -$443,200
7. Jockey Club bought machines to expand its business. One machine costs $981,000 and lasts about 6
years before it disposes. The annual operating cost is $63,000 per machine. What is the equivalent annual
cost of a machine if the required rate of return is 15%?
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A. -$373,651
B. -$333,256
C. -$322,216
D. -$301,563
E. $195,249
8. Your boss decided to purchase of a new $162,800 computer system. 5-year straight-line depreciation
method is applied to the system. It will be worth $30,900 at the end of that time. $50,700 before taxes is
saved per year and working capital is reduced by $15,893 at time 0. Net working capital will return to its
original level when the project ends. The tax rate is 31%. What is IRR for this project?
A. 13.21%
B. 14.33%
C. 15.19%
D. 16.94%
E. 19.46%
Solution:
Self-test We find the initial pretax cost savings necessary to buy the new machine using the tax shield
approach to find OCF. The depreciation each year is:
D1 = $640,000(0.3333) = $213,312
D2 = $640,000(0.4445) = $284,480
D3 = $640,000(0.1481) = $94,784
D4 = $640,000(0.0741) = $47,424
Using the tax shield approach, the OCF each year is:
OCF1 = (S – C)(1 – 0.35) + 0.35($213,312)
OCF2 = (S – C)(1 – 0.35) + 0.35($284,480)
OCF3 = (S – C)(1 – 0.35) + 0.35($94,784)
OCF4 = (S – C)(1 – 0.35) + 0.35($47,424)
OCF5 = (S – C)(1 – 0.35)
After-tax salvage value = $60,000(1 – 0.35) = $39,000
To calculate the necessary cost reduction, we would require a zero NPV.
NPV = 0 = – $640,000 – 55,000 + (S – C)(0.65)(PVIFA12%,5) + 0.35($213,312/1.12
+ $284,480/1.122 + $94,784/1.123 + $47,424/1.124) + ($55,000 + 39,000)/1.125
Solving this equation for the sales minus costs, we get:
(S – C)(0.65)(PVIFA12%,5) = $461,465.41
(S – C) = $196,946.15
Concept Check
1. B
2. D
3. D
4. E
5. E
6. A [-$16,000 – $477,000 – $711,000*0.07 = -$542,770]
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7. C [-$981,000-$63,000*(1-1/(1+0.15)^6)/0.15 = EAC*(1-1/(1+0.15)^6)/0.15; EAC = -$322,216.405]
8. D [OCF = $50,700*(1-0.31) + $162,800/5*0.31 = $45,076.6
NPV=$0= -$162,800 + $15,893 + $45,076.6*(1-1/(1+IRR)^5))/IRR +
(($30,900-$0)*(1-0.31)-$15,893)/((1+IRR)^5);
IRR = 16.9371%]
Chapter 14 Cost of Capital
Cost of capital,
required return
and appropriate
discount rate
Cost of capital
(RD)
Calculating cost
of capital using
DGM approach
Calculating cost
of capital using
SML approach
Cost of debt (RE)
Capital structure
Weighted
average cost of
capital (WACC)
Problems with
WACC
Pure play
approach
Cost of capital, required return, and appropriate discount rate are different phrases
that all refer to the opportunity cost of using capital in one way as opposed to
alternative financial market investments of the same systematic risk.
- required return is from an investor’s point of view
- cost of capital is the same return from the firm’s point of view
- appropriate discount rate to correctly evaluating the project is the same return as
used in a PV calculation
The return that equity-holders require on their investment in the firm. It reflects the
average riskiness of all of the securities it has issued, which may be less risky
(bonds) or more risky (common stock). Also, it depends primarily on the use of the
funds, not the source.
Assumptions: A variant of growing perpetuity; dividends are expected to grow at a
constant rate forever; discount rate is greater than growth rate.
Advantages
Disadvantages
1. easy to understand
1. Only applicable to companies currently paying
2. easy to use
dividends
2. Not applicable if dividends aren’t growing at a
reasonably constant rate
3. Extremely sensitive to the estimated growth rate.
4. Does not explicitly consider risk
Assumptions: Normality of returns and/or quadratic utility functions; no transaction
costs, and other market imperfections; a firm's future risks are similar to its past risks;
constant reward-to-risk ratio.
Advantages
Disadvantages
1. Adjusts for systematic risk
1. both beta and market risk premium vary
2. Applicable to all companies, as through time
long as we can estimate beta
2. Not always reliable, since our estimate is
based on historical data
The return that lenders/creditors require on the firm’s debt. (ie. Interest rate of a loan)
// Interest rate on debt can be current YTM on outstanding debt or by knowing the
bond rating and looking up rates on new issues with the same rating.
The firm’s combination of debt and equity.
The return investors require on the total assets of the firm, ie. weighted average of the
cost of equity and the after-tax cost of debt.
// Overall return the firm must earn on its assets to maintain the value of its stock. It
is a market rate based on market’s perception of the risk of the firm’s assets.
Decisions may be wrongly made through single WACC when
1. The riskiness of project distinctively different from the overall firm
2. The riskiness of one division distinctively different from the overall firm (If only a
single WACC is used, a division will tend to prefer the projects with higher risk.)
 Divisional cost of capital
The use of a WACC that is unique to a particular project, based on companies in
similar lines of business.
I.e. examine other investments outside the firm that are in the same risk class as the
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one we are considering, and use the market required return on these investments as
the discount rate.
Assigns investment to “risk” categories that have higher or lower risk premiums than
the firm as a whole.
The required amount of new bond and stocks if launching new project.
Subjective
Approach
Flotation costs
Note:
 [Coupon rate vs current yield vs YTM] Cost of debt is equal to YTM because it is market rate of
interest that would be required on new debt issues. Coupon rate is the firm’s promised interest
payments on existing debt and current yield is the income portion of total return.
 For divisional cost of capital, overall firm beta is weighted average of the betas of the firm’s
divisions.
 For subjective approach in a multinational setting, adjustments to foreign project hurdle rates should
reflect the effects of foreign exchange risk, political risk, capital market segmentation and
international diversification effects.
Calculations
Cost of equity (RE)
DGM Approach: RE = (D1 / P0) + g
where (D1 / P0) = dividend yield
g = growth rate; capital gains yield
g = historical average / average of analysts’ forecast (Method 1)
g = ROE * b (Method 2)
where
ROE = Net income / Equity
b = Retention rate, also called plowback ratio
b = (EPS-DPS) / EPS
(Assume b is not 0% or 100%)
SML Approach: RE = Rf + βE[E(RM) – Rf] [i.e. CAPM]
where Rf = Risk-free rate,
E(RM) – Rf = Market risk premium,
 = Systematic risk of asset
Cost of Preferred
Stock (RP)
WACC
Note: When we have all the information of both DGM and SML approach, we
calculate both of two figures and take an average to have a final estimate.
RP = D / P0, which is equal to its dividend yield.
= wERE + wDRD(1-TC)
where
E = market value of the firm’s equity
= # of outstanding shares * price per share
D = market value of the firm’s debt
= # of bonds times price per bond or take bond quote as percent of par value and
multiply by total par value
V = combined market value of the firm’s equity and debt
=E+D
(Assuming that there is no preferred stock and current liabilities are negligible. If
this is not the case, then you need to include these components as well. This is
really just the market value version of the balance sheet identity. The market value
of the firm’s assets = market value of liabilities + market value of equity.)
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Weighted average
flotation cost (fA)
wE = E/V = weight of firm’s equity to firm’s assets
wD = D/V = weight of firm’s debt to firm’s assets
RE = Cost of equity
RD = Cost of debt
RD(1-TC) = after-tax cost of debt
Note: Adding other terms into WACC formulae, eg, current liabilities.
WACC = (E/V)RE + (D/V)RD (1-TC) + (P/V)RP + (CL/V)RCL (1-TC)
where CL/V = market value of current liabilities in the firm’s capital structure
V = E + D + P + CL.
For cost of short-term debt: Some types of current liabilities are interest-free, such
as accruals. However, accounts payable has a cost associated with it if the company
forgoes discounts. Cost of notes payable and other current liabilities depends on
market interest rates for short-term loans. Since these loans are negotiated with
banks, cost of short-term loan are the estimates of short-term cost of capital from
the company’s bank. The market value and book value of current liabilities are
usually very similar, so you can use the book value as an estimate of market value.
= wEfE + wDfD
where fE = flotation costs for equity issues
fD = flotation costs for debt issues
Implication:
If fA is 17.2% and project cost is $65 million (no flotation costs), true cost will be
$65 million / (1- fA) = $65 million / 0.828 = $78.5 million, which shows that
flotation costs can be a considerable expense.
Self-test:
1. Assume tax rate is 35%. Market risk premium and risk-free rate are 8% and 4.5% respectively. Find the
WACC based on the below information.
Debt
Common stock
Preferred stock
20-year 8,000 6.5% semiannual coupon bonds outstanding with a market quote
of 92.0.
250,000 shares outstanding, selling for $57 per share; the beta is 1.05.
15,000 5% preferred stock outstanding, currently selling for $93 per share.
2. Suppose Monkey Company has debt-equity ratio of 100%. New $500,000 cleansing plant is planned to
establish. It is expected to generate after-tax cash flows of $73,150 per year forever. The tax rate is 34%.
Using the below information of two financing options, what is NPV of new cleansing plant?
Option A
Option B
A $500,000 new issue of common stock: The
A $500,000 issue of 30-year bonds: The issuance
issuance costs would be 10% of the amount raised.
costs would be 2% of the proceeds. The company
Required return on the company’s new equity is 20%. can raise new debt at 10%.
Concept Check:
1. Other things being equal, which one of the following will decrease a firm's cost of equity if using
security market line approach? Assume current annual dividend and beta are $1 per share and 1.2
respectively.
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A. a reduction in the dividend amount
B. an increase in the dividend amount
C. a reduction in the risk-free rate
D. an increase in the risk-free rate
E. an increase in the market rate of return
2. Which of the following statements are correct?
I. The DGM model considers the risk that future dividends may vary from their estimated values.
II. The SML approach generally produces the same cost of equity as the dividend growth model,
assuming the firm uses debt in capital structure.
III. Pre-tax cost of debt is based on the original yield to maturity on the latest bonds issued by a firm.
IV. Pre-tax cost of debt is based on the coupon rate on the latest bonds issued by a firm.
A. III only
B. IV only
C. I and III only
D. I and IV only
E. None of the above.
3. The current price of Monopoly Inc. common stock is $55.55 per share. Annual dividend is $3.1 per
share. The dividends will expect to be increased by 1.9% annually and are expected to continue doing the
same. What is this firm's cost of equity?
A. 6.01%
B. 6.44%
C. 7.26%
D. 7.59%
E. 7.93%
4. Happy World has a 2% coupon bond issue outstanding that matures in 11 years. The bonds pay interest
semi-annually. The bonds are selling at 37% discount. What is aftertax cost of debt if the tax rate is 29%?
A. 1.42%
B. 2.43%
C. 3.42%
D. 4.86%
E. 6.84%
5. Casio Inc. uses 1:9 debt-to-equity ratio to finance its operations. The cost of equity is 11.3% and aftertax cost of debt is 7.2%. A project to be considered has a cash inflow of $42,000 in year 1. The cash
inflows will then grow at 2% per year forever. What is the maximum amount the company can initially
invest to avoid negative NPV?
A. $311,032
B. $363,519
C. $399,407
D. $445,026
E. $472,441
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Solution:
Self-test
1. MVD = 8,000($1,000)(0.92) = $7,360,000
MVE = 250,000($57) = $14,250,000
MVP = 15,000($93) = $1,395,000
V = $7,360,000 + 14,250,000 + 1,395,000 = $23,005,000
RE = .045 + 1.05(0.08) = .1290 or 12.90%
P0 = $920 = $32.50(PVIFAR%,40) + $1,000(PVIFR%,40)
R = 3.632%
YTM = 3.632% × 2 = 7.26%
And the aftertax cost of debt is:
RD = (1 – 0.35)(0.0726) = 0.0472 or 4.72%
RP = $5/$93 = 0.0538 or 5.38%
WACC = 0.0472(7.36/23.005) + 0.1290(14.25/23.005) + 0.0538(1.395/23.005) = 0.0983 or 9.83%
Notice that we didn’t include the (1 – tC) term in the WACC equation. We used the aftertax cost of debt in
the equation, so the term is not needed here.
2. WACC = 0.5(0.2) + 0.5(0.1)(1-0.34) = 13.3%
Because the cash flows are $73,150 per year forever, the PV of the cash flows at 13.3% per year is:
PV =
$73,150
= $550,000
0.133
If we ignore flotation costs, the NPV is $550,000 – 500,000 = $50,000. With no flotation costs, the
project generates an NPV that is greater than 0, so it should be accepted. What about financing
arrangements and issue costs? Because new financing must be raised, the flotation costs are relevant.
Thus, the weighted average flotation cost fA, is:
fA = (E/V) fE + (D/V) fD
= 0.5(0.1) + 0.5(0.02)
= 6%
Remember, the fact that Monkey can finance the project with all debt or all equity is irrelevant.
Because Monkey needs $500,000 to fund the new plant, the true cost, once we include flotation costs, is
$500,000 / (1- fA) = $500,000 / 0.94 = $531,915. Because the PV of the cash flows is $550,000, the plant
has an NPV of $550,000 - 531,915 = $18,085, so it is still a good investment. However, its value is
slightly lower than without floatation cost.
Concept Check
1. D
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2. E
3. D [($3.1*(1+0.019))/$55.55 + 0.019 = 7.5866%]
4. D [FV $1,000; PMT $10; PV -$630; N 11*2;
so I/Y is 6.84 and After-tax Rd is 0.0684*(1-0.29) = 4.8573%]
5. E [$42,000/((0.9*0.113+0.1*0.072) - 0.02) = $472,440.945]
Chapter 16 Financial Leverage and Capital Structure Policy
Homemade
leverage
M&M
Proposition I
M&M
Proposition II
Business risk
Financial risk
Interest tax
shield
Unlevered
cost of capital
Direct
bankruptcy
costs
Indirect
bankruptcy
costs
Financial
distress costs
Static theory
of capital
structure
The use of personal borrowing to adjusting the level of financial leverage to which the
individual is exposed.
The proposition that the value of the firm (V) is independent of the firm’s capital
structure (D/E).
The proposition that a firm’s cost of equity (RE) is a positive linear function of the firm’s
capital structure (D/E).
The equity risk that comes from the nature of the firm’s operating activities.
The equity risk that comes from the financial policy (the capital structure) of the firm.
The tax saving attained by a firm from interest expense.
The cost of capital for a firm that has no debt.
The costs that are directly associated with bankruptcy, such as legal and administrative
expenses.
The costs of avoiding a bankruptcy filing incurred by a financially distressed firm.
Examples: costs of avoiding bankruptcy, maintaining cash reserve, loss in sales and
valuable employees, increasing difficulty to borrow money, loss in value of assets, etc.
Also, shareholders and bondholders will calculate their own benefits and costs due to
bankruptcy.
The direct and indirect costs associated with going bankrupt or experiencing financial
distress.
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, assumes that the firm is fixed in terms of its assets and operations and it
considers only possible changes in the debt–equity ratio. Thus, optimal capital structure
balances the incremental benefits and costs of borrowing.
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Summary of propositions and formula
Case I
VL = VU
No corporate or personal taxes where VL = Value of levered firm
No bankruptcy costs
VU = Value of unlevered firm
[From M&M I]
Implications:
1. Value of levered firm is same as the value of the unlevered one, so
capital structure is irrelevant. (No optimal capital structure)
2. WACC is independent of capital structure.
WACC = RA = (E/V)RE + (D/V)RD
RE = RA + (RA – RD)(D/E)
[From M&M II]
where RA is the “cost” of the firm’s business risk, i.e., the risk of the
firm’s assets/operation
(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 (if no debt, RE=RA)
Case II (Focus: Taxes)
Corporate taxes, but no
personal taxes
No bankruptcy costs
Implications:
1. RE increases when D/E increases.
2. RE depends on business risk and financial risk.
Assume perpetual cash flows.
VU = EBIT(1-T) / RU
(i.e. PV of expected CFFA for unlevered firm)
where RU = Unlevered cost of capital
[From M&M I]
VL = VU + D(TC)
where TC = Corporate tax rate
D = Debt amount
D(TC) = PV of interest tax shield
[From M&M I]
WACC = RA = (E/V)RE + (D/V)(RD)(1- TC)
[From M&M I]
Implications:
1. Value of levered firm is equal to the value of the unlevered one
plus PV of interest tax shield. The more the firm borrows, the more
it is worth.
2. WACC decreases when D/E increases.
3. Optimal capital structure is almost 100% debt.
RE = RU + (RU – RD)(D/E)(1 – TC)
Case III (Focus: Bankruptcy)
Implications: In general, it is same with case I.
Implications:
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Corporate taxes, but no
personal taxes
Bankruptcy costs
Debt provides interest tax shield, but also bankruptcy cost. Optimal
capital structure is debt-equity mix that minimizes WACC. At some
point, the bankruptcy costs will offset tax-related gains from leverage
gradually. Also, the value of the firm will start to decrease, and cost of
capital and WACC will start to increase as more debt is added.
Self-test:
1. Given the below information, what is the value of equity, cost of equity and WACC?
EBIT = $151.52
TC = 34%
D = $500
RU = 0.2
RD = 0.1
2. Michael, Inc., has a debt–equity ratio of 2.5. The firm’s WACC is 10 percent, and its pretax cost of
debt is 6%. The corporate tax rate is 35%.
(a) What is cost of equity capital?
(b) What is unlevered cost of equity capital?
(c) What would WACC be if the firm’s debt–equity ratio was 0.75? What if it were 1.5?
Concepts check:
1. Which of the following statements are correct?
I. Based on M&M Proposition II with no taxes, cost of equity declines when more leverage is used.
II. Based on M&M Proposition II with no taxes, business risk determines return on assets.
III. Based on M&M Proposition II, capital structure of a firm can affect the firm's value.
IV. Based on M&M Proposition I with tax, a firm's cost of capital is independent of debt-equity mix used
by the firm.
A. I only.
B. II only.
C. II and III only.
D. I, II and III only.
E. All of the above.
2. Which of the following statements are correct?
I. Business risk is the risk that is inherent in the use of leverage.
II. Business risk is wholly dependent upon the financial policy of a firm.
III. As business risk rises so too does the cost of equity.
IV. Business risk is the risk that is inherent in a firm's operations.
A. I and II only.
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B. III and IV only.
C. I, III and IV only.
D. All of the above.
E. None of the above.
3. Edward & John is an all equity firm with 78,000 shares outstanding. 11%, $900,000 bank loan is
borrowed for the repurchase of 18,000 shares outstanding. What is the value of this firm if ignoring taxes?
A. $2.7 million
B. $3.6 million
C. $3.9 million
D. $4.6 million
E. $5.0 million
4. Global Pharmaceutical Inc. has a tax rate of 38%, an unlevered cost of capital of 12%, and expected
EBIT of $15,700. It has $11,000 of 6% par value bonds outstanding that pay interest annually. What is
the cost of equity?
A. 7.88%
B. 7.92%
C. 10.21%
D. 10.63%
E. 12.55%
5. Claire's Toys has a cost of equity of 15%, a pre-tax cost of debt of 6.8%, tax rate of 21% and unlevered
cost of capital of 12.3%. What is the firm's debt-equity ratio?
A. 0.62
B. 0.66
C. 0.69
D. 0.72
E. 0.77
6. Grand Casino has a debt-equity ratio of 0.6. Cost of equity is 13.3% and after-tax cost of debt is 3.8%.
What will the firm's cost of equity be if debt-equity ratio becomes 0.7?
A. 10.66%
B. 11.23%
C. 11.51%
D. 13.89%
E. 15.72%
7. Expected EBIT of Teresa Co. is $200,000 each year forever. It can borrow at 13%. It currently has no
debt, and its cost of equity is 25%. The tax rate is 27%. Teresa will borrow $177,000 and use the proceeds
to repurchase shares. What will the WACC be after recapitalization?
A. 18.31%
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B. 18.97%
C. 21.16%
D. 23.11%
E. 23.89%
Solution:
Self-test
1. VU = $500
VL = $670
E = VL – D = $170
RE = RU + (RU – RD)(D/E)(1 – TC) = 39.4%
WACC = 14.92%
Note: This WACC is substantially lower than the cost of capital of unlevered firm (RU), so debt financing
is highly advantageous.
2. (a) In a world with corporate taxes,
D / V = 2.5 / (2.5 + 1) = 0.7143
E / V = 1 / (2.5 + 1) = 0.2857
WACC = 0.10 = (0.7143)(1 – 0.35)(0.06) + (0.2857)(RE)
RE = 0.2525, or 25.25%
(b) We can use M&M Proposition II with corporate taxes to find the unlevered cost of equity.
0.2525 = R0 + (2.5)(R0 – 0.06)(1 – 0.35)
R0 = 0.1333, or 13.33%
(c) If debt-equity =0.75
D / V = 0.75 / (0.75 + 1) = 0.4286
E / V = 1 / (0.75 + 1) = 0.5714
RE
= 0.1333 + (0.75)(0.1333 – 0.06)(1 – .35)
= 0.1691, or 16.91%
WACC = (0.4286)(1 – 0.35)(0.06) + (0.5714)(0.1691) = 0.1133, or 11.33%
If debt-equity =1.50
RE = 0.1333 + (1.5)(0.1333 – 0.06)(1 – 0.35) = 0.2048, or 20.48%
WACC = (0.6)(1 – 0.35)(0.06) + (0.4)(0.2048) = 0.1053, or 10.53%
Concept check
1. C
2. B
3. C [78,000*($900,000/18,000) = $3,900,000]
4. E [VE = $15,700*(1-0.38)/0.12 + $11,000*0.38 - $11,000 = $74,296.667
RE = 0.12 + (0.12 - 0.06)*(11,000/74,296.667)*(1-0.38) = 12.5508%]
5. A [RE = 0.15 = 0.123 + (0.123 - 0.068)*D/E*(1 - 0.21); D/E = 0.6214]
6. D [WACC = (1/1.6*0.133) + (0.6/1.6*0.038) = 0.097375
WACC = 0.097375 = (1/1.7* RE) + (0.7/1.7*0.038); RE = 13.8938%]
7. D [VU = $200,000*(1 - 0.27)/0.25
= $584,000
VL = $584,000 + 0.27*($177,000) = $631,790
RE = 0.25 + (0.25 - 0.13)*($177,000/($631,790 - $177,000))*(1 - 0.27)
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= 0.28409
FINA2010 Financial Management (2018-2019)
Dr Haynes Yung
WACC = 0.28409/($631,790-$177,000)/$631,790+ 0.13*($177,000/$631,790)*(1-0.27) = 23.109%]
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