Cau hỏi và bài giải môn kế toán tài chính nang cao (thạc sỹ) financial management questions

Câu hỏi và bài giải môn Kế toán tài chính nâng cao (Thạc sỹ) Financial Management Questions

Sole proprietorship; partnership; corporation

Limited partnership; limited liability partnership; professional corporation Stockholder wealth maximization

Money market; capital market; primary market; secondary market

Private markets; public markets; derivatives

Investment banker; financial service corporation; financial intermediary Mutual fund; money market fund

Physical location exchanges; computer/telephone network

Open outcry auction; dealer market; electronic communications network (ECN)

Production opportunities; time preferences for consumption

Real risk-free rate of interest, r*; nominal risk-free rate of interest, pp

Inflation premium (IP); default risk premium (DRP); liquidity; liquidity

premium (LP)

Interest rate risk; maturity risk premium (MRP); reinvestment rate risk

Term structure of interest rates; yield curve

“Normal” yield curve; inverted (“abnormal”) yield curve

Expectations theory

Foreign trade deficit

What are the three principal forms of business organization? What are the advan- tages and disadvantages of each?

What are the three primary det¢rminants of a firm’s cash flow?

What are financial intermediaries, and what economic functions do they perform? Which fluctuate more, long-term or short-term interest rates? Why?

Suppose the population of Area Y is relatively young while that of Area O is rela- tively old, but everything else about the two areas is equal

a Would interest rates likely be the same or different in the two areas? Explain.

CHAPTER 1 An Overview of Financial Management and the Financial Environment

+ Would a trend toward nationwide branching: by banks and savings and loans, and the development of nationwide diversified financial corporations, affect

your answer to part are PQ sa Khối

(1-7) Suppose a new and much more liberal Congress and administration were elected,

and their first order of business was to take away the independence of the Federal

Reserve System, and to force the Fed to greatly expand the money supply What

effect would this have

a Qn the level and slope of the yield curve immediately after the announcement?

b Ơn the level and slope ‹ of the yield curve thar would exist two or three years in

» Solution Appears: in ‘Appendix A

G14) ‘Assuine that it is now January 1: The raté of inflation i is expected to be 4 percent

Inflation Rates throughout the year However, increased government deficits.and renewed vigor in

the economy are then expected to push inflation rates higher Investors expect the

inflation rate to be 5 percent in Year 2, 6 percent in, Year 3, and 7 percent in Year

4 The real risk-free rate, r*, is expected to remain at 2 pe ent over the next 5

years Assume that no maturity risk premiums are required on bonds with 5 years

or less to maturity The current interest rate on 5-year T- bonds i is 8 percent

a What is the average expected inflation rate over the next 4 years?

b What should be the prevailing interest rate on 4-year T-bonds?

c What is the implied expected inflation rate in Year 5, given that Treasury

‘bonds which mature at fhe end of that year yield 8 percent?

Suppose you and most other investors expect the inflation rate to be 7 percent next years, to fall to 5 percent during the following year, and then to remain at a rate of 3 percent thereafter Assume that the real risk-free rate, r*, will remain at

2 percent and that maturity risk premiums on Treasury securities rise from zero

on very short-term securities (those that mature in a few days) to a level of 0.2 percentage point for 1-year securities Furthermore, maturity risk premiums increase 0.2 percentage point for each year to maturity, up to a limit of 1.0 per-

centage point on 5-year or longer-term T-notes and T-bonds

a Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve

b Now suppose ExxonMobil, an AAA-rated company, had bonds with the same maturities as the Treasury bonds As an approximation, plot an ExxonMobil yield curve on the same graph with the Treasury bond yield curve (Hint:

Think about the default risk premium on ExxonMobil’s long-term versus its short-term bonds.)

c Now plot the approximate yield curve of Long Island Lighting Company, a

~ risky nuclear utility

cent for the next 2 years, 3 percent for the following 4 years, and 4 percent

thereafter The maturity risk premium is estimated by this formula: MRP =

0.1% (t — 1) The liquidity premium for the corporate bond is estimated to be

0.7 percent Finally, you may determine the default risk premium, given the company’s bond rating, from the default risk premium table in the text What yield would you predict for each of these two investments?

b Given the following Treasury bond yield information from the March 27,

2003, Federal Reserve Statistical Release, construct a graph of the yield curve

c Based on the information about the corporate bond that was given in part a,

calculate yields and then construct a new yield curve graph that shows both

the Treasury and the corporate bonds.

44 CHAPTER 1 An Overview of Financial Management and the Financial Enviranment

Assume that vou recently graduated with a degree in finance and have just reported to work as an

investment advisor at the brokerage firm of Balik and Kiefer Inc One of the firm’s clients is Michelle [#

DellaTorre, a professional tennis player who has just come to the United States from Chile DellaTorre

is a highly ranked tennis player who would like to start a company to produce and market apparel that

she designs She also expects to invest substantial amounts of money through Balik and Kiefer Della-

Torre is very bright, and, therefore, she would like to understand in general terms what will happen to #

her money Your boss has developed the following set of questions that you must ask and answer to :

explain the U.S financial system to DellaTorre |

a Why is corporate finance important to all managers?

b Describe the organizational forms a company might have as it evolves from a startup to a major corporation List the advantages and disadvantages of each form

c How do corporations “go public” and continue to grow? What are “agency” problems?

d What should be the primary objective of managers?

(1) Do firms have any responsibilities to society at large?

(2} Is stock price maximization good or bad for society?

(3) Should firms behave ethically? ~

e What three aspects of cash flows affect the value of any investment?

“Ni

What are free cash flows? What are the three determinants of free cash flows?

How do free cash flows and the weighted average cost of capiral interact to determine a firm's value?

What are financial assets? Describe some financial instruments

Who are the providers (savers) and users (borrowers) of capital? How is capital transferred

between savers and borrowers?

m How are secondary markets organized?

(1) List some physical location markets and some computer/telephone networks

(2) Explain the differences between open outcry auctions, dealer markets, and electronic commu- ff

n What do we call the price that a borrower must pay for debt capital? What is the price of equity l capital? What are the four most fundamental factors that affect the cost of money, or the general ƒ level of interest rates, in the economy?

o What is the real risk-free rate of interest (r*) and the nominal risk-free rate (tgp)? How are these

two rates measured?

p Define the terms inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP) Which of these premiums is included when determining the inter-

est rate on (1) short-term U.S Treasury securities, (2) long-term U.S Treasury securities, (3) short-

term corporate securities, and (4) long-term corporate securities? Explain how the premiums would vary over time and among the different securities listed above

q What is the term structure of interest rates? What is a yield curve? H

r Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year, and 8 percent thereafter The real risk-free rate is 3 percent The maturity risk premium is zero

for securities that mature in 1 year or less, 0.1 percent for 2-year securities, and then the MRP

increases by 0.1 percent per year thereafter for 20 years, after which it is stable What is the inter-

est rate on I-year, 10-year, and 20-year Treasury securities? Draw a yield curve with these data

What factors can explain why this constructed yield curve is upward sloping?

s At any given time, how would the yield curve facing an AAA-rated company compare with the

yield curve for U.S Treasury securities? At any given time, how would the yield curve facing a BB- rated company compare with the yield curve for U.S Treasury securities? Draw a graph to illus-

of PV; i; INT; FV,; PVA,; FVA,; PMT; m; TNom

FVIF,„; PVIF, „; FVIFA,„;PVIFA, -

Opportunity cost rate |

Annuity; lump sum payment; cash flow; uneven cash flow stream

Ordinary (deferred) annuity; annuity due

Perpetuity; consol

Outflow; inflow; time line; terminal value

Compounding; discounting

Annual, semiannual, quarterly, monthly, and daily compounding

Effective annual-rate (EAR); nominal (quoted) interest rate; APR; periodic rate _

‘Amortization schedule; principal versus interest component of a payment;

amortized loan - số :

Self-Test Problems 83

(2-2) What is an opportunity cost rate? How is this rate used in discounted cash flow analysis, and where is it shown on a time line? Is the opportunity rate a single

number that is used in all situations?

(2-3) An annuity is defined as a series of payments of a fixed amount for a specific

number of periods Thus, $100 a year for 10 years is an annuity, but $100 in Year

1, $200 in Year 2, and $400 in Years 3 through 10 does mot constitute an annuity However, the second series contains an annuity Is this statement true or false?

(2-4) If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100 percent, but the annual growth rate would be less than 10 percent True or false? Explain

2-5) Would you rather have a savings account that pays 5 percent interest compounded semiannually or one that pays 5 Y percent interest compounded daily? Explain

(ST-1) Assume that one year from now, you will deposit $1,000 into a savings account Future Value that pays 8 percent

a If the bank compounds interest annually, how much will you have in your

account four-years from now?

b What would your balance four years from now be if the bank used quarterly compounding rather than annual compounding?

c Suppose you deposited the $1,000 in 4 payments of $250 each at Year 1, Year

2, Year 3, and Year 4 How much would you have in your account at Year 4, based on 8 percent annual compounding?

d Suppose you deposited 4 equal payments in your account at Year 1, Year 2, Year 3, and Year 4 Assuming an 8 percent interest rate, how large would each

of your payments have to be for you to obtain the same ending balance as you ' calculated in part a?

(ST-2) Assume that you will need $1,000 four years from now Your bank compounds Time Value of interest at an 8 percent annual rate

Money 4 How much must you deposit one year from now to have a balance of $1,000

four years from now?

b If you want 'to make equal payments at Years 1 through 4, to accumulate the

$1,000, how large must each of the 4 payments be?

c If your ‘father were to offer either to make the payments calculated in part b ($221.92) orto give you a lump sum of $750 one year from now, which would you choose?

d If you have only $750 one year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 four years from now?

e Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4 What interest rate, with annual compounding, must you seek out to achieve your goal?

f To help you reach your $1,000 goal, your father offers to give you $400 one year from now You will get a part-time job and make 6 additional payments

of equal amounts each 6 months thereafter If all of this money is deposited in

a bank which pays 8 percent, compounded semiannually, how large must each

of the 6 payments be?

g What is the effective annual rate being paid by the bank in part f?

{ST-3) Bank A pays 8 percent interest, compounded quarterly, on its money market

Effective Annual account The managers of Bank B want its money market account to equal Bank

ate:

84 CHAPTER 2 Time Value of Money

A’s effective annual rate, but interest is to be compounded on a monthly basis

What nominal, or quoted, rate must Bank B set?

PROBLEMS

(2-4) Find the following values, using the equations, and then work the problems using a Present and Future financial calculator to check your answers Disregard rounding differences (Hint: If

Values for Different : :

Periods YOU are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable Then, without clearing the TVM - register, you can “override” the variable which changes by simply entering a new value for it and then pressing the key for the unknown variable to obtdin the sec- ond answer This procedure can be used in parts b and d, and in many other situa- tions, to see how changes in input variables affect the output variable.) a An initial $500 compounded for 1 year at 6 percent

b An initial $500 compounded for 2 years at 6 percent

c The present value of $500 due in 1 year at a discount rate of 6 percent

d The present value of $500 due in 2 years at a discount rate of 6 percent

(2-2) Use equations and a financial calculator to find the following values See the hint

Present and Future for Problem 2-1 ‘ ẹ

Values for Diferent An initial $500 compounded for 10 years at 6 percent

An initial $500 compounded for 10 years at 12 percent

The present value of $500 due in 10 years at a 6 percent discount rate

The present value of $1,552.90 due in 10 years at a 12 percent discount rate and at a 6 percent rate Give a verbal definition of the term present value, and illustrate it using a time line with data from this problem As a part of your answer, explain why present values are dependent upon interest rates

(2-3) To the closest year, how long will it take $200 to double if it is deposited and

Time fora lump earns the following rates? [Notes: (1) See the hint for Problem 2-1 (2) This prob- Sum to Double tem cannot be solved exactly with some financial calculators For example, if you enter PV = —200, PMT = 0, FV = 400, and I = 7 in.an HP-12C, and then press

the N key, you will get 11 years for part a The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up However, the HP-10B gives the

(2-4) Find the future value of the following annuities The first payment in these annu-

Future Value of ities is made at the end an Annuity "che hint _ to Problem 2-1 Also, note that you can leave values of Year 1; that is, they are ordinary annuities (Note: See — in the TVM register,

switch to “BEG,” press FV, and find the FV of the annuity due.) a $400 per year for 10 years

at 10percent, - oe

- $200 per year for 5 years at 5 percent —

$400 per year for 5 years at 0-percent - - -ˆ Now rework parts a,'b, andc assuming that payments are made at the begin-

7 ming of each year; that is, they ate annuities due

(2-5) Find the present value of the following ordinary ¿

Present Value of ee an Annuity $400 per year for 10’ years at-10 percent.” oi Tae “ary

ano

ities (see note to Problem 2-4):

$200 per year for 5 years at 5 percent

$400 per year for 5 years at 0 percent —

Now rework ‘parts a,b, and ¢ assuming th ning of each year; that is, they are annuit

yments are made at the

Future Value of an

Annuity for Various

a Find the present values of the following cash flow streams The appropriate

interest rate is 8 percent (Hint: It is fairly easy to work this problem dealing

with the individual cash flows However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as

the ones in this problem This will take a little time, but the investment will

pay huge dividends throughout the course Note, if you do work with the cash

flow register, then you must enter CF) = 0.)

b What is the value of each cash flow stream at a 0 percent interest rate?

Find the interest rates, or rates of return, on each of the following:

a You borrow $700.and promise to pay back $749 at the end of 1 year

b You lend $700 and receive a promise to be paid $749 at the end of 1 year

c You borrow $85,000 and promise to pay back $201,229 at the end of 10

years

d You borrow $9,000 and promise to make payments of $2,684.80 per year for

Find the amount to which $500 will grow under each of the following conditions:

a 12 percent compounded annually for 5 years

b 12 percent compounded semiannually for 5 years

c 12 percent compounded quarterly for 5 years

d 12 percent compounded monthly for 5 years

Find the present value of $500 due in the future under each of the following

a 12 percent nominal rate, semiannual compounding, discounted back 5 years

b 12 percent nominal rate, quarterly compounding, discounted back 5 years

c 12 percent nominal rate, monthly compounding, discounted back 1 year

Find the future values of the following ordinary annuities:

a FV of $400 each 6 months for 5 years at a nominal rate of 12 percent, com- pounded semiannually

b FV of $200 cach 3 months for 5 years at a nominal rate of 12 percent, com- —

c The annuities described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over

the 5 years Why does this occur? - Universal Bank pays 7 percent interest, compounded annually, on time deposits Regional Bank pays 6 percent interest, compounded quarterly

a Based on effective interest rates, in which bank would you prefer to deposit

b Could your choice of banks be influenced by the fact that you might want to

withdraw your funds during the year as opposed to at the end of the year? In

answering this question, assume, that funds must be left on deposit during the

entire compounding period in order for you to receive any interest

86 CHAPTER 2

t2!) Amortization

Time Value of Money

a Set up an amortization schedule for a $25,000 loan to be repaid in equal install- ments at the end of each of the next 5 years The interest rate is 10 percent

b How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent and that the loan is paid off over

c How large must each payment be if the loan is for $50,000, the interest rate is

10 percent, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods Why are these pay- ments not half as large as the payments on the loan in partb? - , Hanebury Corporation’s current sales were $12 million: Sales were $6 million 5

a To the nearest percentage point, at what rate have sales been growing?

b Suppose someone calculated the sales growth for Hanebury: Corporation in part a as follows: “Sales doubled in 5 years This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to

be 20 percent per year.” Explain what is wrong with this calculation

Washington-Pacific invests $4 million to clear a tract of land and to set out some young pine trees The trees will mature in 10 years, at which time Washington-Pacific plans to sell the forest at an expected price of $8 million What is Washington- Pacific’s expected rate of return?

A mortgage company offers to lend you $85,000; the loan calls for payments of

$8,273.59 per year for 30 years What interest rate is the mortgage company charging you?

To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, Starting next year (that is, you will need to withdraw the first $10,000 one year from today) Your rich uncle offers

to put you through school, and he will deposit in a bank paying 7 percent interest

a sum of money that is sufficient to provide the four payments of $10,000 each

His deposit will be made today

a How large must the deposit be?

b How much will be in the account immediately after you make the first with- drawal? After the last withdrawal?

While Mary Corens was a student at the University of Tennessee, she borrowed

$12,000 in student loans at an annual interest rate of 9 percent If Mary repays

$1,500 per year, how long, to the nearest year, will it take her to repay the loan?

You need to accumulate $10,000 To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent annual interest Your last deposit will be less than $1,250 if less is needed to round out to $10,000 How many-years will it take you to reach your $10,000 goal, and how large will the last deposit be?

What is the present value of a perpetuity of $100 per year if the appropriate dis- count rate is 7 percent? If interest rates in general were to double and the appro- priate discount rate rose to 14 percent, what would happen to the present value of the perpetuity?

Assume that you inherited some money A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities that call for four payments, $50 at the end of each of the next 3 years, plus a payment of

$1,050 at the end of Year 4 Your friend says she can get you some of these secu- rities at a cost of $900 each Your money is now invested in a bank that pays an

8 percent nominal (quoted) interest rate but with quarterly compounding You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that Y a

Your company is planning to borrow $1,000,000 on a 5-year, 15%, annual pay- ment, fully amortized term loan What fraction of the payment made at the end of the second year will represent repayment of principal?

a It is now January 1 You plan to make 5 deposits of $100 each, one every 6 months, with the first payment being made today If the bank pays a nominal interest rate of 12 percent but uses semiannual compounding, how much will

be in your account after 10 years?

b You must make a payment of $1,432.02 ten years from today To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quarters, in a bank that pays a nominal interest rate of 12 percent, quarterly compounding How large must each of the 5 payments be?

Anne Lockwood, manager of Oaks Mall Jewelry, wants to sell on credit, giving cus- tomers 3 months in which to pay However, Anne will have to borrow from her bank to carry the accounts payable The bank will charge a nominal 15 percent, but with monthly compounding Anne wants to quote a nominal rate to her customers (all of whom are expected to pay on time) that will exactly cover her financing costs What nominal annual rate should she quote to her credit customers?

Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85 He wants a fixed retirement income that has the same purchasing power at the time

he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires) His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments Inflation is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of

8 percent per year, annual compounding To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?

OPREARSHEEL PROBLEM

(2-26)

Build a Model: The

Time Value of Money

e-resource

Start with the partial model in the file FM11 Ch 02 P26 Build a Model.xls from the textbook’s Web site Answer the following questions, using a spreadsheet model to do the calculations

a Find the FV of $1,000 invested to earn 10 percent after 5 years Answer this question by using a math formula and also by using the Excel function wizard

b Now create a table that shows the FV at 0 percent, 5 percent, and 20 percent for 0, 1, 2, 3, 4, and 5 years Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results

c Find the PV of $1,000 due in 5 years if the discount rate is 10 percent Again, work the problem with a formula and also by using the function wizard.

CHAPTER 2 Time Value of Money

A security has a cost of $1,000 and will return $2,000 after 5 years What rate of return does the security provide?

Suppose California’s population is 30 million people, and its population is expected to grow by 2 percent per year How long would it take for the popu- lation to double?

Find the PV of an annuity that pays $1,000 at the end of each of the next 5

years if the interest rate is 15 percent Then find the FV of that same annuity

How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary annuity?

What would the FV and the PV for parts a and c be if the interest rate were

10 percent with semiannual compounding rather than 10 percent with annual

Find the PV and the FV of an investment that makes the following end-of-year

payments The interest rate is 8 percent

(1) Create a graph that shows how the payments are divided between inter-

(2) Suppose the loan called for 10 years of monthly payments, with the same original amount and the same nominal interest rate What would the amortization schedule show now?

Annual report; balance sheet; income statement

Common stockholders’ equity, or net worth; retained earnings

Statement of retained earnings; statement of cash flows

Depreciation; amortization; EBITDA

Operating current assets; operating current liabilities; net operating working capital; total net operating capital

Accounting profit; net cash flow; NOPAT; free cash flow

Market Value Added; Economic Value Added

Progressive tax; taxable i income; marginal and average tax rates

Capital gain or loss; tax loss carry-back and carry- forward

Improper accumulation; S corporation

What four statements are contained in most annua! reports?

Ifa “typical” firm reports $20 million of retained earnings on its balance sheet, could its directors declare a $20 million cash dividend without any qualms

whatsoever?

Explain the following statement: “While the balance sheet can be thought of as a

snapshot of the firm’s financial position at a point in time, the income statement reports on operations over a period of time.”

What is operating capital, and why is it important?

Explain the difference between NOPAT and net income Which is a better measure

of the performance of a company’s operations?

What is free cash flow? Why is it the most important measure of cash flow?

If you were starting a business, what tax considerations might cause you to prefer

to set it up as a proprietorship ora partnership rather than as a corporation?

120) CHAPTER 3 Financial Statements, Cash Flow, and Taxes

(Sta) Last year Rattner Robotics had $5,000,000 in operating income (EBIT) The com-

Net Income, Cash pany had a net depreciation expense of $1,000,000 and an interest expense of

Flow and EVA %1 000,000; its corporate tax rate was 40 percent The company has $14,000,000

in non-interest-earning current assets and $4,000,000 in non-interest-bearing

current liabilities; it has $15,000,000 in net plant and equipment It estimates

that it has an after-tax cost of capital of 10 percent Assume that Rattner’s only

noncash item was depreciation

What was the company’s net income for the year?

What was the company’s net cash flow?

What was the company’s net operating profit after taxes (NOPAT)?

If capital in the previous year was $24,000,000, what was the company’s free

cash flow (FCF) for the year?

e What was the company’s Economic Value Added (EVA)?

a

Note: By the time this book is published, Congress might have changed rates and/or other provisions of current tax law—as noted in the chapter, such changes i occur fairly often Work all problems on the assumption that the information in

the chapter is applicable

(3-1) An investor recently purchased a corporate bond which yields 9 percent The Personal After-Tax Yield investor is in the 36 percent combined federal and state tax bracket What is the

bond’s after-tax yield?

(3-2) Corporate bonds issued by Johnson Corporation currently yield 8 percent Munic- {

Personal ARerTax Yield ipal bonds of equal risk currently yield 6 percent At what tax rate would an

investor be indifferent between these two bonds?

(3-3) The Talley Corporation had a taxable income of $365,000 from operations after f

Corporate Tax Liability all operating costs but before (1) interest charges of $50,000, (2) dividends

received of $15,000, (3) dividends paid of $25,000, and (4) income taxes What is

the firm’s income tax liability and its after-tax income? What are the company’s marginal and average tax rates on taxable income?

(3-4) The Wendt Corporation had $10.5 million of taxable income

Corporate Tax Liability a, What is the company’s federal income tax bill for the year?

b Assume the firm receives an additional $1 million of interest income from some bonds it owns What is the tax on this interest income?

c Now assume that Wendt does not receive the interest income but does receive

an additional $1 million as dividends on some stock it owns What is the tax

on this dividend income?

(3-5) The Shrieves Corporation has $10,000 that it plans to invest in marketable securi-

Corporate After’ ties, It is choosing among AT&T bonds, which yield 7.5 percent, state of Florida

tex Yield uni bonds, which yield 5 percent, and AT&T preferred stock, with a dividend yield

of 6 percent Shrieves’s corporate tax rate is 35 percent, and 70 percent of the divi-

dends received are tax exempt Assuming that the investments are equally risky and

that Shrieves chooses strictly on the basis of after-tax returns, which security should ả

be selected? What is the after-tax rate of return on the highest-yielding security? 4 (3-6) The Klaven Corporation has operating income (EBIT) of $750,000 The company’s

Cash Flow depreciation expense is $200,000 Klaven is 100 percent equity financed, and it faces

a 40 percent tax rate What is the company’s net income? What is its net cash flow?

(3-7) The Menendez Corporation expects to have sales ‘of $12 million Costs other than

Income and cash depreciation are expected to be 75 percent of sales, and depreciation is expected

owena¥5S to be $1.5 million All sales revenues will be collected in cash, and costs other

than depreciation must be paid for during the year Menendez’s federal-plus-state

€

d

Problems 121

Set up an income statement What is Menendez’s expected net cash flow?

Suppose Congress changed the tax laws so that Menendez’s depreciation expenses doubled No changes in operations occurred What would happen to

reported profit and to net cash flow?

Now suppose that Congress, instead of doubling Menendez’s depreciation, reduced it by 50 percent How would profit and net cash flow be affected?

If this were your company, would you prefer Congress to cause your deprecia- tion expense to be doubled or halved? Why?

(3%) You have just obtained financial information for the past 2 years for Powell

Free Cash Flow Panther Corporation Answer the following questions _

TP What is the net operating profit after taxes (NOPAT) for 2004?

What are the amounts of net operating working capital for both years?

What are the amounts of total net operating capital for both years?

What is the free cash flow for 20042 How can you explain the large increase in dividends in 2004?

Powell Panther Corporation: Income Statements for Year Ending December 31 (Millions of Dollars)

2004 2003

Galac ¢790n fH ¢c1 ann no

Risk and Return: The Basics

Define the following terms, using graphs or equations to illustrate your answers wherever feasible:

Stand-alone risk; risk; probability distribution Expected rate of return, ?

Continuous probability distribution

Standard deviation, o; variance, 02; coefficient of variation, CV

Risk aversion; realized rate of return, f Risk premium for Stock i, RP;; market risk premium, RPy, Capital Asset Pricing Model (CAPM)

Expected return on a portfolio, f,; market portfolio

Correlation coefficient, p; correlation

Market risk; diversifiable risk; relevant risk Beta coefficient, b; average stock’s beta, by Security Market Line (SML); SML equation Slope of SML as a measure of risk aversion

Security A has an expected return of 7 percent, a standard deviation of returns of

35 percent, a correlation coefficient with the market of —0.3, and a beta coeffi- cient of —1.5 Security B has an expected return of 12 percent, a standard devia- tion of returns of 10 percent, a correlation with the market of 0.7, and a beta coefficient of 1.0 Which security is riskier? Why?

Suppose you owned a portfolio consisting of $250,000 worth of long-term U.S

government bonds

a ‘Would your portfolio be riskless?

b Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury bills Every 30 days your bills mature, and you reinvest the principal ($250, 000) in a new batch of bills Assume that you live on the investment income from your portfolio and that you want to maintain a constant stan- dard of living Is your portfolio truly riskless?

-c ' Can you think of any asset that would be completely riskless? Could someone

‘develop such an asset? Explain

If investors’ aversion to risk increased, would the risk premium on a high-beta stock i increase more or less than that on a low-beta stock? Explain

if a ‘company s beta were to double, would its expected return double?

ossible to construct a portfolio of stocks which has an expected return equal :

‘to e risk- free rate?

‘Solutions Appear in Appendix A

Stocks A and B have the following historical returns:

Year - Stock’ As Returns, Th Stock B’s Returns, rạ

Problems 16s

Calculate the average rate of return for each stock during the 5-year period

Assume that someone held a portfolio consisting of 50 percent of Stock A and

50 percent of Stock B What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the port- folio during this period?

Now calculate the standard deviation of returns for each stock and for the portfolio Use Equation 4-3a

Looking at the annual returns data on the two stocks, would you guess that the correlation coefficient between returns on the two stocks is closer to 0.8 or

to —0.8?

If you added more stocks at random to the portfolio, which of the following is - the most accurate statement of what would happen to Ty?

(1) o, would remain constant

(2) o, would decline to somewhere in the vicinity of 20 percent

(3) o, would decline to zero if enough stocks were included

{$2} ECRI Corporation is a holding company with four main subsidiaries The percent-

age of its business coming from each of the subsidiaries, and their respective betas,

What is the holding company’s beta?

Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent What is the holding company’s required rate of return?

ECRI is considering a change in its strategic focus: it will reduce its reliance on the electric utility subsidiary, so the percentage of its business from this sub- sidiary will be 50 percent At the same time, ECRI will increase its reliance on the international/special projects division, so the percentage of its business

from that subsidiary will rise to 15 percent What will be the shareholders’

required rate of return if they adopt these changes?

(4-2) An individual has $35,000 invested in a stock which has a beta of 0.8 and

Portfolio Beta $40,000 invested in a stock with a beta of 1.4 If these are the only two invest-

ments in her portfolio, what is her portfolio’s beta?

Risk and Return: The Basics \

Assume that the risk-free rate is 5 percent and the market risk premium is 6 per- cent What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2?

* Assume that the risk-free rate is 6 percent and the expected return on the market

is 13 percent What is the required rate of return on a stock that has a beta

a Calculate the expected rates of return for the market and Stock J

b Calculate the standard deviations for the market and Stock J

c Calculate the coefficients of variation for the market and Stock J

Suppose rpp = 5%, ry = 10%, and ry = 12%

a Calculate Stock A’s beta

b If Stock A’s beta were 2.0, what would be A’s new required rate of return?

> Suppose rpp = 9%, ty = 14%, and b, = 1.3

a What is r,, the required rate of return on Stock i?

b Now suppose rep (1) increases to 10 percent or (2) decreases to 8 percent

The slope of the SML remains constant How would this affect ry, and r,?

c Now assume rp remains at 9 percent but ry, (1) increases to 16 percent or (2) falls to 13 percent The slope of the SML does not remain constant

How would these changes affect r,?

» Suppose you hold a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks The portfolio beta is equal to 1.12 Now, suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7,500 and to use these proceeds to buy another stock for your portfolio Assume the new stock’s beta is equal to 1.75 Calculate your portfolio’s new beta

Suppose you are the money manager of a $4 million investment fund The fund consists of 4 stocks with the following investments and betas:

Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return

on an average stock is 13 percent, and the risk-free rate of return is 7 percent By how much does the required return on the riskier stock exceed the required return

c Calculate the standard deviation of returns for each stock and for the portfolio

d Calculate the coefficient of variation for each stock and for the portfolio

e If you are a risk-averse investor, would you prefer to hold Stock A, Stock B,

or the portfolio? Why?

Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent

a What are the betas of Stocks X and Y?

b What are the required rates of return for Stocks X and Y?

c What is the required rate of return for a portfolio consisting of 80 percent of Stock X and 20 percent of Stock Y?

d If Stock X’s expected return is 22 percent, is Stock X under- or overvalued?

BARTMAN INDUSTRIES REYNOLDS INCORPORATED MARKET INDEX

Year Stock Price Dividend Stock Price Dividend Includes Divs

168 CHAPTER 4 Risk and Return: The Basics

a Use the data given to calculate annual returns for Bartman, Reynolds, and the Market Index, and then calculate average returns-over the 5-year period

(Hint: Remember, returns are calculated by subtracting the beginning price

from the ending price to get the capital gain or loss, adding the dividend to

the capital gain or loss, and dividing the result by the beginning price Assume

that dividends are already included in the index Also, you cannot calculate

the rate of return for 1999 because you do not have 1998 data.)

b Calculate the standard deviations of the returns for Bartman, Reynolds, and

the Market Index (Hint: Use the sample standard deviation formula given in

the chapter, which corresponds to the STDEV function in Excel.)

c Now calculate the coefficients of variation for Bartman, Reynolds, and the

Market Index

d Construct a scatter diagram graph that shows Bartman’s and Reynolds’s returns

on the vertical axis and the Market Index’s returns on the horizontal axis

e Estimate Bartman’s and Reynolds’s betas by running regressions of their

returns against the Index’s returns Are these betas consistent with your graph?

f The risk-free rate on long-term Treasury bonds is 6.04 percent Assume that

the market risk premium is 5 percent What is the expected return on the

market? Now use the SML equation to calculate the two companies’ required returns

g If you formed a portfolio that consisted of 50 percent of Bartman stock and 50 percent of Reynolds stock, what would be its beta and its required return?

h Suppose an investor wants to include Bartman Industries’ stock in his or her portfolio Stocks A, B, and C are currently in the portfolio, and their betas are

0.769, 0.985, and 1.423, respectively Calculate the new portfolio’s required

return if it consists of 25 percent of Bartman, 15 percent of Stock A, 40 per-

cent of Stock B, and 20 percent of Stock C

204 CHAPTER 5 Risk and Return: Portfolio Theory and Asset Pricing Models

Capital Asset Pricing Model (CAPM); Capital Market Line (CML)

Characteristic line; beta coefficient, b

Arbitrage Pricing Theory (APT); Fama-French three-factor model; behavioral -°

and a beta coefficient of 0.5 Which security is more risky? Why?

DSELETEST PROBLEM Solution Appears in Appendix A

(ST-4) You are planning to invest $200,000 Two securities, A and B, are available, and

Risk and Return you can invest in either of them or in a portfolio with some of each You estimate —

that the following probability distributions of returns are applicable for A and B:

c Construct a table giving †, and ơ, for portfolios with w, = 1.00, 0.75, 0.50, 0.25, 0.0, and the minimum risk value of w, (Hint: For wa, = 0.75,f, =

16.25% and ap = 8.5%; for wy = 0.5, 2, = 17.5% and o, = 11.1%; for wa =

d Graph the feasible set of portfolios and identify the efficient frontier of the

feasible set oe

e Suppose your risk/return trade-off function, or indifference curve, is tangent to

the efficient set at the point where ?, = 18% Use this information, plus the graph constructed in part d, to locate (approximately) your optimal portfolio Draw in a reasonable indifference curve, indicate the percentage of your funds

invested in each security, and determine the optimal portfolio’s o, and ¢, (Hint:

Estimate o, and £, graphically, and then use the equation for #, to determine w,.)

f Now suppose a riskless asset with a return tgp = 10% becomes available

How would this change the investment opportunity set? Explain why the effi-

cient frontier becomes linear sẽ |

Given the indifference curve in part e, would you change your ‘portfolio? If so,

how? (Hint: Assume the indifference curves are parallel.)

h What are the beta coefficients of Stocks A and B? [Hints: (1) Recognize that r,

= rạp + b£w ~ rạp) and solve for b, and (2) assume that your preferences

match those of most other investors |

c Assuming (1) that the situation during Years 1 to 7 is expected to hold true in the future (that is, fy = fx; fy = fs and both ox and by in the future will equal their past values), and (2) that Stock X is in equilibrium (that is ki it t plots

on the Security Market Line), what is the risk-free rate? tử

d Plot the Security Market Line

e Suppose you hold a large, well-diversified portfolio and are considering adding to the portfolio either Stock X or another stock, Stock Y, that has the same’ beta as Stock X but a higher standard deviation of returns Stocks X and Y have the same expected returns; that is, ?y = ty = 10.6% Which stock should you choose?

b Give a verbal interpretation of what the repression line and the beta coefficient show about Stock Y’s volatility and relative riskiness as compared with those

of other stocks

c Suppose the scatter of points had been more spread out, but the regression line was exactly where your present graph shows it How would this affect (1) the firm’s risk if the stock is held in a one-asset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly?

206 CHAPTER 5 Risk and Return: Portfolio Theory and Asset Pricing Models

d Suppose the regression line had been downward sloping-and the beta coefficient

had been negative What would this imply about (1) Stock Y’s relative riskiness, (2) its correlation with the market, and (3) its probable risk premium?

3-2) The beta coefficient of an asset can be expressed as a function of the asset’s corre-

SML and CML’ Jation with the market as follows:

Comparison

bị - Đ MỚI

Om

a Substitute this expression for beta into the Security Market Line (SML), Equa-

tion 5-9, This results in an alternative form of the SML

b Compare your answer to part a with the Capital Market Line (CML), Equa-

tion 5-6 What similarities are observed? What conclusions can be drawn?

(5-4) Suppose you are given the following information The beta of company i, b, is 1.1,

CAPM and the fama: the risk-free rate, rrp, is 7 percent, and the expected market premium, ty — rạp, is French Three-Factor € 5 percent (Assume that a; = 0.0.) Model

a Use the Security Market Line (SML) of CAPM to find the required return for this company

b Because your company is smaller than average and more successful than aver-

age (that is, it has a low book-to-market ratio), you think the Fama-French three-

factor model might be more appropriate than the CAPM You estimate the additional coefficients from the Fama-French three-factor model: The coeffi- cient for the size effect, c,, is 0.7, and the coefficient for the book-to-market

effect, dj, is —0.3 If the expected value of the size factor is 5 percent and the expected value of the book-to-market factor is 4 percent, what is the required

return using the Fama-French three-factor model?

242 CHAPTER 6 Bonds and Their Valuation

maturity value (the difference is a call premium)-A-firm will typically call a 4

bond if interest rates fall substantially below the coupon rate tổ

* A redeemable bond gives the investor the right to sell the bond back to the issu-

ing company at a previously specified price This is a useful feature (for investors) if interest rates rise or if the company engages in unanticipated risky

activities,

* A sinking fund is a provision that requires the corporation to retire a portion of

the bond issue each year The purpose of the sinking fund is to provide for the

orderly retirement of the issue A sinking fund typically requires no call pre-

mium

The value of a bond is found as the present value of an annuity (the interest

payments) plus the present value of a lump sum (the principal) The bond is

evaluated at the appropriate periodic interest rate over the number of periods

for which interest payments are made

* The equation used to find the value of an annual coupon bond is:

(YTC) The YTC is found as the present value of the interest payments received

while the bond is outstanding plus the present value of the call price (the par

value plus a call premium)

° The longer the maturity of a bond, the more its price will change in response to

a given change in interest rates; this is called interest rate risk However, bonds

with short maturities expose investors to high reinvestment rate risk, which is

the risk that income from a bond portfolio will decline because cash flows received from bonds will be rolled over at lower interest rates

* Corporate and municipal bonds have default risk If an issuer defaults,

investors receive less than the promised return on the bond Therefore,

investors should evaluate a bond’s default risk before making a purchase vs

*- There are many different types of bonds with different sets of features These include convertible bonds, bonds with warrants, income bonds, purchasing “5 power (indexed) bonds, mortgage bonds, debentures, subordinated debentures, junk bonds, development bonds, and insured municipal bonds The return

- required on each type of bond is determined by the bond’s riskiness

* Bonds-are assigned ratings that reflect the probability of their going into

default The highest rating is AAA, and they go down to D The higher a

bond's rating, the lower its risk and therefore its interest rate

(6-1) Define each of the following terms:

Bond; Treasury bond; corporate bond; municipal bond; foreign bond Par value; maturity date; coupon payment; coupon interest rate

_ Floating-rate bond; zero coupon bond; original issue discount bond (OID)

~ Call provision; redeemable bond; sinking fund ca

- Converfible bond; warrant; income bond; indexed, or purchasing power, bond remiygn bond; discount bond

Problems 243

4, Indentures; mortgage bond; debenture; subordinated debenture

j Development bond; municipal bond insurance; junk bond; investment-grade

- bond

(6-2) “The values of outstanding bonds change whenever the going rate of interest

changes In general, short-term interest rates are more volatile than long-term interest rates Therefore, short-term bond prices are more sensitive to interest rate -changes than are long-term bond prices.” Is this statement true or false? Explain

(6-3): The rate of return you would get if you bought a bond and held it to its maturity date is called the bond’s yield to maturity If interest rates in the economy rise after a bond has been issued, what will happen to the bond’s price and to its YTM? Does the length of time to maturity affect the extent to which a given

change in interest rates will affect the bond’s price? 6-4) If you buy a callable bond and interest rates decline, will the value of your bond

rise by as much as it would have risen if the bond had not been callable? Explain (6-5) A sinking fund can be set up in one of two ways: OS

(1) The corporation makes annual payments to the trustee, who invests the pro-

ceeds in secutities (frequently government bonds) and uses the accumulated

total to retire the bond issue at maturity — os

(2) The trustee uses the annual payments to retire a portion of the issue each year, either calling a given percentage of the issue by a lottery’ and paying a

specified price per bond or buying bonds on the open market, whichever is

- Discuss the advantages and disadvantages of each procedure from the viewpoint) =

of both 'the firm and its bondholders "1 sưng

Solution Appears in Appendix A

4 What was the YTM of Pennington’s bonds on January 1, 1981?

b What was the price of the bond on January 1, 1986, five year later, assuming

- that the level of interest rates had fallen to 10 percent?

c Find the current yield and capital gains yield on the bond on January 1, 1986, given the price as determined in part b " "` ¬

-d On July 1, 2004, Pennington’s bonds sold for $916.42 What was the YTM at What were the current yield and capital gains yield on July 1, 2004?:

Now, assume that you purchased an outstanding Pennington bond on March

1, 2004, when the going rate of interest was 15.5 percent How large a check mist you have written to complete the transaction? This is a hard question! -

_ ⁄ (6-1) Callaghan Motors? bonds have 10 years remaining to maturity Interest is paid

-° Bond Valuation annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 per-

cent The bonds have a yield to maturity of 9 percent What is the current market

- “price of these bonds? vn | heck (6-2) Wilson Wonders’ bonds have 12 years remaining to maturity Interest is paid

Yield to Mati; annually, the bonds have a $1,000 par value, and the coupon interest rate is 10

Financial Calflator n „ren, The bonds sell at a price of $850 What is their yield to maturity?

Bond S a maturity of 1 year

a What will be the value of each of these bonds when the going rate of interest

Bonds and Their Valuation

Thatcher’ Corporation’s bonds will mature in 10 years The bonds have a face

and a yield to maturity of 8.5 percent What is the price of the bonds?

4

value of $1,000 and an 8 percent coupon rate, paid semiannually The price of t 1

bonds is $1,100 The bonds are callable in 5 years at a call price of $1,050 What

is the yield to maturity? What is the yield to call? os Heath Foods’ bonds have 7 years Temaining to maturity The bonds have a face value of $1,000 and a yield to maturity of 8 percent They pay interest annually : and have a 9 percent coupon rate What is their current yield? : Nungesser Corporation has issued bonds that have a 9 percent coupon rate,

payable semiannually The bonds mature in 8 years, have a face value of $1,000,

The Garraty Company has two bond issues outstanding Both bonds pay $100

annual interest plus $1,000 at maturity Bond L has a maturity of 15 years, and

is (1) 5 percent, (2) 8 percent, and (3) 12 percent? Assume that there is only

One more interest payment to be made on Bond S

b Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)? The Heymann Company’s bonds have 4 years remaining to maturity Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is

9 percent

a What is the yield to maturity at a current market price of (1) $829 or (2) $1,104?

b Would you pay $829 for one of these bonds if you thought that the appropri- ate rate of interest was 12 percent—that is, if ry = 12%? Explain your answer

Six years ago, The Singleton Company sold a 20-year bond issue with a 14 per- cent annual coupon rate and a 9 percent call premium Today, Singleton called the bonds The bonds originally were sold at their face value of $1,000 Compute the

realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price

A 10-year, 12 percent semiannual coupon bond, with a par value of $1,000, may

be called in 4 years at a call price of $1,060 The bond sells for $1,100 (Assume that the bond has just been issued.)

a What is the bond’s yield to maturity?

b What is the bond’s current yield?

¢ What is the bond’s capital gain or loss yield?

d What is the bond’s yield to call?- You just purchased a bond which matures in 5 years The bond has a face value of

$1,000, and has an 8 percent annual coupon The bond has a current yield of 8.21 percent What is the bond’s yield to maturity?

A bond that matures in 7 years sells for $1,020 The bond has a face value of

$1,000 and a yield to maturity of 10.5883 percent The bond pays coupons semi- annually What is the bond’s current yield?

Lloyd Corporation’s 14 percent coupon rate, semiannual payment, $1,000 par

value bonds, that mature in 30 years, are callable S years from now at a price of $1,050, The bonds sell at a price of $1,353.54, and the yield curve is flat Assum- ing that interest rates in the economy are expected to remain at their current level,

what is the best estimate of Lloyd’s nominal interest rate on new bonds?

Suppose Ford Motor Company sold an issue of bonds with a 10-year maturity, a 1,000 par value, a 10 percent coupon rate, and semiannual interest payments

a Two years after the bonds were issued, the going rate of interest on bonds "such as these fell to 6 percent At what price would the bonds sell?

dsh et Problem 245 |

a _ to 12 percent At what price would the bonds sell? ee ie

mained a 6 nh HỆ, da) for nhe next 8 years "What would tape : the price of

_ the Ford Motor Company bonds over time? ¬ ¬

(eu) A bond trade: hased each: of the follo 4

- interest Rate- 8 percent Immediately after she purchased the bonds, interest rates.fell to 7 per-

$ song Tang cent What is the percentage change in the price of cach bond after the decline in

interest Yates? Fill i in the following table:

(6-15) An investor has t two bonds in his portfolio Each bond matures in 4 years, has a

nen ratuation, face value of $1,000, and has a yield to maturity equal to 9.6 percent One bond,

" “Needed Bond C, pays an annual coupon of 10 percent; the other bond, Bond Z, is a zero

coupon bond

a Assuming that the yield to maturity of each bond remains at 9 6-percent over the next 4 years, what will be the price of each of the bonds at: th following time periods? Fill in the following table:

b Plot the time path of the prices for each of the two bonds

(6-16) Start with the partial model in the file FM11 Ch 06 P16 Build a Model.xls from -Buid a Model; the textbook’s Web site Rework Problem 6-9 After completing parts a through d,

Bond Valuation 2 nswer the following related questions

e How would the price of the bond be affected by changing interest rates?

(Hint: Conduct a sensitivity analysis of price to changes in the yield to matu- rity, which is also the going market interest rate for the bond, Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate That is an oversimplification, but assume it anyway for purposes

of this problem.)

f Now assume that the date is October 25, 2004 Assume further that our 12

percent, 10-year bond was issued on July 1, 2004, is callable on July 1, 2008,

at $1,060, will mature on June 30, 2014, pays interest semiannually (January

1 and July 1), and sells for $1, 100 Use your spreadsheet to find (1) the bond’s

là yield to maturity and (2) its yield to call

é-resource

278 CHAPTER 7 Stocks and Their Valuation

* The horizon (terminal) value is the value at the horizon date of all future divi

- The marginal investor is a representative investor whose actions reflect the

beliefs of those people who are currently trading a stock It is the marginal investor who determines a stock’s price

* Equilibrium is the condition under which the expected return on a security as _

seen by the marginal investor is just equal to its required return, f = r Also, the 9

stock’s intrinsic value must be equal to its market price,P, = Pp

* The Efficient Markets Hypothesis (EMH) holds (1) that stocks are always in

equilibrium and (2) that it is impossible for an investor who does not have inside information to consistently “beat the market.” Therefore, according to the EMH, stocks are always fairly valued (Py = Py), the required return on a

stock is equal to its expected return (r = £), and all stocks’ expected returns plo

on the SML

- Differences can and do exist between expected and realized returns in the stock - and bond markets—only for short-term, risk-free assets are expected and actual

(or realized) returns equal

> When U.S investors purchase foreign stocks, they hope (1) that stock prices

will increase in the local market and (2) that the foreign currencies will rise rel-

ative to the U.S dollar

* Preferred stock is a hybrid security having some characteristics of debt and some of equity

* Most preferred stocks are perpetuities, and the value of a share of perpetual

preferred stock is found as the dividend divided by the required rate of return:

D

= —?

V, = =

p

* Maturing preferred stock is evaluated with a formula that is identical in form

to the bond value formula

-QUESHONS

(7-1) Define each of the following terms:

a Proxy; proxy fight; takeover; preemptive right; classified stock; founders’ shares - Closely held corporation; publicly owned corporation

Secondary market; primary market; going public; initial public offering (IPO)

Intrinsic value Py); market price (Po)

Required rate of return, r,; expected rate of return, r,; actual, or realized, rate

Capital gains yield; dividend yield; expected total return

Normal, or constant, growth; supernormal, or nonconstant, growth; zero

holds stocks for 2 years, while the other normally holds stocks for 10 years On the : basis of the type of analysis done in this chapter, they should both be willing to pay» the same price for AT&T’s stock True or false? Explain

(7-3) A bond that pays interest forever and has no maturity date is a perpetual bond In what respect is a perpetual bond similar to a no-growth common stock, and to a [ share of preferred stock?

Solutions Appear in Appendix A

Ewald Company’s current stock price is $36, and its last dividend was $2.40 In view of Ewald’s strong financial position and its consequent low risk, its required rate of return is only 12 percent If dividends are expected to grow at a constant rate, g, in the future, and if r, is expected to remain at 12 percent, what is Ewald’s expected stock price 5 years from now?

Snyder Computer Chips Inc is experiencing a period of rapid growth Earnings and dividends are expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the third year, and at a constant rate of 6 percent thereafter Snyder’s last dividend was $1.15, and the required rate of return on the stock is

7 percent a year The required rate of return on the stock, r,, is 15 percent What

is the value per share of the company’s stock?

Harrison Clothiers’ stock currently sells for $20 a share The stock just paid a div- idend of $1.00 a share (i.e., Dg = $1.00) The dividend is expected to grow at a constant rate of 10 percent a year What stock price is expected 1 year from now? What is the required rate of return on the company’s stock?

Fee Founders has preferred stock outstanding which pays a dividend of $5 at the end of each year The preferred stock sells for $60 a share What is the preferred stock’s required rate of return?

A company currently pays a dividend of $2 per share, Dy = 2 It is estimated that the company’s dividend will grow at a rate of 20 percent per year for the next 2 years, then the dividend will grow at a constant rate of 7 percent thereafter The company’s stock has a beta equal to 1.2, the risk-free rate is 7.5 percent, and the market risk premium is 4 percent What would you estimate is the stock’s current price?

A stock is trading at $80 per share The stock is expected to have a year-end divi- dend of $4 per share (D, = 4), which is expected to grow at some constant rate g throughout time The stock’s required rate of return is 14 percent If you are an analyst who believes in efficient markets, what would be your forecast of g?

You are considering an investment in the common stock of Keller Corp The stock

is expected to pay a dividend of $2 a share at the end of the year (D, = $2.00)

The stock has a beta equal to 0.9 The risk-free rate is 5.6 percent, and the market risk premium is 6 percent The stock’s dividend is expected to grow at some con- stant rate g The stock currently sells for $25 a share Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of

3 years? (That is, what is P3?) x What will be the nominal rate of return on a preferred stock with a $100 par value, a stated dividend of 8 percent of par, and a current market price of (a) $60,

(b) $80, (c) $100, and (d) $1402 :

Stocks and Their Valuation

Martell Mining Company’s ore reserves are being depleted, so its sales are

falling Also, its pit is getting deeper each year, so its costs are rising As a result,

the company’s earnings and dividends are declining at the constant rate of

5 percent per year, If Dy = $5 and r, = 15%, what is the value of Martell Mining’s stock?

The beta coefficient for Stock C is be = 0.4, whereas that for Stock D is by =

—0.5 (Stock D’s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall There are very few negative beta stocks,

although collection agency stocks are sometimes cited as an example.)

a If the risk-free rate is 9 percent and the expected rate of return on an average stock is 13 percent, what are the required rates of return on Stocks C and D?

b For Stock C, suppose the current price, Po, is $25; the next expected dividend, D,, is $1.50; and the stock’s expected constant growth rate is 4 percent Is the

stock in equilibrium? Explain, and describe what will happen if the stock is

not in equilibrium

Assume that the average firm in your company’s industry is expected to grow ata constant rate of 6 percent and its dividend yield is 7 percent Your company is about as risky as the average firm in the industry, but it has just successfully com- pleted some R&D work that leads you to expect that its earnings and dividends will grow at a rate of 50 percent [D, = Do(1 + g) = Do(1.50)] this year and 25 percent the following year, after which growth should match the 6 percent indus-

try average rate The last dividend paid (Do) was $1 What is the value per share

Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, herice it does not pay any dividends However, investors expect Microtech to begin paying dividends, with the first dividend of $1.00 coming 3 years from today The dividend should grow rapidly—at a rate of 50 percent per year—during Years 4 and 5 After Year 5, the company should grow at a constant rate of 8 percent per year If the required return on the stock is 15 percent, what is

Ezzell Corporation issued preferred stock with a stated dividend of 10 percent of

par Preferred stock of this type currently yields 8 percent, and the par value is

$100 Assume dividends are paid annually

a What is the value of Ezzell’s preferred stock?

b Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent What would be the value of Ezzell’s preferred stock?

Your broker offers to sell you some shares of Bahnsen & Co common stock that paid a dividend of $2 yesterday You expect the dividend to grow at the rate of

5 percent per year for the next 3 years, and, if you buy the stock, you plan to hold

it for 3 years and then sell it

a Find the expected dividend for each of the next 3 years; that is, calculate Dị,

D,, and Dị Note that Do = $2

b Given that the appropriate discount rate is 12 percent and that the first of these dividend payments will occur 1 year from now, find the present value of the dividend stream; that is, calculate the PV of D,, D,, and D,, and then sum these PVs -

c You expect the price of the stock 3 years from now to be $34.73; that is, you expect P; to equal $34.73 Discounted at a 12 percent rate, what is the present

ae of this expected future stock price? In other words, calculate the PV of

34.73

d If you plan to buy the stock, hold it for 3 years, and then sell it for $34.73,

what is the most you should pay for it?

e Use Equation 7-2 to calculate the present value of this stock Assume that -g = 5%, and it is constant

You buy a share of The Ludwig Corporation stock for $21.40 You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years ˆ

a Calculate the growth rate in dividends

b Calculate the expected dividend yield

c Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to get the expected total rate of return What is this stock’s expected total rate of return?

Investors require‘a 15 percent rate of return on Levine Company’s stock (r, = 15%)

a What will be Levine’s stock value if the previous dividend was Dy = $2 and if investors expect dividends to grow at a constant compound annual rate of

(1) —5 percent, (2) 0 percent, (3) 5 percent, and (4) 10 percent?

b Using data from part a, what is the Gordon (constant growth) model value for Levine’s stock if the required rate of return is 15 percent and the expected growth rate is (1) 15 percent or (2) 20 percent? Are these reasonable results? Explain

c Is it reasonable to expect that a constant growth stock would have g > r,? Wayne-Martin Electric Inc (WME) has just developed a solar panel capable of generating 200 percent more electricity than any solar panel currently on the mar- ket As a result, WME is expected to experience a 15 percent annual growth rate for the next 5 years By the end of 5 years, other firms will have developed com- parable technology, and WME’s growth rate will slow to 5 percent per year indef- initely Stockholders require a return of 12 percent on WME'’s stock The most recent annual dividend (Dy), which was paid yesterday, was $1.75 per share

a Calculate WME’s expected dividends for t = 1,t = 2,t = 3,t=4,andt = 5

b Calculate the value of the stock today, Py Proceed by finding the present value

of the dividends expected at t = 1,t = 2,t = 3,t = 4, and t = 5 plus the pres- ent value of the stock price which should exist at t = 5,P; TheP, stock price can be found by using the constant growth equation Notice that to find P., you use the dividend expected at t = 6, which is 5 percent greater than the

t = 5 dividend

c Calculate the expected dividend yield, D,/Po, the capital gains yield expected during the first year, and the expected total return (dividend yield plus capital gains yield) during the first year (Assume that Py = Po, and recognize that the capital gains yield is equal to the total return minus the dividend yield.) Also

calculate these same three yields for t = 5 (e.g., D,/Ps)

Taussig Technologies Corporation (TTC) has been growing at a rate of 20 percent per year in recent years This same growth rate is expected to last for another

c What will be TTC’s dividend yield and capital gains yield once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the cal- culations are very easy.)

d Of what interest to investors is the changing relationship between dividend yield and capital gains yield over time?

The risk-free rate of return, rer, is 11 percent; the required rate of return on the

market, ry, 14 percent; and Upton Company’s stock has a beta coefficient of 1.5

Ƒ

⁄

282 CHAPTER 7 Stocks and Their Valuation

a If the dividend expected during the coming year, D,, is $2.25, and if g = a constant 5%, at what price should Upton’s stock sell?

b Now, suppose the Federal Reserve Board increases the money supply, causin the risk-free rate to drop to 9 percent and ry, to fall to 12 percent What would this do to the price of the stock?

c In addition to the change in part b, suppose investors’ risk aversion declines; % this fact, combined with the decline in rpy, causes r), to fall to 11 percent At 3 what price would Upton’s stock sell?

d Now, suppose Upton has a change in management The new group institutes policies that increase the expected constant growth rate to 6 percent Also, th new management stabilizes sales and profits, and thus causes the beta coeffi- cient to decline from 1.5 to 1.3 Assume that rp, and ry, are equal to the val- ues in part c After all these changes, what is Upton’s new equilibrium price? (Note: D, goes to $2.27.)

SPREADSHEET PROBLEM

(7-20) Start with the partial model in the file FM11 Ch 07 P20 Build a Model.xls from ' Build a Model: the textbook’s Web site Rework Problem 7-18, parts a, b, and c, using a spread-

Ôn te Veluaiien sheet model For part b, calculate the price, dividend yield, and capital gains yield q

as called for in the problem

Please go to our Web site, academic.cengage.com/finance/brigham, to access any Cyberproblems

(8-1) Define each of the following terms:

a Option; call option; put option

b Exercise value; strike price

c Black-Scholes Option Pricing Model

(8-2) Why do options sell at prices higher than their exercise values?

(8-3) Describe the effect on a call option°s price.caused by an-trcfeäS€ in cach of

the following factors: (1) stock price, (2) exercise price, (3) time to expiration, -

(4) risk-free rate, and (5) variance of stock return - ý

- | SEI F-TEST PROBLEMS Solutions Appear in Appendix A

(ST-1) A call option on the stock of Bedrock Boulders has a market price of $7 The

Options stock sells for $30 a share, and the option has an exercise price of $25 a share

a What is the exercise value of the call option?

b What is the premium on the option? "

§T-2) Which of the following events are likely to increase the market value of a call

Options option on a common stock? Explain

An increase in the stock’s price

An increase in the volatility of the stock price

An increase in the risk-free rate

A decrease in the time until the option expires

(8-1) Assume you have been given the following information on Purcell Industries:

k:Scholes Model

Current stock price = $15 Exercise price of option = $15

Time to maturity of option = 6 months Risk-free rate = 6%

Variance of stock return = 0.12 d, = 0.24495

d, = 0.00000 N(d,) = 0.59675

N(d,) = 0.50000

Using the Black-Scholes Option Pricing Model, what would be the value of the option?

{8-2} The exercise price on one of Flanagan Company’s options is $15, its exercise value

Options is $22, and its premium is $5 What are the option’s market value and the price of

Financial Options and Their Valuation

Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) exercise price is $35, (3) time to expira tion is 4 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0,25, - ve :

The current price of a stock is $20 In 1 year, the price will be either $26 or $16 The annual risk-free rate is § percent Find the price of a call option on the stock : that has an exercise price of $21 and that expires in 1 year (Hint: Use daily :

The current price of a stock is $15 In 6 months, the price will be either $18 or

$13 The annual risk-free rate is 6 percent Find the price of a call option on the

stock that has an exercise price of $14 and that expires in 6 months (Hint: Use

daily compounding.) The current price of a stock is $33, and the annual risk-free rate is 6 percent A call option with an exercise price of $32 and 1 year until expiration has a curren: value of $6.56 What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?

Start with the-partial model in the file FM11 Ch 08 P07 Build a Model.xls from

the textbook’s Web site Rework Problem 8-1 Then work the next two parts of this problem given below

a Construct data tables for the exercise value and Black-Scholes option value for 7 this option, and graph this relationship Include possible stock price values ranging up to $30.00

b Suppose this call option is purchased today Draw the profit diagram of this

Self-Test Problem 335

(9-1) Define each of the following terms:

a Weighted average cost of capital, WACC; after-tax cost of debt, rạ(1 — T)

b Cost of preferred stock, r„„; cost OÍ common equity or cost of common

stock, r,

c Target capital structure

d Flotation cost, F; cost of new external common equity, r, (9-2) In what sense is the WACC an average cost? A marginal cost?

(9-3) How would each of the following affect a firm’s cost of debt, rg(1 — T); its cost of equity, r,; and its weighted average cost of capital, WACC? Indicate by a plus (+),

a minus (—), or a zero (0 0) if the factor would raise, lower, or have an indetermi-

nate effect on the item in question Assume other things are held constant Be pre-

pared to justify your answer, but recognize that several of the parts probably have

no single correct answer; these questions are designed to stimulate thought and discussion

The firm doubles the amount of capital

it raises during the year — — —

e The firm expands into a risky new area — — —

f Investors become more risk averse — — —

{9-4) Distinguish between beta (or market) risk, within-firm (or corporate) risk, and

stand-alone risk for a potential project Of the three measures, which is theoreti-

cally the most relevant, and why?

(9-5) Suppose a firm estimates its cost of capital for the coming year to be 10 percent What might be reasonable costs of capital for average-risk, high-risk, and low-risk projects?

(ST-1) Longstreet Communications Inc (LCI) has the following capital structure, which

WACC it considers to be optimal: debt = 25%, preferred stock = 15%, and common

LCI’s tax rate is 40 percent and investors expect earnings and dividends to grow at a constant rate of 6 percent in the future LCI paid a dividend of $3.70

per share last year (Do), and its stock currently sells at a price of $60 per share

Treasury bonds yield 6 percent, the market risk premium is 5 percent, and LCI’s beta is 1.3 These terms would apply to new security offerings:

Preferred: New preferred could be sold to the public at a price of $100 per share,

with a dividend of $9 Flotation costs of $5 per share would be

incurred

Debt: — Debt could be sold at an interest rate of 9 percent

a Find the component costs of debt, preferred stock, and common stock

Assume LCI does not have to issue any additional shares of common stock

b What is the WACC?

David Ortiz Motors has a target capital structure of 40 percent debt and 60 per- 3

cent equity The yield to maturity on the company’s outstanding bonds is 9 per- 3 cent, and the company’s tax rate is 40 percent Ortiz’s CFO has calculated the 3

company’s WACC as 9.96 percent What is the company’s cost of equity capital? ¡

Tunney Industries can issue perpetual preferred stock at a price of $50 a share

The issue is expected to pay a constant annual dividend of $3.80 a share The flotation cost on the issue is estimated to be 5 percent What is the company’s cost 4

of preferred stock, r,,? 4

Javits & Sons’ common stock is currently trading at $30 a share The stock is expected to pay a dividend of $3.00 a share at the end of the year (Dị = $3.00), 4 and the dividend is expected to grow at a constant rate of 5 percent a year What ï

is the cost of common equity?

Calculate the after-tax cost of debt under each of the following conditions:

a Interest rate, 13 percent; tax rate, 0 percent

b Interest rate, 13 percent; tax rate, 20 percent

c Interest rate, 13 percent; tax rate, 35 percent

The Heuser Company’s currently outstanding 10 percent coupon bonds have a yield to maturity of 12 percent Heuser believes it could issue at par new bonds that would provide a similar yield to maturity If its marginal tax rate is 35 per- cent, what is Heuser’s after-tax cost of debt?

Trivoli Industries plans to issue some $100 par preferred stock with an 11 percent 3 dividend The stock is selling on the market for $97.00, and Trivoli must pay 1 flotation costs of 5 percent of the market price What is the cost of the preferred stock for Trivoli?

A company’s 6 percent coupon rate, semiannual payment, $1,000 par value bond 4 which matures in 30 years sells at a price of $515.16 The company’s federal-plus- | state tax rate is 40 percent What is the firm’s component cost of debt for pur- = poses of calculating the WACC? (Hint: Base your answer on the nominal rate.) The earnings, dividends, and stock price of Carpetto Technologies Inc are

expected to grow at 7 percent per year in the future Carpetto’s common stock

sells for $23 per share, its last dividend was $2.00, and the company will pay a dividend of $2.14 at the end of the current year

a Using the discounted cash flow approach, what is its cost of equity?

b If the firm’s beta is 1.6, the risk-free rate is 9 percent, and the expected return

on the market is 13 percent, what will be the firm’s cost of equity using the

c If the firm’s bonds earn a return of 12 percent, what will r, be using the bond- 3 yield-plus-risk-premium approach? (Hint: Use the midpoint of the risk pre- 4 mium range.)

d On the basis of the results of parts a through c, what would you estimate Carpetto’s cost of equity to be?

The Bouchard Company’s current EPS is $6.50 It was $4.42 5 years ago The company pays out 40 percent of its earnings as dividends, and the stock sells for $36

a Calculate the past growth rate in earnings (Hint: This is a 5-year growth period.)

b Calculate the next expected dividend per share, D, (Dy = 0.4($6.50) =

$2.60.) Assume that the past growth rate will continue

c What is the cost of equity, r,, for the Bouchard Company?

F

-b If Sidmamreinvests earnings in projects with average returns equal to the

stock’s expected rate of return, what will be next year’s EPS? ~

On January 1, the total market value of the Tysseland Company was $60 million During the year, the company plans to raise and invest $30 million in new projects The firm’s present market value capital structure, shown below, is considered to be optimal Assume that there is no short-term debt

so $1.20/§30 = 4%.) The marginal corporate tax rate is 40 percent

a To maintain the present capital structure, how much of the new investment

must be financed by common equity? NUNG Tổ nhổ

b Assume that there is sufficient cash flow such that Tysseland can maintain its target capital structure without issuing additional shares of equity What is the

c Suppose now that there is not enough internal cash flow and the firm must issue new shares of stock Qualitatively speaking, what will happen to the WACC?

Suppose the Schoof Company has this book value balance sheet:

Current assets’ — $30,000,000 Current liabilities $10,000,000

Fixed assets 50,000,000 Long-term debt ' 30,000,000

going rate of interest on new long-term debt, ry, is 10 percent, and this is the present

338 CHAPTER 9

ie (6) Ata recent ca ference, TII’s financial vice president polled some pension fund _ investment managers on the minimum rate of return they would have to _ expect on TIls-common to make them willing to buy the common rather _ -\, than TH bonds, when the bonds yielded 12 percent The responses suggested

a tisk premiugn over TIE bonds of 4 to 6 percentage points

- (7) THis in the 4

(8) TIPs principal investment banker, Henry, Kaufman & Company, predicts a

The Cost of Capital

Travellers Inn: December 31, 2004 (Millions of Dollars)

Accounts receivable 20 Accruals Inventories ve _ 20 ‘Short-term debt Current assets $ 50 Current liabilities

Net fixed assets 50 Long-term debt

Preferred stock

Common equity

Common stock

Retained earnings Total common equity Total assets c® — Q © Total liabilities and equity

These facts are also given for TH:

(1) Short-term debt consists of bank loans that currently cost 10 percent, with

interest payable quarterly These loans are used to finance receivables and inventories on a seasonal basis, so in the off-season, bank loans are zero

(2) The long-term debt consists of 20-year, semiannual payment mortgage bond with a coupon rate of 8 percent Currently, these bonds provide a yield to investors of ry = 12% If new bonds were sold, they would yield investors

(3) THs perpetual preferred stock has a $100 par value, pays a quarterly divi- dend of $2, and has a yield to investors of 11 percent New perpetual pre- ferred would:have to provide the same yield to investors, and the company | would incur a 5 percent flotation cost to sell it 4 (4) The company has 4 million shares of common stock outstanding Pp = — q

$20, but the stock has recently traded in a range of $17 to $23 Dy = $1 and EPS, = $2 ROE based on average equity was 24 percent in 2004, but management expects to increase this return on equity to 30 percent; — however, security analysts are not aware of management’s optimism in this regard °

(5) Betas, as reported by security analysts, range from 1.3 to 1.7; the T-bond

' Fate is 10 percent; and RP,, is estimated by various brokerage houses to be

in the range of 4.5 to 5.5 percent Brokerage house reports forecast growth rates in the range of 10 to 15 percent over the foreseeable future However, some analysts do not explicitly forecast growth rates, but they indicate to their clients that they expect TII’s historical trends as shown in the table

percent federal-plus-state tax bracket

decline in interest rates, with rq falling to 10 percent and the T-bond rate to _ 8 percent, although Henry, Kaufman & Company acknowledges that an increase in the

expected ‘inflation rate could lead to an increase rather than orical record of EPS and DPS:

“Year DPS Year EPS DPS

1990 1991 $0.00 ˆ 1992 $0.40 _ $0/00

-.0,00 ” 1993 0.52 0.00ˆ

: (g-14) Rework Problem 9-3, assuming that new stock will be issued The stock will be

Bastion Cost and issued for $30 and the flotation cost is 10 percent of the issue proceeds The

ee ost of Equity expected dividend and growth remain at $3.00 per share and 5 percent, respectively

(9-15) Suppose a company will issue new 20-year debt with a par value of $1,000 and a

jotation Costs and coupon rate of 9 percent, paid annually The tax rate is 40 percent If the flotation

“the Cost of Debt : : :

° cost is 2 percent of the issue proceeds, what is the after-tax cost of debt?

: (9-16) Start with the partial model in the file FM11 Ch 09 P16 Build a Model.xls from

shored watt the revtbook’ Web site The stock of Gao Computing sells for 850, amd last years

dividend was $2.10 A flotation cost of 10 percent would be required to issue new

common stock Gao’s preferred stock pays a dividend of $3.30 per share, and new

preferred could be sold at a price to net the company $30 per share Security ana-

lysts are projecting that the common dividend will grow at a rate of 7 percent a

e year The firm can also issue additional long-term debt at an interest rate {or -

before-tax cost) of 10 percent, and its marginal tax rate is 35 percent The market

risk premium is 6 percent, the risk-free rate is 6.5 percent, and Gao’s beta is 0.83

In its cost of capital calculations, Gao uses a target capital structure with 45 per-

cent debt, 5 percent preferred stock, and 50 percent common equity,

a Calculate the cost of each capital component (that is, the after-tax cost of

debt), the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs) with the DCF method and the CAPM method

b Calculate the cost of new stock using the DCF model sẽ

c What is the cost of aew common stock, based on the CAPM? (Hint: Find the

difference between r, and r, as determined by the DCF method and add that

differential to the CAPM value for r,.) Vee an

d Assuming that Gao will not issue new equity and will continue to use the

same target capital structure, what is the company’s WACC? ty

e Suppose Gao is evaluating three projects with the following characteristics:

(1) Each project has a cost of $1-million They will all be financed using the

target mix of long-term debt, preferred stock, and common equity The cost of the common equity for each project should be based on the beta

estimated for the project All equity will come from retained earnings

(2) Equity invested in Project A would have a beta of 0.5 and an expected

Questions 369

The discounted payback method is similar to the regular payback method -

except that it discounts cash flows at the project's cost of capital It considers

the time value of money, but it ignores cash flows beyond the payback period

The net present value (NPV) method discounts all cash flows at the project’s

cost of capital and then sums those cash flows The project should be accepted

_ The internal rate of return (IRR) is defined as the discount rate that forces a

project’s NPV to equal zero The project should be accepted if the IRR is

The NPV and IRR methods make the same accept/reject decisions for indepen-

dent projects, but if projects are mutually exclusive, then ranking conflicts:can

arise If conflicts arise, the NPV method should be used The NPV and IRR

methods are both superior to the payback, but NPV is superior to IRR

The NPV method assumes that cash flows will be reinvested at the firm’s-cost

of capital, while the IRR method assumes reinvestment at the project’s IRR

Reinvestment at the cost of capital is generally a better assumption because it

The modified IRR (MIRR) method corrects some of the problems with the regular

IRR MIRR involves finding the terminal value (TV) of the cash inflows, com-

pounded at the firm’s cost of capital, and then determining the discount rate that

forces the present value of the TV to equal the present value of the outflows

The profitability index (PI) shows the dollars of present value divided by the

initial cost, so it measures relative profitability

Sophisticated managers consider all of the project evaluation measures because

each measure provides a useful piece of information

The post-audit is a key element of capital budgeting By comparing actual

results with predicted results and then determining why differences occurred,

decision makers can improve both their operations and their forecasts of

projects’ outcomes

Small firms tend to use the payback method rather than a discounted cash flow

method This may be rational, because (1) the cost of conducting a DCF analy-

sis may outweigh the benefits for the project being considered, (2) the firm’s

cost of capital cannot be estimated accurately, or (3) the small-business owner

may be considering nonmonetary goals

If mutually exclusive projects have unequal lives, it may be necessary to adjust

the analysis to put the projects on an equal life basis This can be done using

the replacement chain (common life) approach

A project’s true value may be greater than the NPV based on its physical life if

it can be terminated at the end of its economic life

Flotation costs and increased riskiness associated with unusually large expan-

sion programs’‘can cause the marginal cost of capital to rise as the size of the

Capital rationing occurs when management places a constraint on the size of

the firm’s capital budget during a particular period

UESLO—_—————

5-1) Define each of the following terms:

Capital budgeting; regular payback period; discounted payback period

Independent projects; mutually exclusive projects

DCF techniques; net present value (NPV) method; internal rate of return

Modified internal rate of return (MIRR) method; profitability index

Nonnormal cash flow projects; normal cash flow projects; multiple IRRs

Hurdle rate; reinvestment rate assumption; post-audit

Replacement chain; economic lifes capital rationing

370 CHAPTER 10 The Basics of Capital Budgeting: Evaluating Cash Flows

_ fto-2) How is.a project classification scheme (for example, replacement, expansion into “new markets, and so forth) used in the capital budgeting process?

(10-3) Explain why the NPV of a relatively long-term project, defined as one for which a

high percentage of its cash flows are expected in the distant future, is more sens

tive to changes in the cost of capital than is the NPV of a short-term project

{20-4) Explain why, if two mutually exclusive projects are being compared, the short-

term project might have the higher ranking under the NPV criterion if the cost of:

capital is high, but the long-term project might be deemed better if the cost of cap ital is low Would changes in the cost of capital ever cause a change in the IRR ranking of two such projects?

(10-5) -In what sense is a reinvestment rate assumption embodied in the NPV, IRR, and MIRR methods? What is the assumed reinvestment rate of each method? (10-6) Suppose a firm is considering two mutually exclusive projects One has a life of

6 years and the other a life of 10 years Would the failure to employ some type of: replacement chain analysis bias an NPV analysis against one of the projects? Explain

pORETEST PROBLEM Solution Appears in Appendix A

{ST-1) You are a financial analyst for the Hittle Company The director of capital budget-

Project Analysis ing has asked you to analyze two proposed capital investments, Projects X and Y, : Each project has a cost of $10,000, and the cost of capital for each project is 12

percent The projects’ expected net cash flows are as follows:

EXPECTED NET CASH FLOWS

Đ of return (IRR), and modified internal rate of return (MIRR) Calculate each project’s payback period, net present value (NPV), internal rat

Which project or projects should be accepted if they are independent?

Which project should be accepted if they are mutually exclusive?

How might a change in the cost of capital produce a conflict between the

” NPV and IRR rankings of these two projects? Would this conflict exist if r

» Were 5%? (Himt: Plot the NPV profiles.) _- e.,.Why does the conflict exist?

{10-1) Project K has a cost of $52,125, its expected net cash inflows are $12,000 per

Decision Methods year for 8 years, and its cost of capital is 12 percent (Hint: Begin by constructing’ a@ time line.) mộ

,

a What is the project’s payback period (to the closest year)?

b What is the project’s discounted payback period?

-.¢s What is the project’s NPV?) -

~ d What is the project’s IRR? -

©: ` What is the projects MIRR?2