3 23.8 17.0

4 (7.2) 2.5

5 6.6 7.6

6 20.5 19.9

7 30.6 18.2

a. Use a calculator with a linear regression function (or a spreadsheet) to determine

Stock ABC™s beta coef¬cient, or else plot these data points on a scatter diagram,

draw in the regression line, and then estimate the value of the beta coef¬cient

“by eye.”

b. Determine the arithmetic average rates of return for Stock ABC and the NYSE

over the period given. Calculate the standard deviations of returns for both

Stock ABC and the NYSE.

c. Assuming (1) that the situation during Years 1 to 7 is expected to hold true in

the future (that is, rABC “ABC; “M rM; and both ABC and bABC in the future

ˆ ˆ

r r

will equal their past values), and (2) that Stock ABC is in equilibrium (that is, it

plots on the SML), what is the implied risk-free rate?

d. Plot the Security Market Line.

e. Suppose you hold a large, well-diversi¬ed portfolio and are considering adding

to the portfolio either Stock ABC or another stock, Stock Y, that has the same

beta as Stock ABC but a higher standard deviation of returns. Stocks ABC and

ˆ ˆ

Y have the same expected returns; that is rABC rY 10.6%. Which stock

should you choose?

(28-17) The beta coef¬cient of an asset can be expressed as a function of the asset™s corre-

SML and CML lation with the market, its standard deviation, and the market™s standard deviation:

Comparison

i,M i

bi

M

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

Equation 28-16. This results in an alternative form of the SML.

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

28-14. What similarities are observed? What conclusions can be drawn?

(28-18) Axxon Inc. is expected to pay a $0.75 per share dividend at the end of the year

(i.e., D1 $0.75). The dividend is expected to grow at a constant rate of 7 percent

Constant Growth

Valuation

a year. The required rate of return on the stock, rs, is 15 percent. What is the value

of a share of the company™s stock?

(28-19) Pic-A-Shoe™s stock currently sells for $25. The stock just paid a dividend of $1.25,

that is, D0 $1.25. The dividend is expected to grow at a constant rate of 8 per-

Constant Growth

Valuation

cent a year. What stock price is expected 1 year from now? What is the required

rate of return?

(28-20) Escrow Oil™s petroleum reserves are being depleted, so its sales revenues are

falling. Also, its reserves are becoming increasingly deep each year, so the costs of

Declining Growth Stock

Valuation

bringing oil to the surface are rising. As a result, the company™s earnings and divi-

dends are declining at a constant rate of 5 percent per year. If D0 $6 and rS

15%, what is the value of Escrow Oil™s stock?

28-30 Basic Financial Tools: A Review

Chapter 28

(28-21) Assume that an average ¬rm in your company™s industry is expected to grow at a

Supernormal Growth constant rate of 7 percent and has a dividend yield of 6 percent. Your company is

Stock Valuation of average risk, but it has just successfully completed some R&D work which

leads you to expect that its earnings and dividends will grow at a rate of 50 per-

cent [D1 D0(1 g) D0(1.50)] this year, and 25 percent the following year,

after which growth should match the 7 percent industry average rate. The last div-

idend paid (D0) was $2.00. What is the value per share of your ¬rm™s stock today?

(Hint: use Equation 28-21 to ¬nd the required rate of return.)

(28-22) Jonesboro Corporation issued preferred stock with a stated dividend of 9 percent

of par. Preferred stock of this type currently yields 7 percent, and the par value is

Preferred Stock

Valuation

$100. Assume dividends are paid annually.

a. What is the value of Jonesboro Corporation™s preferred stock?

b. Suppose interest rate levels rise to the point where preferred stock yields 12

percent. Now what would be the value of Jonesboro™s preferred stock?

Cyberproblem

Please go to our web site, http://brigham.swlearning.com, to access the

Cyberproblems.

With your Xtra! CD-ROM, access the Thomson Analytics Problems and use the

Thomson Analytics Academic online database to work this chapter™s problems.

Spreadsheet Problem

(28-23) Start with the partial model in the ¬le Ch 28 P23 Build a Model.xls from the text-

Build a Model: book™s Student CD or web site. Set up an amortization schedule for a $30,000

Loan Amortization loan to be repaid in equal installments at the end of each of the next 20 years at

an interest rate of 10 percent.

a. What is the annual payment?

b. Set up an amortization schedule for a $60,000 loan to be repaid in 20 equal

annual installments at an interest rate of 10 percent. What is the annual

payment?

c. Set up an amortization schedule for a $60,000 loan to be repaid in 20 equal

annual installments at an interest rate of 20 percent. What is the annual

payment?

Mini Case

Susan Greene is a ¬nancial planner. Her job is to suggest and some general information about investments and their risks,

implement investment and savings plans for clients, some of and then to arrange individual meetings for follow-up. She

whom are of modest means and some of whom are quite has asked you to help her with the seminar by working out

wealthy. Last month a Fortune 500 ¬rm contracted with some examples to illustrate savings and investment plans,

Susan™s ¬rm to provide ¬nancial planning services to all 150 and to prepare some information about the risks and

of its middle level managers over a 3-month period. Susan™s rewards of investments in common stock. She particularly

plan is ¬rst to conduct an hour-long seminar to provide wants you to explain how risk and return are related. Please

28-31

Mini Case

answer the following questions and prepare the following (1) Calculate the expected return, standard deviation,

illustrations for her. and CV for HT and the T-bills.

a. Draw time lines (1) for a $100 lump sum due at the end (2) How do HT™s return, standard deviation, and CV

of Year 2 and (2) for a 3-year $100 annuity. Explain how compare with those of the other assets, and what are

each investment of $100 grows to its future value after 3 the implications of these comparisons?

years if the interest rate is 10 percent. g. Suppose you created a 2-stock portfolio by investing

b. What is the present value of the $100 lump sum due at $50,000 in HT and $50,000 in Collections.

the end of 2 years and the 3-year, $100 annuity in part a? (1) Calculate the expected return (rP), the standard devi-

How much would you need to invest in an account that ation ( p) and coef¬cient of variation (CVp) for this

earns 10 percent in order to fund this annuity? portfolio.

c. If in¬‚ation is 3 percent per year, then an annual salary of (2) How does the riskiness of this portfolio compare to the

$60,000 today will rise to about $145,000 in 30 years. riskiness of the individual stocks if held in isolation?

One of Susan™s clients wants to maintain a purchasing

h. Explain what happens to the risk and expected return on

power of $60,000 in today™s dollars, at least for the ¬rst

a portfolio constructed from randomly picked stocks if

year of retirement, so she is planning to draw $145,000

we start with a 1-stock portfolio and add more and more

a year at year-end after retirement. How much must she

stocks.

save monthly to retire in 30 years and draw an annual

pension of $145,000 for 20 years after retirement? i. How are risk and return related under the CAPM?

Assume a 10 percent per year return on investments. Speci¬cally, how is beta calculated and how are required

rates of return determined? Use the SML to calculate

d. Susan has also asked you to prepare some information

required rates of return for the three stocks in part f.

about various investments that might be used to meet

How do these required returns compare with the stocks™

these retirement goals. To do this you will need to discuss

expected returns?

not only how bonds and stocks are priced but also the

concept of the trade-off between risk and return. To j. Explain why the price of a share of stock is calculated as

begin, describe the key features of a bond and show how the present value of its expected future dividends, using

its value is determined. Find the value of a 10-year, a time line to help with your explanation.

$1,000 par value bond with a 10 percent annual coupon

k. One of Susan™s clients has just inherited some stock of a

and a required rate of return of 10 percent.

company named Bon Temps, and he asked her to evalu-

e. (1) What would be the value of the bond described in ate the stock for him. Use the dividend growth model to

part d if, just after it had been issued, the expected ¬nd the price of a share of Bon Temps stock. Bon Temps

in¬‚ation rate rose by 3 percentage points, causing has a beta coef¬cient of 1.2, the risk-free rate is 7 per-

investors to require a 13 percent return? cent, the required rate of return on the market is 12 per-

cent. Bon Temps is a constant growth ¬rm whose last

(2) What would happen to the bond™s value if in¬‚ation

dividend (D0) was $2 and whose dividend is expected to

fell, causing rd to decline to 7 percent?

grow at a rate of 6 percent inde¬nitely.

(3) What would happen to the value of the 10-year bond

l. If Bon Temps were selling for $30.29, what would be its

over time if the required rate of return remained at

implied expected rate of return?

13 percent? If it remained at 7 percent?

m. Now assume that Bon Temps is expected to experi-

f. As an alternative to bond investments, Susan wants you

ence supernormal growth of 30 percent for the next 3

to present some data on stock investments. The follow-

years, then to return to its long-run constant growth

ing table has the returns that should occur under various

rate of 6 percent. What is the stock™s value under these

states of the economy for a variety of assets. Some of the

conditions?

output variables have been calculated, but blanks are

shown for others.

ESTIMATED RATE OF RETURN

STOCKS

State of the Economy Probability T-Bills HT Collections USR Market Portfolio

Recession 0.1 8.0% (22.0%) 28.0% 10.0% (13.0%)

Below Average 0.2 8.0 (2.0) 14.7 (10.0) 1.0

Average 0.4 8.0 20.0 0.0 7.0 15.0

Above Average 0.2 8.0 35.0 (10.0) 45.0 29.0

Boom 0.1 8.0 50.0 (20.0) 30.0 43.0

ˆ

r 1.7% 13.8% 15.0%

0 13.4 18.8

CV 7.7 1.4

b 1.30 0.87 0.89 1.00

28-32 Basic Financial Tools: A Review

Chapter 28

Selected Additional References and Cases

For a more complete discussion of the mathe- erences for bond valuation appear in the Chapter

matics of ¬nance, see 4 references. Additional references for stock valu-

ation appear in the Chapter 5 references. Addi-

Atkins, Allen B., and Edward A. Dyl, “The Lotto

tional references on CAPM theory appear in the

Jackpot: The Lump Sum versus the Annuity,”

Chapter 3 references.

Financial Practice and Education, Fall/Winter

1995, 107“111.

The following cases from the Finance Online

Cissell, Robert, Helen Cissell, and David C.

Case Library cover many of the concepts dis-

Flaspohler, Mathematics of Finance, 8th ed.

cussed in this chapter and are available at

(Boston: Houghton Mif¬‚in, 1990).

http://www.textchoice.com:

Lindley, James T., “Compounding Issues

Case 2, “Peachtree Securities, Inc. (A),” which deals

Revisited,” Financial Practice and Education,

with risk and return and CAPM concepts.

Fall 1993, 127“129.

Case 3, “Peachtree Securities, Inc. (B),” which

focuses on valuation concepts.

Many investment textbooks cover risk and return

concepts and bond and stock valuation models in Case 56, “Laura Henderson,” which focuses on

depth and detail. Some of the better ones are valuation, risk, and portfolio construction.

listed in the Chapter 2 references. Additional ref-