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 ABCÔÇ™s beta coef´¬ücient, or else plot these data points on a scatter diagram,
draw in the regression line, and then estimate the value of the beta coef´¬ücient
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 ÔÇ“ABC; ÔÇ“M rM; and both ABC and bABC in the future
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´¬üed 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
Y have the same expected returns; that is rABC rY 10.6%. Which stock
should you choose?
(28-17) The beta coef´¬ücient of an asset can be expressed as a function of the assetÔÇ™s corre-
SML and CML lation with the market, its standard deviation, and the marketÔÇ™s standard deviation:
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
a year. The required rate of return on the stock, rs, is 15 percent. What is the value
of a share of the companyÔÇ™s stock?
(28-19) Pic-A-ShoeÔÇ™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-
cent a year. What stock price is expected 1 year from now? What is the required
rate of return?
(28-20) Escrow OilÔÇ™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
bringing oil to the surface are rising. As a result, the companyÔÇ™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 OilÔÇ™s stock?
28-30 Basic Financial Tools: A Review
(28-21) Assume that an average ´¬ürm in your companyÔÇ™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 ´¬ürmÔÇ™s stock today?
(Hint: use Equation 28-21 to ´¬ünd 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
$100. Assume dividends are paid annually.
a. What is the value of Jonesboro CorporationÔÇ™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 JonesboroÔÇ™s preferred stock?
Please go to our web site, http://brigham.swlearning.com, to access the
With your Xtra! CD-ROM, access the Thomson Analytics Problems and use the
Thomson Analytics Academic online database to work this chapterÔÇ™s problems.
(28-23) Start with the partial model in the ´¬üle Ch 28 P23 Build a Model.xls from the text-
Build a Model: bookÔÇ™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
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
Susan Greene is a ´¬ünancial 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 ´¬ürm contracted with some examples to illustrate savings and investment plans,
SusanÔÇ™s ´¬ürm to provide ´¬ünancial planning services to all 150 and to prepare some information about the risks and
of its middle level managers over a 3-month period. SusanÔÇ™s rewards of investments in common stock. She particularly
plan is ´¬ürst to conduct an hour-long seminar to provide wants you to explain how risk and return are related. Please
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 HTÔÇ™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´¬ücient 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 SusanÔÇ™s clients wants to maintain a purchasing
h. Explain what happens to the risk and expected return on
power of $60,000 in todayÔÇ™s dollars, at least for the ´¬ürst
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
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´¬ücally, 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 stocksÔÇ™
these retirement goals. To do this you will need to discuss
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 SusanÔÇ™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 ´¬ünd the price of a share of Bon Temps stock. Bon Temps
in´¬‚ation rate rose by 3 percentage points, causing has a beta coef´¬ücient 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 ´¬ürm whose last
(2) What would happen to the bondÔÇ™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´¬ünitely.
(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 stockÔÇ™s value under these
states of the economy for a variety of assets. Some of the
output variables have been calculated, but blanks are
shown for others.
ESTIMATED RATE OF RETURN
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
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
Selected Additional References and Cases
For a more complete discussion of the mathe- erences for bond valuation appear in the Chapter
matics of ´¬ünance, see 4 references. Additional references for stock valu-
ation appear in the Chapter 5 references. Addi-
Atkins, Allen B., and Edward A. Dyl, ÔÇťThe Lotto
tional references on CAPM theory appear in the
Jackpot: The Lump Sum versus the Annuity,ÔÇŁ
Chapter 3 references.
Financial Practice and Education, Fall/Winter
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).
Lindley, James T., ÔÇťCompounding Issues
Case 2, ÔÇťPeachtree Securities, Inc. (A),ÔÇŁ which deals
Revisited,ÔÇŁ Financial Practice and Education,
with risk and return and CAPM concepts.
Fall 1993, 127ÔÇ“129.
Case 3, ÔÇťPeachtree Securities, Inc. (B),ÔÇŁ which
focuses on valuation concepts.
Many investment textbooks cover risk and return
concepts and bond and stock valuation models in Case 56, ÔÇťLaura Henderson,ÔÇŁ 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-