PROBLEMS
9-1 DPS calculation Warr Corporation just paid a dividend of $1.50 a share (that is, D 0
$1.50). The dividend is expected to grow 7 percent a year for the next 3 years and then at
5 percent a year thereafter. What is the expected dividend per share for each of the next
5 years?
9-2 Constant growth valuation Thomas Brothers is expected to pay a $0.50 per share
dividend at the end of the year (that is, D1 $0.50). The dividend is expected to grow
at a constant rate of 7 percent a year. The required rate of return on the stock, r s, is
15 percent. What is the stock’s value per share?
9-3 Constant growth valuation Harrison Clothiers’ stock currently sells for $20 a share. It
just paid a dividend of $1.00 a share (that is, D 0 $1.00). The dividend is expected to
Pˆ0 D0
rs g
Easy
Problems 1–6
319Chapter 9 Stocks and Their Valuation
grow at a constant rate of 6 percent a year. What stock price is expected 1 year from
now? What is the required rate of return?
9-4 Nonconstant growth valuation Hart Enterprises recently paid a dividend, D0 , of $1.25. It
expects to have nonconstant growth of 20 percent for 2 years followed by a constant rate
of 5 percent thereafter. The firm’s required return is 10 percent.
a. How far away is the terminal, or horizon, date?
b. What is the firm’s horizon, or terminal, value?
c. What is the firm’s intrinsic value today, Pˆ0?
9-5 Corporate value model Smith Technologies is expected to generate $150 million in free
cash flow next year, and FCF is expected to grow at a constant rate of 5 percent per year
indefinitely. Smith has no debt or preferred stock, and its WACC is 10 percent. If Smith
has 50 million shares of stock outstanding, what is the stock’s value per share?
9-6 Preferred stock valuation Fee Founders has perpetual preferred stock outstanding that
sells for $60 a share and pays a dividend of $5 at the end of each year. What is the
required rate of return?
9-7 Preferred stock rate of return What will be the nominal rate of return on a perpetual
preferred stock with a $100 par value, a stated dividend of 8 percent of par, and a cur-
rent market price of (a) $60, (b) $80, (c) $100, and (d) $140?
9-8 Preferred stock valuation Ezzell Corporation issued perpetual preferred stock with a
10 percent annual dividend. The stock currently yields 8 percent, and its par value is $100.
a. What is the stock’s value?
b. Suppose interest rates rise and pull the preferred stock’s yield up to 12 percent.
What would be its new market value?
9-9 Preferred stock returns Bruner Aeronautics has perpetual preferred stock outstanding with
a par value of $100. The stock pays a quarterly dividend of $2, and its current price is $80.
a. What is its nominal annual rate of return?
b. What is its effective annual rate of return?
9-10 Valuation of a declining growth stock 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 ris-
ing. As a result, the company’s earnings and dividends are declining at the constant rate of
5 percent per year. If D0 $5 and rs 15%, what is the value of Martell Mining’s stock?
9-11 Valuation of a constant growth stock A stock is expected to pay a dividend of $0.50 at
the end of the year (that is, D1 0.50), and it should continue to grow at a constant rate
of 7 percent a year. If its required return is 12 percent, what is the stock’s expected price
4 years from today?
9-12 Valuation of a constant growth stock Investors require a 15 percent rate of return on
Levine Company’s stock (that is, rs 15%).
a. What is its value if the previous dividend was D0 $2 and investors expect divi-
dends to grow at a constant annual rate of (1) 5 percent, (2) 0 percent, (3) 5 per-
cent, or (4) 10 percent?
b. Using data from part a, what would the Gordon (constant growth) model value be
if the required rate of return were 15 percent and the expected growth rate were
(1) 15 percent or (2) 20 percent? Are these reasonable results? Explain.
c. Is it reasonable to think that a constant growth stock could have g rs?
9-13 Rates of return and equilibrium Stock C’s beta coefficient is bC 0.4, while Stock D’s is
bD 0.5. (Stock D’s beta is negative, indicating that its return rises when 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 7 percent and the expected rate of return on an average stock
is 11 percent, what are the required rates of return on Stocks C and D?
b. For Stock C, suppose the current price, P0, is $25; the next expected dividend, D1, is
$1.50; and the stock’s expected constant growth rate is 4 percent. Is the stock in equi-
librium? Explain, and describe what would happen if the stock is not in equilibrium.
9-14 Constant growth You are considering an investment in Keller Corp’s stock, which is
expected to pay a dividend of $2 a share at the end of the year (D1 $2.00) and has a
beta of 0.9. The risk-free rate is 5.6 percent, and the market risk premium is 6 percent.
Keller currently sells for $25 a share, and its dividend is expected to grow at some constan
