Chapter 7 Stocks-Characteristics and Valuation 143
34. You have a chance to purchase a perpetual security that has a stated annual payment (cash flow)
of $50. However, this is an unusual security in that the payment will increase at an annual rate of
5 percent per year; this increase is designed to help you keep up with inflation. The next payment
to be received (your first payment, due in 1 year) will be $52.50. If your required rate of return is
15 percent, how much should you be willing to pay for this security?
a.
$350
b.
$482
c.
$525
d.
$556
e.
$610
35. Suppose you are willing to pay $30 today for a share of stock which you expect to sell at the end
of one year for $32. If you require an annual rate of return of 12 percent, what must be the
amount of the annual dividend which you expect to receive at the end of Year 1?
a.
$2.25
b.
$1.00
c.
$1.60
d.
$3.00
e.
$1.95
36. Carlson Products, a constant growth company, has a current market (and equilibrium) stock price
of $20.00. Carlson’s next dividend, D1, is forecasted to be $2.00, and Carlson is growing at an
annual rate of 6 percent. Carlson has a beta coefficient of 1.2, and a required rate of return on the
market is 15 percent. As Carlson’s financial manager, you have access to insider information
concerning a switch in product lines which would not change the growth rate, but would cut
Carlson’s beta which would not change the growth rate, but would cut Carlson’s beta coefficient
in half. If you buy the stock at the current market price, what is your expected percentage capital
gain?
a.
23%
b.
33%
c.
43%
d.
53%
e.
There would be a capital loss.
144 Chapter 7 Stocks-Characteristics and Valuation
37. Given the following information, calculate the expected capital gains yield for Chicago Bears
Inc.: beta = 0.6; kM = 15%; kRF = 8%; = $2.00; P0 = $25.00. Assume the stock is in equilibrium
and exhibits constant growth.
a.
3.8%
b.
0%
c.
8.0%
d.
4.2%
e.
None of the above.
38. Over the past few years, Swanson Company has retained, on the average, 70 percent of its
earnings in the business. The future retention rate is expected to remain at 70 percent of earnings,
and long-run earnings growth is expected to be 10 percent. If the risk-free rate, kRF, is 8 percent,
Chapter 7 Stocks-Characteristics and Valuation 145
the expected return on the market, kM, is 12 percent, Swanson’s beta is 2.0, and the most recent
dividend, D0, was $1.50, what is the most likely market price and P/E ratio (P0/E1) for Swanson’s
stock today?
a.
$27.50; 5.0x
b.
$33.00; 6.0x
c.
$25.00; 5.0x
d.
$22.50; 4.5x
e.
$45.00; 4.5x
39. Yesterday BrandMart Supplies paid its common stockholders a dividend equal to $3 per share.
BrandMart expects to pay a $5 per share one year from today. After the $5 dividend is paid, the
company expects its growth rate will remain constant at 4 percent per year forever. If
BrandMart’s investors demand a 12 percent rate of return, what should be the current market
price of the company’s stock?
a.
$62.50
b.
$65.00
c.
$62.27
d.
$37.50
e.
None of the above is correct.
40. Philadelphia Corporation’s stock recently paid a dividend of $2.00 per share (D0 = $2), and the
stock is in equilibrium. The company has a constant growth rate of 5 percent and a beta equal to
1.5. The required rate of return on the market is 15 percent, and the risk-free rate is 7 percent.
Philadelphia is considering a change in policy which will increase its beta coefficient to 1.75. If
market conditions remain unchanged, what new constant growth rate will cause the common
stock price of Philadelphia to remain unchanged?
a.
8.85%
b.
18.53%
146 Chapter 7 Stocks-Characteristics and Valuation
c.
6.77%
d.
5.88%
e.
13.52%
41. Hard Hat Construction’s stock is currently selling at an equilibrium price of $30 per share. The
firm has been experiencing a 6 percent annual growth rate. Last year’s earnings per share, E0,
were $4.00, and the dividend payout ratio is 40 percent. The risk-free rate is 8 percent, and the
market risk premium is 5 percent. If systematic risk (beta) increases by 50 percent, and all other
factors remain constant, by how much will the stock price change? (Hint: Use four decimal places
in your calculations.)
a.
-$7.33
b.
+$7.14
c.
-$15.00
d.
-$15.22
e.
+$22.63
Chapter 7 Stocks-Characteristics and Valuation 147
42. The Hart Mountain Company has recently discovered a new type of kitty litter which is extremely
absorbent. It is expected that the firm will experience (beginning now) an unusually high growth
rate (20 percent) during the period (3 years) it has exclusive rights to the property where the raw
material used to make this kitty litter is found. However, beginning with the fourth year the firm’s
competition will have access to the material, and from that time on the firm will achieve a normal
growth rate of 8 percent annually. During the rapid growth period, the firm’s dividend payout
ratio will be relatively low (20 percent) in order to conserve funds for reinvestment. However, the
decrease in growth in the fourth year will be accompanied by an increase in dividend payout to 50
percent. Last year’s earnings were E0 = $2.00 per share, and the firm’s required return is 10
percent. What should be the current price of the common stock?
a.
$66.50
b.
$87.96
c.
$71.53
d.
$61.78
e.
$93.50
148 Chapter 7 Stocks-Characteristics and Valuation
43. NYC Company has decided to make a major investment. The investment will require a
substantial early cash outflow, and inflows will be relatively late. As a result, it is expected that
the impact on the firm’s earnings for the first 2 years will cause a negative growth of 5 percent
annually. Further, it is anticipated that the firm will then experience 2 years of zero growth, after
which it will begin a positive annual sustainable growth of 6 percent. If the firm’s required return
is 10 percent and its last dividend, D0, was $2 per share, what should be the current price per
share?
a.
$32.66
b.
$47.83
c.
$53.64
d.
$38.47
e.
$42.49
44. Club Auto Parts’ last dividend, D0, was $0.50, and the company expects to experience no growth
for the next 2 years. However, Club will grow at an annual rate of 5 percent in the third and
fourth years, and, beginning with the fifth year, it should attain a 10 percent growth rate which it
will sustain thereafter. Club has a required rate of return of 12 percent. What should be the price
per share of Club stock at the beginning of the third year, P2?
a.
$19.98
b.
$25.06
c.
$31.21
d.
$19.48
e.
$27.55
Chapter 7 Stocks-Characteristics and Valuation 149
45. Modular Systems Inc. just paid dividend D0, and it is expecting both earnings and dividends to
grow by 0 percent in Year 2, by 5 percent in Year 3, and at a rate of 10 percent in Year 4 and
thereafter. The required return on Modular is 15 percent, and it sells at its equilibrium price, P0 =
$49.87. What is the expected value of the next dividend, ? (Hint: Draw a time line and then set up
and solve an equation with the unknown, .)
a.
It cannot be estimated without more data.
b.
$1.35
c.
$1.85
d.
$2.35
e.
$2.85
150 Chapter 7 Stocks-Characteristics and Valuation
46. Laserclok Corporation paid a dividend for 50 years until it experienced financial difficulty three
years ago, at which time the dividend payment was suspended (that is, a dividend has not been
paid during the past three years). The company is now much stronger financially, but Laserclok
does not expect to pay a dividend for the next five years. Beginning six years from today, the
company will pay a dividend equal to $2.10, which is 5 percent greater than the last dividend paid
three years ago. After the dividend payments start again, Laserclok expects the dividend to
continue to be paid and to grow at a constant rate of 5 percent. If the appropriate market rate for
investments similar to Laserclok’s stock is 15 percent, at what price should the stock currently be
selling in the financial markets?
a.
$21.00
b.
$10.44
c.
$14.00
d.
There is not enough information to answer the question.
e.
None of the above.
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
47. Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for
1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is
expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10
percent. What is the current price of the common stock?
a.
$53.45
b.
$60.98
c.
$64.49
d.
$67.47
e.
$69.21
Chapter 7 Stocks-Characteristics and Valuation 151
48. Garcia Inc. has a current dividend of $3.00 per share (D0 = $3.00). Analysts expect that the
dividend will grow at a rate of 25 percent a year for the next three years, and thereafter it will
grow at a constant rate of 10 percent a year. The company’s cost of equity capital is estimated to
be 15 percent. What is the current stock price of Garcia Inc.?
a.
$75.00
b.
$88.55
c.
$95.42
d.
$103.25
e.
$110.00
152 Chapter 7 Stocks-Characteristics and Valuation
49. Worldwide Inc., a large conglomerate, has decided to acquire another firm. Analysts are
forecasting a period (2 years) of extraordinary growth (20 percent), followed by another 2 years
of unusual growth (10 percent), and finally a normal (sustainable) growth rate of 6 percent
annually. If the last dividend was D0 = $1.00 per share and the required return is 8 percent, what
should the market price be today?
a.
$93.70
b.
$72.76
c.
$99.66
d.
$98.57
e.
$68.87
50. Assume that the average firm in your company’s industry is expected to grow at a constant rate of
5 percent, and its dividend yield is 4 percent. You company is about as risky as the average firm
in the industry, but it has just developed a line of innovative new products which leads you to
expect that its earnings and dividends will grow at a rate of 40 percent. ( = D0 ((1 + g) = D0
(1.40)) this year and 25 percent the following year, after which growth should match the 5 percent
Chapter 7 Stocks-Characteristics and Valuation 153
industry average rate. The last dividend paid (D0) was $2. What is the value per share of your
firm’s stock?
a.
$42.60
b.
$82.84
c.
$91.88
d.
$101.15
e.
$110.37
51. Assume that you would like to purchase 100 shares of preferred stock that pays an annual
dividend of $6 per share. However, you have limited resources now, so you cannot afford the
purchase price. In fact, the best that you can do now is to invest your money in a bank account
earning a simple interest rate of 6 percent, but where interest is compounded daily (assume a 365–
day year). Because the preferred stock is riskier, it has a required annual rate of return of 12
percent (assume that this rate will remain constant over the next 5 years). For you to be able to
purchase this stock at the end of 5 years, how much must you deposit in your bank account today,
at t = 0?
a.
$2,985.00
b.
$4,291.23
c.
$3,138.52
d.
$3,704.18
e.
$4,831.25
154 Chapter 7 Stocks-Characteristics and Valuation
52. A financial analyst has been following Fast Start Inc., a new high-growth company. She estimates
that the current risk-free rate is 6.25 percent, the market risk premium is 5 percent, and that Fast
Start’s beta is 1.75. The current earnings per share (EPS0) is $2.50. The company has a 40 percent
payout ratio. The analyst estimates that the company’s dividend will grow at a rate of 25 percent
this year, 20 percent next year, and 15 percent the following year. After three years the dividend
is expected to grow at a constant rate of 7 percent a year. The company is expected to maintain its
current payout ratio. The analyst believes that the stock is fairly priced. What is the current price
of the stock?
a.
$16.51
b.
$17.33
c.
$18.53
d.
$19.25
e.
$19.89
Chapter 7 Stocks-Characteristics and Valuation 155
53. Assume an all equity firm has been growing at a 15 percent annual rate and is expected to
continue to do so for 3 more years. At that time, growth is expected to slow to a constant 4
percent rate. The firm maintains a 30 percent payout ratio, and this year’s retained earnings net of
dividends were $1.4 million. The firm’s beta is 1.25, the risk-free rate is 8 percent, and the market
risk premium is 4 percent. If the market is in equilibrium, what is the market value of the firm’s
common equity (1 million shares outstanding)?
a.
$6.41 million
b.
$12.96 million
c.
$9.18 million
d.
$10.56 million
e.
$7.32 million
156 Chapter 7 Stocks-Characteristics and Valuation