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10-24. Solution:
North Pole Cruise Lines
a. Original price
$6.00 $100
.06
p
p
p
D
PK
= = =
b. Current value
$6.00 $42.86
.14 =
c. The price of preferred stock will increase as yields decline.
Since preferred stock is a fixed income security, its price is
25. Preferred stock value (LO10-4) X-Tech Company issued preferred stock many years ago.
It carries a fixed dividend of $12.00 per share. With the passage of time, yields have soared
from the original 10 percent to 17 percent (yield is the same as required rate of return).
a.What was the original issue price?
b. What is the current value of this preferred stock?
c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price
of the preferred stock be affected?
10-25. Solution:
X-Tech Company
a. Original price
$12.00 $120
0.10
p
p
p
D
PK
= = =
b. Current value
$12.00 $70.59
0.17 =
c. The price of preferred stock will increase as yields decline.
Since preferred stock is a fixed income security, its price is
26. Analogue Technology has preferred stock outstanding that pays a $9 annual dividend. It has
a price of $76. What is the required rate of return (yield) on the preferred stock?
10-26. Solution:
Analogue Technology
$9 11.84%
$76
p
p
p
D
KP
= = =
(All of the following problems pertain to the common stock section of the chapter.)
27. Common stock value (LO10-5) Stagnant Iron and Steel currently pays a $12.25 annual
cash dividend (D0). The company plans to maintain the dividend at this level for the
foreseeable future as no future growth is anticipated. If the required rate of return by
common stockholders (Ke) is 18 percent, what is the price of the common stock?
10-27. Solution:
Stagnant Iron and Steel
0
0
$12.25 $68.06
0.18
e
D
PK
= = =
28. BioScience Inc. will pay a common stock dividend of $3.20 at the end of the year (D1). The
required return on common stock (Ke) is 14 percent. The firm has a constant growth rate (g)
of 9 percent. Compute the current price of the stock (P0).
10-28. Solution:
BioScience Inc.
1
0
$3.20 $3.20 $64.00
.14 .09 .05
e g
D
PK
-
= = = =
-
29. Common stock value under different market conditions (LO10-5) Ecology Labs Inc.
will pay a dividend of $6.40 per share in the next 12 months (D1). The required rate of
return (Ke) is 14 percent and the constant growth rate is 5 percent.
a.Compute P0.
(For parts b, c, and d in this problem, all variables remain the same except the one
specifically changed. Each question is independent of the others.)
b. Assume Ke, the required rate of return, goes up to 18 percent. What will be the new
value of P0?
c. Assume the growth rate (g) goes up to 9 percent. What will be the new value of P0? Ke
goes back to its original value of 14 percent.
d. Assume D1 is $7.00. What will be the new value of P0? Assume Ke is at its original
value of 14 percent and g goes back to its original value of 5 percent.
10-29. Solution:
Ecology Labs Inc.
1
0
e
D
PK g
=-
a.
$6.40 $6.40 $71.11
0.14 0.05 0.09
= =
-
b.
$6.40 $6.40 $49.23
0.18 0.05 0.13
= =
-
c.
$6.40 $6.40 $128.00
0.14 0.09 0.05
= =
-
d.
$7.00 $7.00 $77.78
0.14 0.05 0.09
= =
-
30. Maxwell Communications paid a dividend of $3 last year. Over the next 12 months, the
dividend is expected to grow at 8 percent, which is the constant growth rate for the firm
(g). The new dividend after 12 months will represent D1. The required rate of return (Ke)
is 14 percent. Compute the price of the stock (P0).
10-30. Solution:
Maxwell Communications
1
0
e
D
PK g
=-
1 0
(1 ) $3.00 (1.08) $3.24D D g= + = =
0
$3.24 $3.24 $54
.14 .08 0.06
P= = =
-
31. Common stock value based on determining growth rate (LO10-5) Justin Cement
Company has had the following pattern of earnings per share over the last five years:
Year Earnings per Share
20X1........................... $5.00
20X2........................... 5.30
20X3........................... 5.62
20X4........................... 5.96
20X5........................... 6.32
The earnings per share have grown at a constant rate (on a rounded basis) and will continue
to do so in the future. Dividends represent 40 percent of earnings. Project earnings and
dividends for the next year (20X6).
If the required rate of return (Ke) is 13 percent, what is the anticipated stock price (P0) at
the beginning of 20X6?
10-31. Solution:
Justin Cement Company
Earnings have been growing at a rate of 6 percent per year.
Base Period
This is the value for D1.
Ke (required rate of return) is 13 percent and the growth rate is 6
percent.
1
0
$2.68 $2.68
(20X6) $38.29
0.13 0.06 0.07
e
D
PK g
= = = =
- -
32. Common stock required rate of return (LO10-5) A firm pays a $4.80 dividend at the end
of year one (D1), has a stock price of $80, and a constant growth rate (g) of 5 percent.
Compute the required rate of return (Ke).
10-32. Solution:
1
0
e
D
K g
P
= +
$4.80 5% 6% 5% 11.00%
$80.00
e
K= + = + =
33. Common stock required rate of return (LO10-5) A firm pays a $1.50 dividend at the end
of year one (D1), has a stock price of $155 (P0), and a constant growth rate (g) of 10
percent.
a.Compute the required rate of return (Ke).
Indicate whether each of the following changes would make the required rate of return
(Ke) go up or down. (Each question is separate from the others. That is, assume only
one variable changes at a time.) No actual numbers are necessary.
b. The dividend payment increases.
c. The expected growth rate increases.
d. The stock price increases.
10-33. Solution:
a.
1
0
e
D
K g
P
= +
$1.50 10% .97% 10% 10.97%
$155.00
e
K= + = + =
b. If the dividend payment increases, the dividend yield
(D1/P0) will go up, and the required rate of return (Ke) will
c. If the expected growth rate (g) increases, the required rate
d. If the stock price increases, the dividend yield (D1/P0) will
34. Trump Office Supplies paid a $3 dividend last year. The dividend is expected to grow at a
constant rate of 7 percent over the next four years. The required rate of return is 14 percent
(this will also serve as the discount rate in this problem). Round all values to three places to
the right of the decimal point where appropriate.
a.Compute the anticipated value of the dividends for the next four years. That is, compute
D1, D2, D3, and D4—for example, D1 is $3.21 ($3.00 × 1.07).
b. Discount each of these dividends back to the present at a discount rate of 14 percent
and then sum them.
c. Compute the price of the stock at the end of the fourth year (P4).
5
4
e
D
PK g
=-
(D5 is equal to D4 times 1.07)
d. After you have computed P4, discount it back to the present at a discount rate of 14
percent for four years.
e. Add together the answers in part b and part d to get P0, the current value of the stock.
This answer represents the present value of the four periods of dividends, plus the
present value of the price of the stock after four periods (which, in turn, represents the
value of all future dividends).
f. Use Formula 10-8 to show that it will provide approximately the same answer as part e.
1
0
e
D
PK g
=-
For Formula 10-8, use D1 = $3.21, Ke = 14 percent, and g = 7 percent. (The slight
difference between the answers to part e and part f is due to rounding.)
g. If current EPS is equal to $5.32 and the P/E ratio is 1.1 times higher than the industry
average of 8, what would the stock price be?
h. By what dollar amount is the stock price in part g different from the stock price in part
f?
i. In regard to the stock price in part f, indicate which direction it would move if (1) D1
increases, (2) Ke increases, and (3) g increases.
10-34. Solution:
Trump Office Supplies
b. Dividends PV(14%) PV of Dividends
c.
5
4 5
3.932 (1.07) $4.207
e
D
P D
K g
= = =
-
4
$4.207 $4.207 $60.10
.14 .07 .07
P= = =
-
f.
1
0
$3.21 $3.21 $45.857
14.07 .07
e
D
PK g
= = = =
-
10-34. (Continued)
g. Price = P/E × EPS
i. 1) D1 increases, stock price increases
Calculator Solution:
(b)
N I/Y PV PMT FV
Answer: $2.82 PV of D1
N I/Y PV PMT FV
Answer: $2.64 PV of D2
N I/Y PV PMT FV
Answer: $4.83 PV of D3
N I/Y PV PMT FV
Answer: $2.33 PV of D4
Total = 2.82 + 2.64 + 2.48 + 2.33 = $10.27.
(d)
N I/Y PV PMT FV
Answer: $35.58 PV of P4
35. Common stock value based on PV calculations (LO10-5) Beasley Ball Bearings paid a
$4 dividend last year. The dividend is expected to grow at a constant rate of 2 percent over
the next four years. The required rate of return is 15 percent (this will also serve as the
discount rate in this problem). Round all values to three places to the right of the decimal
point where appropriate.
a.Compute the anticipated value of the dividends for the next four years. That is, compute
D1, D2, D3, and D4—for example, D1 is $4.08 ($4 × 1.02).
b. Discount each of these dividends back to present at a discount rate of 15 percent and
then sum them.
c. Compute the price of the stock at the end of the fourth year (P4).
5
4
e
D
PK g
=-
(D5 is equal to D4 times 1.02.)
d. After you have computed P4, discount it back to the present at a discount rate of 15
percent for four years.
e. Add together the answers in part b and part d to get P0, the current value of the stock.
This answer represents the present value of the four periods of dividends, plus the
present value of the price of the stock after four periods, (which, in turn, represents the
value of all future dividends).
f. Use Formula 10-8 to show that it will provide approximately the same answer as part e.
1
0
e
D
PK g
=-
For Formula 10-8, use D1 = $4.08, Ke = 15 percent, and g = 2 percent. (The slight
difference between the answers to part e and part f is due to rounding.)
g. If current EPS were equal to $4.98 and the P/E ratio is 1.2 times higher than the
industry average of 6, what would the stock price be?
h. By what dollar amount is the stock price in part g different from the stock price in part
f?
i. In regard to the stock price in part f, indicate which direction it would move if (1) D1
increases, (2) Ke increases, and (3) g increases.
