Chapter 10: Valuation and Rates of Return
10-31
1
e
0
D
Kg
P
=+
e
$3.80
K 4% 7.6% 4% 11.6%
$50.00
= + = + =
33. Common stock required rate of return (LO5) A firm pays a $1.50 dividend at the
end of year one (D1), has a stock price of $60 (P0), and a constant growth rate (g) of
8 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
e
0
D
Kg
P
=+
e
$1.50
K 8% 2.5% 8% 10.5%
$60.00
= + = + =
b. If the dividend payment increases, the dividend yield
(D1/P0) will go up, and the required rate of return (Ke)
new level.
Chapter 10: Valuation and Rates of Return
10-32
also go down.
34. Common stock value based on PV calculations (LO5) Hunter Petroleum
Corporation paid a $2 dividend last year. The dividend is expected to grow at a
constant rate of 5 percent over the next three years. The required rate of return is 12
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 three years. That is,
compute D1, D2, and D3; for example, D1 is $2.10 ($2.00 × 1.05).
b. Discount each of these dividends back to the present at a discount rate of
12 percent and then sum them.
c. Compute the price of the stock at the end of the third year (P3).
4
3
e
D
PKg
=−
(D4 is equal to D3 times 1.05)
d. After you have computed P3, discount it back to the present at a discount rate of
12 percent for three 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 first three periods of
dividends, plus the present value of the price of the stock after three periods
(which, in turn, represents the value of all future dividends).
f. Use Formula 10-9 to show that it will provide approximately the same answer
as part e.
1
0
e
D
PKg
=−
(10–9)
For Formula 10-9 use D1 = $2.10, Ke = 12 percent, and g = 5 percent. (The slight
difference between the answers to part e and part f is due to rounding.)
Chapter 10: Valuation and Rates of Return
10-33
10–34. Solution:
Hunter Petroleum Corporation
a. D1= $2.00 (1.05) = $2.10
b. Dividends PV(12%) PV of Dividends
D1 $2.10 .893 $1.875
c.
4
34
e
D
P D $2.315 (1.05) $2.431
Kg
= = =
−
3
$2.431 $2.431
P $34.729
.12 .05 .07
= = =
−
d. PV of P3 for n = 3, i = 12%
e. answer to part b (PV of dividends) $ 5.280
f.
1
0
e
D$2.10 $2.10
P $30.00
K g .12 .05 .07
= = = =
−−
35. Common stock value based on PV calculations (LO5) Beasley Ball Bearings
paid a $4 dividend last year. The dividend is expected to grow at a constant rate of 6
percent over the next four years. The required rate of return is 13 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 $4.24 ($4 × 1.06).
Chapter 10: Valuation and Rates of Return
10-34
b. Discount each of these dividends back to present at a discount rate of 13 percent
and then sum them.
c. Compute the price of the stock at the end of the fourth year (P4).
5
4
e
D
PKg
=−
(D5 is equal to D4 times 1.06)
d. After you have computed P4, discount it back to the present at a discount rate of
13 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 10–9 to show that it will provide approximately the same answer
as part e.
1
0
e
D
PKg
=−
For Formula 10–9 use D1 = $4.24, Ke = 13 percent, and g = 6 percent. (The
slight difference between the answers to part e and part f is due to rounding.)
g. If current EPS were equal to $5.70 and the P/E ratio is 1.2 times higher than the
industry average of 9, 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, (3) g increases.
10–35. Solution:
Beasley Ball Bearings
a. D1 $4.00 (1.06) = $4.24
Chapter 10: Valuation and Rates of Return
10-35
b. Dividends PV(13%) PV of Dividends
D1 $4.24 .885 $ 3.752
c.
5
45
e
D
P D 5.050 (1.06) $5.353
Kg
= = =
−
4
$5.353 $5.353
P $76.471
.13 .06 .07
= = =
−
d. PV of P4 for n = 4, i = 13%
e. Answer to part b (PV of dividends) $13.688
f.
1
0
e
D$4.24 $4.24
P $60.571
K g .13 .06 .07
= = = =
−−
g. Price = P/E × EPS
Chapter 10: Valuation and Rates of Return
10-36
10–35. (Continued)
h. Part g $61.56
Part f – 60.57
$ .99
i. 1) D1 increases, stock price increases
COMPREHENSIVE PROBLEM
Healthy Products (Dividend valuation model, P/E ratio) (LO5) Allie Reynolds,
the Chief Financial Officer of Healthy Products, Inc., has been asked to do an
evaluation of Fiber Cereal, Inc., by the President and Chairman of the Board, Gail
Martinez. Healthy Products was planning a joint venture with Fiber Cereals (which
was privately traded), and Gail and Allie needed a better feel for Fiber Cereals’
common stock value because they thought they might be interested in buying the
firm in the future.
Fiber Cereals paid a dividend at the end of year 1 of $1.20, the anticipated growth
rate was 10 percent, and the required rate of return was 13 percent.
a. What is the value of the stock based on the dividend valuation model
(Formula 10–9 on page ___)?
b. Indicate that the value you computed in part a is correct by showing the value of
D1, D2, and D3 and discounting each to the present 13 percent. D1 is $1.20 and it
increases by 10 percent (g) each year. Also discount back the anticipated stock
price at the end of year 3 to the present and add it to the present value of the
three dividend payments.
The value of the stock at the end of year 3 is:
( )
4
3 4 3
e
D
P D D 1 g
Kg
= = +
−
If you have done all these steps correctly, you should get an answer
approximately equal to the answer in part a.
c. As an alternative measure, you also examine the value of the firm based on the
price-earnings (P/E) ratio times earnings per share.
Since the company is privately traded (not in the public stock market), you will
get your anticipated P/E ratio by taking the average value of five publicly traded
food industry companies. These P/E ratios were as follows during the time
period under analysis:
Chapter 10: Valuation and Rates of Return
10-37
P/E Ratio
Del Monte……………… 12
General Mills …………. 15
Heinz ……………………. 14
Kellogg …………………. 22
Kraft …………………….. 17
Assume Fiber Cereals has earnings per share of $2.45. What is the stock value
based on the P/E ratio approach? Multiply the average P/E ratio you computed
times earnings per share. How does this value compare to the dividend valuation
model values that you computed in parts a and b?
d. If in computing the industry average P/E, you decide to weight Kellogg by
40 percent and the other four firms by 15 percent, what would be the new
weighted average industry P/E? (Note: You decided to weight Kellogg more
heavily because it is similar to Fiber Cereals.) What will the new stock price be?
Earnings per share will stay at $2.45.
e. By what percent will the stock price change as a result of using the weighted
average industry P/E ratio in part d as opposed to that in part c?
CP 10-1. Solution:
Healthy Products—Fiber Cereals
a.
1
0
e
D$1.20 $1.20
P $40.00
K g 0.13 0.10 .03
= = = =
−−
b. Future Value of Dividends
D1 $1.20
Present Value of Dividends
Dividends PV (13%) (PV of Dividend)
D1 $1.20 .885 $1.06