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Chapter 10: Valuation and Rates of Return
10-35. Solution:
Beasley Ball Bearings
b. Dividends PV(15%) PV of Dividends
$11.966
c.
5
4 5
4.330 (1.02) $4.417
e
D
P D
K g
= = =
-
4
$4.417 $4.417 $33.977
.15 .02 .13
P= = =
-
e. Answer to part b (PV of dividends) $11.966
f.
1
0
$4.08 $4.08 $31.385
.15 .02 .13
e
D
PK g
= = = =
- -
g. Price = P/E × EPS
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
10-35. (Continued)
i. 1) D1 increases, stock price increases
Calculator Solution:
(b)
N I/Y PV PMT FV
Answer: $3.550 PV of D1
N I/Y PV PMT FV
Answer: $3.146 PV of D2
N I/Y PV PMT FV
Answer: $2.793 PV of D3
N I/Y PV PMT FV
Answer: $2.477 PV of D4
(d)
N I/Y PV PMT FV
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
Answer: $19.426 PV of P4
COMPREHENSIVE PROBLEM
Preston Products (Dividend valuation model, P/E ratio) (LO10-5)
Mel Thomas, the chief financial officer of Preston Resources, has been asked to do
an evaluation of Dunning Chemical Company by the president and Chair of the
Board, Sarah Reynolds. Preston Resources was planning a joint venture with
Dunning (which was privately traded), and Sarah and Mel needed a better feel for
what Dunning’s stock was worth because they might be interested in buying the
firm in the future.
Dunning Chemical paid a dividend at the end of year one of $1.30, the anticipated
growth rate was 10 percent, and the required rate of return was 14 percent.
a. What is the value of the stock based on the dividend valuation model
(Formula 10-8)?
b. Indicate that the value you computed in part a is correct by showing the value of
D1, D2, and D3 and discounting each back to the present at 14 percent. D1 is
$1.30 and it increases by 10 percent (g) each year. Also discount back the
anticipated stock price at the end of year three 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 three is:
( )
4
3 4 3 1
e
D
P D D g
K g
= = +
-
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
chemical companies. The P/E ratios were as follows during the time period under
analysis:
P/E Ratio
Dow Chemical........... 15
DuPont....................... 18
Georgia Gulf.............. 7
3M.............................. 19
Olin Corp................... 21
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
Assume Dunning Chemical has earnings per share of $2.10. 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 Olin Corp. 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 Olin Corp. more
heavily because it is similar to Dunning Chemical.) What will the new stock
price be? Earnings per share will stay at $2.10.
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?
Present Value of Principal Payment at Maturity
PV = FV × PVIF (n = 20, i = 11%) (Appendix B)
PV = $1,000 × .124 = $124
Total Present Value
Present value of interest payments.......................... $ 939.63
Present value of principal payment at maturity...... 124.00
Total present value, or price, of the bond............. $1,063.63
The discount rate of 11 percent gives us a value slightly lower than the bond
price of $1,085. The rate for the bond must fall between 10 and 11 percent.
Using linear interpolation, the answer is 10.76 percent
$1,153.65 PV @ 10% $1,153.65 PV @ 10%
1,063.63 PV @ 11% 1,085.00 bond price
$ 90.02 $ 68.65
( ) ( )
$68.65
10% 1% 10% .76 1% 10.76%
$90.02
+ = + =
CP 10-1. Solution:
Preston Resources—Dunning Chemical
a.
1
10
$1.30 $1.30 $32.50
.14 .10 .04
e
D
PK g
= = = =
- -
b. Future Value of Dividends
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
Present Value of Dividends
Dividends PV (14%) (PV of Dividend)
Value of Stock Price at the end of Year 3
4
3 4 3
P (1 ) 1.573 (1.10) $1.730
e
DD D g
K g
= = + = =
-
3
$1.730 $1.730 $43.25
.14 .10 .04
P= = =
-
Present Value of Future Stock Price
Total stock prices:
CP 10-1. (Continued)
c. Average P/E Ratio of Five Chemical Firms
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
80 16 Average P/E
5=
Stock Price = P/E × EPS
16 × $2.10 = $33.60
The stock price using the P/E ratio approach is slightly
higher than the value using the dividend valuation
model approach ($33.60 versus $32.50).
d. P/E Ratio Weights
Weighted
Average
CP 10-1. (Continued)
Chapter 10: Valuation and Rates of Return
for the foreseeable future. The required rate of return is 12 percent (this will
also serve as the discount rate).
a. Compute the anticipated value of the dividends for the next three years
(D1, D2, and D3).
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
PK g
=-
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 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.)
10A–1. Solution
Surgical Supplies Corporation
b. Supernormal
Dividends
Discount
Rate
Ke = 12%
Present Value of
Dividends During
the Supernormal
Growth Period
c.
4
3
e
D
PK g
=-
4 3 (1.07) $2.19 (1.07) $2.34D D= = =
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
Chapter 10: Valuation and Rates of Return
3
$2.34 $2.34 $46.80
.12 .07 0.05
P= = =
-
d. PV of P3 for n = 3, i = 12%
e. Answer to part b (PV of dividends) $ 4.20
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
