978-1259277160 Chapter 10 Solution Manual Part 5

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

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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

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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

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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

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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

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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= = =

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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

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