978-1259277160 Chapter 13 Solution Manual Part 4

13-21. Solution:

Oklahoma Pipeline Company

a. Standard deviation—year 1

D

( )D D–

2

( )D D–

P

2

( )D D–

P

( )D D–

2

( )D D–

2

( )D D–

13-21. (Continued)

d. Yes. The larger risk over time is consistent with the larger

differences in the present value interest factors (PVIF) over

Year Inflow PVIF (12%) PV

d. Accept the investment.

22. Portfolio effect of a merger (LO13-5) Treynor Pie Company is a food company

specializing in high-calorie snack foods. It is seeking to diversify its food business and

lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food

company, and a nutritional products firm. Each of these companies can be bought at the

same multiple of earnings. The following table represents information about all the

companies:

Company

Correlation

with Treynor

Pie Company

Sales

($ millions)

Expected

Earnings

($ millions)

Standard

Deviation

in Earnings

($ millions)

Treynor Pie Company…………. + 1.0 $126 $10 $4.0

Gourmet restaurant……………… + .4 63 9 1.4

Baby food company……………. + .3 52 5 1.6

Nutritional products

company……………………………. − .7 77 7 3.2

a. Using the last two columns, compute the coefficient of variation for each of the four

companies. Which company is the least risky? Which company is the most risky?

b. Discuss which of the acquisition candidates is most likely to reduce Treynor Pie

Company’s risk. Explain why.

13-22. Solution:

Treynor Pie Company

a.

Standard deviation

Coefficient of variation ( ) Expected value

V=

(millions)

The Gourmet Restaurant chain is the least risky with

a. Because the nutritional products firm is highly negatively

correlated (–.7) with Treynor Pie Company, it is most likely

Thus, Treynor Pie Company would reduce its risk to the

largest extent by acquiring the company with the highest

coefficient of variation (.46) as computed in part a. This

23. Portfolio effect of a merger (LO13-5) Hooper Chemical Company, a major chemical firm

that uses such raw materials as carbon and petroleum as part of its production process, is

examining a plastics firm to add to its operations. Before the acquisition, the normal

expected outcomes for the firm were as follows:

Outcomes

($ millions) Probability

Recession……………………….. $20 .30

Normal economy…………….. 40 .40

Strong economy………………. 60 .30

After the acquisition, the expected outcomes for the firm would be:

Outcomes

($ millions) Probability

Recession……………………….. $10 .3

Normal economy…………….. 40 .4

Strong economy………………. 80 .3

a. Compute the expected value, standard deviation, and coefficient of variation before

the acquisition.

b. After the acquisition, these values are as follows:

Expected value…………………………………. 43.0 ($ millions)

Standard deviation…………………………….. 27.2 ($ millions)

Coefficient of variation………………………. .633

Comment on whether this acquisition appears desirable to you.

c. Do you think the firm’s stock price is likely to go up as a result of this acquisition?

d. If the firm was interested in reducing its risk exposure, which of the following three

industries would you advise it to consider for an acquisition? Briefly comment on

your answer.

(1) Chemical company

(2) Oil company

(3) Computer company

13-23. Solution:

Hooper Chemical Co.

D DP=

å

D P PD

2

( )D D Ps= –

å

D

( )D D–

2

( )D D–

P

2

( )D D–

P

b. No, it does not appear to be desirable. Although the expected

value is $3 million higher, the coefficient of variation is more

c. Probably not. There may be a higher discount rate applied

d. The oil company may provide the best risk reduction

24. Efficient frontier (LO13-5) Ms. Sharp is looking at a number of different types of

investments for her portfolio. She identifies eight possible investments.

Return Risk Return Risk

(a)……………… 11% 2% (e)……………… 14% 5.0%

(b)……………… 11 2.5 (f)………………. 16 5.0

(c)……………… 13 3.0 (g)……………… 15 5.8

(d)……………… 13 4.2 (h)……………… 18 7.0

a. Graph the data in a manner similar to Figure 13-11. Use the axes that follow for your

data:

b. Draw a curved line representing the efficient frontier.

c. What two objectives do points on the efficient frontier satisfy?

d. Is there one point on the efficient frontier that is best for all investors?

13-24. Solution:

Ms. Sharp

a., b.

c. Achieve the highest possible return for a given risk level.

d. No. Each investor must assess his or her own preferences

25. Certainty equivalent approach (LO13-1) Sheila Goodman recently received her MBA

from the Harvard Business School. She has joined the family business, Goodman Software

Products Inc., as vice president of finance.

She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees

to go along with her. Her approach is somewhat different than the risk-adjusted discount

rate approach, but achieves the same objective.

She suggests that the inflows for each year of a project be adjusted downward for lack

of certainty and then be discounted back at a risk-free rate. The theory is that the

adjustment penalty makes the inflows the equivalent of risk-less inflows, and therefore a

risk-free rate is justified.

A table showing the possible coefficient of variation for an inflow and the associated

adjustment factor is shown next:

Coefficient

of Variation

Adjustment

Factor

0 – .25…………….. .90

.26 – .50…………….. .80

.51 – .75…………….. .70

.76 – 1.00…………… .60

1.01 – 1.25………….. .50

Assume a $184,000 project provides the following inflows with the associated coefficients

of variation for each year:

Year Inflow Coefficient of Variation

1

……………………….. $32,200 .12

2

……………………….. 59,500 .28

3

……………………….. 79,900 .45

4

……………………….. 59,200 .79

5

……………………….. 65,5600 1.15

a. Fill in the following table:

Year Inflow

Coefficient of

Variation

Adjustment

Factor

Adjusted

Inflow

1

……………………. $32,200 .12 ___________

_

____________

2

……………………. 59,500 .28 ___________

_

____________

3

……………………. 79,900 .45 ___________

_

____________

4

……………………. 59,200 .79 ___________

_

____________

5

……………………. 65,600 1.15 ___________

_

____________

b. If the risk-free rate is 5 percent, should this $184,000 project be accepted? Compute

the net present value of the adjusted inflows.

13-25. Solution:

Goodman Software Products

a. Adjusted Inflows

Year Inflow

Coefficient

of Variation

Adjustment

Factor

Adjusted

Inflow

b. Net Present Value

Year

Adjusted

Inflow

PVIF

at 5%

Present

Value

should not be accepted.