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13-21. Solution:
Oklahoma Pipeline Company
a. Standard deviation—year 1
D
D
( )D D-
2
( )D D-
P
2
( )D D-
P
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 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.
