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Chapter 13: Risk and Capital Budgeting
13-41
COMPREHENSIVE PROBLEMS
Comprehensive Problem 1.
Gibson Appliance Co. (portfolio effect of a merger) (LO5) Gibson Appliance Co. is a very
stable billion-dollar company with a sales growth of about 7 percent per year in good or bad
economic conditions. Because of this stability (a coefficient of correlation with the economy
of +.4, and a standard deviation of sales of about 5 percent from the mean), Mr. Hoover, the
vice-president of finance, thinks the company could absorb a small risky company that could
add quite a bit of return without increasing the company’s risk very much. He is trying to decide
which of the two companies he will buy, using the figures below. Gibson’s cost of capital is
12 percent.
Genetic Technology Co.
(cost $80 million)
Silicon Microchip Co.
(cost $80 million)
Cash Flow
for 10 Years
($ millions)
Probability
Cash Flow
for 10 Years
($ millions)
Probability
$ 2
.2
$ 5
.2
8
.3
7
.2
16
.2
18
.3
25
.2
24
.3
40
.1
a. What is the expected cash flow from both companies?
b. Which company has the lower coefficient of variation?
c. Compute the net present value of each company.
d. Which company would you pick, based on the net present values?
e. Would you change your mind if you added the risk dimensions to the problem? Explain.
f. What if Genetic Technology Co. had a coefficient of correlation with the economy
of –.2 and Silicon Microchip Co. had one of +.5? Which of these companies would
give you the best portfolio effects for risk reduction?
g. What might be the effect of the acquisitions on the market value of Gibson Appliance
Co.’s stock?
Chapter 13: Risk and Capital Budgeting
13-42
CP 13-1 Solution:
Portfolio Effect of a Merger
Gibson Appliance Co.
a. Genetic Technology Co. Silicon Microchip Co.
D
P
DP
D
P
DP
$ 2
.2
.4
$ 5
.2
1.0
8
.3
2.4
7
.2
1.4
16
.2
3.2
18
.3
5.4
25
.2
5.0
24
.3
7.2
40
.1
4.0
Expected Value
of Cash Flows
$15.0
(million)
Expected Value
of Cash Flows
$15.0
(million)
b. Coefficient of variation for Genetic Technology Co.
D
D
(D D)−
2
(D D)−
P
2
(D D)−
P
$ 2
$15
$–13
$169
.2
$33.8
8
15
–7
49
.3
14.7
16
15
+1
1
.2
.2
25
15
+10
100
.2
20.0
40
15
+25
625
.1
62.5
$131.2
131.2 $11.45 (million)
==
Chapter 13: Risk and Capital Budgeting
CP 13-1. (Continued)
Coefficient of variation for Silicon Microchip Co.
D
D
(D D)−
2
(D D)−
P
2
(D D)−
P
$ 5
$15
$–103
$100
.2
$20.0
7
15
–8
64
.2
12.8
18
15
+3
9
.3
2.7
24
15
+9
81
.3
24.3
$59.8
Chapter 13: Risk and Capital Budgeting
13-44
the economy is –.2.
g. Because Gibson Appliance Co. is a stable billion-dollar company,
this investment of $80 million would probably not have a great
impact on the stock price in the short run. There could be some
discuss risk-return trade-offs and market reactions.
Comprehensive Problem 2.
Kennedy Trucking Company (investment decision based on probability analysis) (LO1)
Five years ago, Kennedy Trucking Company was considering the purchase of 60 new diesel
trucks that were 15 percent more fuel-efficient than the ones the firm is now using. Mr. Hoffman,
the president, had found that the company uses an average of 10 million gallons of diesel fuel per
year at a price of $1.25 per gallon. If he can cut fuel consumption by 15 percent, he will save
$1,875,000 per year (1,500,000 gallons times $1.25).
Mr. Hoffman assumed that the price of diesel fuel is an external market force that he cannot
control and that any increased costs of fuel will be passed on to the shipper through higher rates
endorsed by the Interstate Commerce Commission. If this is true, then fuel efficiency would save
more money as the price of diesel fuel rises (at $1.35 per gallon, he would save $2,025,000 in
total if he buys the new trucks). Mr. Hoffman has come up with two possible forecasts shown
below—each of which he feels has about a 50 percent chance of coming true. Under assumption
number 1, diesel prices will stay relatively low; under assumption number 2, diesel prices will
rise considerably. Sixty new trucks will cost Kennedy Trucking $5 million. Under a special
provision from the Interstate Commerce Commission, the allowable depreciation will be
25 percent in year 1, 38 percent in year 2, and 37 percent in year 3. The firm has a tax rate of
40 percent and a cost of capital of 10 percent.
a. First compute the yearly expected price of diesel fuel for both assumption 1 (relatively
low prices) and assumption 2 (high prices) from the forecasts below.
Forecast for assumption 1 (low fuel prices):
Chapter 13: Risk and Capital Budgeting
13-45
Probability
(same for each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$ .80
$ .90
$1.00
.2
1.00
1.10
1.10
.3
1.10
1.20
1.30
.2
1.30
1.45
1.45
.2
1.40
1.55
1.60
Forecast for assumption 2 (high fuel prices):
Probability
(same For each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$1.20
$1.50
$1.70
.3
1.30
1.70
2.00
.4
1.80
2.30
2.50
.2
2.20
2.50
2.80
b. What will be the dollar savings in diesel expenses each year for assumption 1 and for
assumption 2?
c. Find the increased cash flow after taxes for both forecasts.
d. Compute the net present value of the truck purchases for each fuel forecast
assumption and the combined net present value (that is, weigh the NPV by .5).
e. If you were Mr. Hoffman, would you go ahead with this capital investment?
f. How sensitive to fuel prices is this capital investment?
CP 13-2 Solution:
Investment Decision Based on Probability Analysis
Kennedy Trucking Company
a. Assumption One:
Chapter 13: Risk and Capital Budgeting
13-46
Yr.1
Yr.2
Yr.3
Probability
D
DP
D
DP
D
DP
.1
$0.80
.08
$0.90
.09
$1.00
.10
.2
1.00
.20
1.10
.22
1.10
.22
.3
1.10
.33
1.20
.36
1.30
.39
.2
1.30
.26
1.45
.29
1.45
.29
.2
1.40
.28
1.55
.31
1.60
.32
Expected value
$1.15/gallon
$1.27/gallon
$1.32/gallon
Assumption Two:
Yr.1
Yr.2
Yr.3
Probability
D
DP
D
DP
D
DP
.1
$1.20
.12
$1.50
.15
$1.70
.17
.3
1.30
.39
1.70
.51
2.00
.60
.4
1.80
.72
2.30
.92
2.50
1.00
.2
2.20
.44
2.50
.50
2.80
.56
Expected value
$1.67/gallon
$2.08/gallon
$2.33/gallon
13-CP 2. (Continued)
b. Assumption One:
Yr.
Expected
Cost/gal.
#of Gals.
Without
Efficiency=
Cost
% Savings
with
Efficiency
Total
$ Saved
1
$1.15
10 million
$11,500,000
15%
$1,725,000
2
1.27
12,700,000
1,905,000
3
1.32
13,200,000
1,980,000
Assumption Two:
Chapter 13: Risk and Capital Budgeting
13-47
Yr.
Expected
Cost/gal.
#of Gals.
without
Efficiency=
Cost
% Savings
with
Efficiency
Total
$ Saved
1
$1.67
10 million
$16,700,000
15%
$2,505,000
2
2.08
20,800,000
3,120,000
3
2.33
23,300,000
3,495,000
c. First compute annual depreciation: Then proceed to the analysis.
Year 1
25% × $5 mil. = 1.25 mil.
Year 2
38% × $5 mil. = 1.90 mil.
Year 3
37% × $5 mil. = 1.85 mil.
13-CP 2. (Continued)
Assumption One:
Year 1
Year 2
Year 3
Increase in EBDT
$1,725,000
$1,905,000
$1,980,000
– Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
475,000
5,000
130,000
– Taxes 40 percent
190,000
2,000
52,000
Increase in EAT
285,000
3,000
78,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$1,535,000
$1,903,000
$1,928,000
Assumption Two:
Chapter 13: Risk and Capital Budgeting
13-48
Year 1
Year 2
Year 3
Increase in EBDT
$2,505,000
$3,120,000
$3,495,000
- Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
1,255,000
1,220,000
1,645,000
- Taxes 40 percent
502,000
488,000
658,000
Increase in EAT
753,000
732,000
987,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$2,003,000
$2,632,000
$2,837,000
13-CP 2. (Continued)
d. Present Value
Assumption One:
Year
Cash Flow
PVIF @ 10%
Present Value
1
$1,535,000
.909
$1,395,315
2
1,903,000
.826
1,571,878
3
1,928,000
.751
1,447,928
PV of inflows
$4,415,121
PV of outflows
5,000,000
NPV
$ (584,879)
Assumption Two:
Year
Cash Flow
PVIF @ 10%
Present Value
1
$2,003,000
.909
$1,820,727
2
2,632,000
.826
2,174,032
3
2,837,000
.751
2,130,587
PV of inflows
$6,125,346
PV of outflows
5,000,000
NPV
$1,125,346
Chapter 13: Risk and Capital Budgeting
13-49
Combined NPV:
Outcome
NPV
Probability
Assumption One
–584,879
.5
–292,440
Assumption Two
1,125,346
.5
562.673
Expected Outcome
$270,233
e. Yes—The combined expected value of the outcomes is positive.
