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13-8. Solution:
Coefficient of Variation (V) = Standard deviation/Expected
value
Ranking from
Lowest to Highest
9. Coefficient of variation and time (LO13-1) Digital Technology wishes to determine its
coefficient of variation as a company over time. The firm projects the following data (in
millions of dollars):
Year
Profits:
Expected Value Standard Deviation
1
............................................
$180 $62
3
............................................
240 104
6
............................................
300 166
9
............................................
400 292
a. Compute the coefficient of variation (V) for each time period.
b. Does the risk (V) appear to be increasing over a period of time? If so, why might this
be the case?
13-9. Solution:
Digital Technology
a.
Year
Profits:
Expected Value
Standard
Deviation
Coefficient
of Variation
b. Yes, the risk appears to be increasing over time. This may
10. Risk-averse (LO13-2) Tim Trepid is highly risk-averse, while Mike Macho actually enjoys
taking a risk.
a. Which one of the four investments should Tim choose? Compute coefficients of
variation to help you in your choice.
Investments
Returns:
Expected Value
Standard
Deviation
Buy stocks............................. $ 9,140 $ 6,140
Buy bonds.............................. 7,680 2,560
Buy commodity futures......... 19,100 26,700
Buy options........................... 17,700 18,200
b. Which one of the four investments should Mike choose?
13-10. Solution:
Coefficient of Variation (V) = Standard Deviation / Expected
Value
a. Tim should buy the bonds because bonds have the lowest
b. Mike should buy the commodity futures because they have
11. Risk-averse (LO13-2) Mountain Ski Corp. was set up to take large risks and is willing to
take the greatest risk possible. Lakeway Train Co. is more typical of the average
corporation and is risk-averse.
a. Which of the following four projects should Mountain Ski Corp. choose? Compute
the coefficients of variation to help you make your decision.
b. Which one of the four projects should Lakeway Train Co. choose based on the same
criteria of using the coefficient of variation?
Year
Returns:
Expected Value Standard Deviation
13-11. Solution:
Mountain Ski Corp. and Lakeway Train Co.
Coefficient of Variation (V) = Standard Deviation / Expected
Value
a. Mountain Ski Corp should choose Project C because it has
b. Lakeway Train Co. should choose Project B because it has
12. Coefficient of variation and investment decision (LO13-1) Kyle’s Shoe Stores Inc. is
considering opening an additional suburban outlet. An aftertax expected cash flow of $130
per week is anticipated from two stores that are being evaluated. Both stores have positive
net present values.
Which store site would you select based on the distribution of these cash flows? Use
the coefficient of variation as your measure of risk.
Site A Site B
Probability Cash Flows Probability Cash Flows
.3 80 .2 50
.3 130 .2 80
.1 160 .3 130
.3 170 .1 180
.2 235
13-12. Solution:
Kyle’s Shoe Stores Inc.
Standard Deviations of Sites A and B
Site A
D
D
( )D D-
2
( )D D-
P
2
( )D D-
P
Site A is the preferred site since it has the smallest coefficient of
13. Risk-adjusted discount rate (LO13-3) Waste Industries is evaluating a $70,000 project
with the following cash flows:
Year Cash Flows
1
..........................
$11,000
2
..........................
16,000
3
..........................
21,000
4
..........................
24,000
5
..........................
30,000
The coefficient of variation for the project is .847.
Based on the following table of risk-adjusted discount rates, should the project be
undertaken? Select the appropriate discount rate and then compute the net present value.
Coefficient
of Variation Discount Rate
0 – .25.................. 6%
.26 – .50.................. 8
.51 – .75.................. 10
.76 – 1.00.................. 14
1.01 – 1.25................... 20
13-13. Solution:
Waste Industries
Year Inflows PVIF @ 14% PV
Based on the negative net present value, the project should not
be undertaken.
Calculator solution:
Find the PV of cash inflow using a financial calculator at 14 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 70,000 and press +|–, press the Enter key.
Press down arrow, enter 11,000, and press Enter.
Press down arrow, enter 1, and press Enter.
14. Risk-adjusted discount rate (LO13-3) Dixie Dynamite Company is evaluating two
methods of blowing up old buildings for commercial purposes over the next five years.
Method one (implosion) is relatively low in risk for this business and will carry a 12
percent discount rate. Method two (explosion) is less expensive to perform but more
dangerous and will call for a higher discount rate of 16 percent. Either method will require
an initial capital outlay of $75,000. The inflows from projected business over the next five
years are given next. Which method should be selected using net present value analysis?
Years Method 1 Method 2
1
..........................
$18,000 $20,000
2
..........................
24,000 25,000
3
..........................
34,000 35,000
4
..........................
26,000 28,000
5
..........................
14,000 15,000
13-14. Solution:
Dixie Dynamite Co.
Method 1 Method 2
Year Inflows
PVIF
@
12% PV Inflows
PVIF
@
16% PV
Select Method 1
Calculator solution:
Method 1:
Find the PV of cash inflow using a financial calculator at 12 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 75,000 and press +|–, press the Enter key.
Press down arrow, enter 18,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 24,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 34,000, and press Enter.
Method 2:
Find the PV of cash inflow using a financial calculator at 16 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, enter 75,000 and press +|–, press the Enter key.
Press down arrow, enter 20,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 25,000, and press Enter.
Solution: Select Method 1
15. Discount rate and timing (LO13-1) Fill in the following table from Appendix B. Does a
high discount rate have a greater or lesser effect on long-term inflows compared to recent
ones?
Discount Rate
Years 5% 20%
1
..................................
_______ _______
10
..................................
_______ _______
20
..................................
_______ _______
13-15. Solution:
Discount Rate
Years 5% 20%
The impact of a high discount rate is much greater on long-term
value. For example, after the first year, the high rate discount
16. Expected value with net present value (LO13-1) Debby’s Dance Studios is considering
the purchase of new sound equipment that will enhance the popularity of its aerobics
dancing. The equipment will cost $27,900. Debby is not sure how many members the new
equipment will attract, but she estimates that her increased annual cash flows for each of
the next five years will have the following probability distribution. Debby’s cost of capital
is 15 percent.
Cash Flow Probability
$4,570
............................................ .1
5,550
............................................ .3
7,400
............................................ .4
9,930
............................................ .2
a. What is the expected value of the cash flow? The value you compute will apply to
each of the five years.
b. What is the expected net present value?
c. Should Debby buy the new equipment?
13-16. Solution:
Debby’s Dance Studios
a. Expected Cash Flow
Cash Flow P
b. Net Present Value (Appendix D)
$7,068 × 3.352 (PVIFA @ 15%, n = 5) =
c. Debby should not buy this new equipment because the net
present value is negative.
Calculator solution:
b.
Find the PV of cash inflow using a financial calculator at 15 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
17. Deferred cash flows and risk-adjusted discount rate Highland Mining and Minerals Co.
is considering the purchase of two gold mines. Only one investment will be made. The
Australian gold mine will cost $1,649,000 and will produce $353,000 per year in years 5
through 15 and $503,000 per year in years 16 through 25. The U.S. gold mine will cost
$2,054,000 and will produce $282,000 per year for the next 25 years. The cost of capital is
13 percent.
a. Which investment should be made? (Note: In looking up present value factors for this
problem, you need to work with the concept of a deferred annuity for the Australian
mine. The returns in years 5 through 15 actually represent 11 years; the returns in
years 16 through 25 represent 10 years.)
b. If the Australian mine justifies an extra 2 percent premium over the normal cost of
capital because of its riskiness and relative uncertainty of cash flows, does the
investment decision change?
