13-7. Solution:
Coefficient of variation (V) = Standard deviation/Mean return
Ranking from
lowest to highest
A $1,200/$5,000 = .24 E (.09)
B $600/$4,000 = .15 B (.15)
8. Coefficient of variation (LO13-1) Five investment alternatives have the following returns
and standard deviations of returns:
Alternative
Returns:
Expected Value
Standard
Deviation
A
………………………………….….…… $ 1,980 $ 970
B
………………………………….….…… 820 1,190
C
………………………………….….…… 12,700 3,100
D
………………………………….….…… 1,140 630
E
………………………………….….…… 62,700 14,100
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.
13-8. Solution:
Coefficient of Variation (V) = Standard deviation/Expected
value
Ranking from
Lowest to Highest
A $970/$1,980 = .49 E (.22)
13-1
13-2
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
1 180 62 .34
3 240 104 .43
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
13-3
Buy stocks……….…………….… $ 9,140 $ 6,140
Buy bonds………………………... 7,680 2,560
Buy commodity futures…...... 19,100 26,700
13-4
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
Buy Stocks $6,140/9,140 = .672
a. Tim should buy the bonds because bonds have the lowest
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
A……………………………………….527,000 834,000
B…………………………….…………682,000 306,000
C…………………………….…………74,000 135,000
D……………………………………….140,000 89,000
13-5
13-11. Solution:
Mountain Ski Corp. and Lakeway Train Co.
Coefficient of Variation (V) = Standard Deviation / Expected
Value
Project A $834,000/527,000 = 1.58
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
13-6
Site A
D
D
( )D D–
2
( )D D–
P
2
( )D D–
P
$ 80 $130 $–50 $2,500 .3 $750
A1,320 $36.33 s= =
Site B
D
D
( )D D–
2
( )D D–
P
2
( )D D–
P
$ 50 $130 $–80 $6,400 .2 $ 1,280
80 130 –50 2,500 .2 500
130 130 –0– –0– .3 –0–
Site A is the preferred site since it has the smallest coefficient of
13-7
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
1 $11,000 .877 $ 9,647
2 16,000 .769 12,304
3 21,000 .675 14,175
4 24,000 .592 14,208
13-8
Calculator solution:
Find the PV of cash inflow using a financial calculator at 14 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 21,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 14 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
13-9
13-14. Solution:
Dixie Dynamite Co.
Method 1 Method 2
Year Inflows
PVIF
@
12% PV Inflows
PVIF
@
16% PV
1 $18,000 .893 $16,074 $20,000 .862 $17,240
2 24,000 .797 19,128 25,000 .743 18,575
3 34,000 .712 24,208 35,000 .641 22,435
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.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 34,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 12 and press Enter.
Method 2:
Find the PV of cash inflow using a financial calculator at 16 percent:
13-10
Press the following keys: 2nd, CF, 2nd, Clear.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 35,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 16 and press Enter.
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
…………………………….
_______ _______
13-11