Chapter 13
Discussion Questions
13-1.
If corporate managers are risk-averse,does this mean they will not take risks? Explain.
Risk-averse corporate managers are not unwilling to take risks,but will require a higher return from risky investments,There must be a premium or additional compensation for risk taking.
13-2.
Discuss the concept of risk and how it might be measured.
Risk may be defined in terms of the variability of outcomes from a given investment,The greater the variability,the greater the risk,Risk may be measured in terms of the coefficient of variation,in which we divide the standard deviation (or measure of dispersion) by the mean,We also may measure risk in terms of beta,in which we determine the volatility of returns on an individual stock relative to a stock market index.
13-3.
When is the coefficient of variation a better measure of risk than the standard deviation?
The standard deviation is an absolute measure of dispersion while the coefficient of variation is a relative measure and allows us to relate the standard deviation to the mean,The coefficient of variation is a better measure of dispersion when we wish to consider the relative size of the standard deviation or compare two or more investments of different size.
13-4.
Explain how the concept of risk can be incorporated into the capital budgeting process.
Risk may be introduced into the capital budgeting process by requiring higher returns for risky investments,One method of achieving this is to use higher discount rates for riskier investments,This risk-adjusted discount rate approach specifies different discount rates for different risk categories as measured by the coefficient of variation or some other factor,Other methods,such as the certainty equivalent approach,also may be used.
13-5.
If risk is to be analyzed in a qualitative way,place the following investment decisions in order from the lowest risk to the highest risk:
New equipment.
New market.
Repair of old machinery.
New product in a foreign market.
New product in a related market.
Addition to a new product line.
Referring to Table 13-3,the following order would be correct:
repair old machinery (c)
new equipment (a)
addition to normal product line (f)
new product in related market (e)
completely new market (b)
new product in foreign market (d)
13-6.
Assume a company,correlated with the economy,is evaluating six projects,of which two are positively correlated with the economy,two are negatively correlated,and two are not correlated with it at all,Which two projects would you select to minimize the company's overall risk?
In order to minimize risk,the firm that is positively correlated with the economy should select the two projects that are negatively correlated with the economy.
13-7.
Assume a firm has several hundred possible investments and that it wants to analyze the risk-return trade-off for portfolios of 20 projects,How should it proceed with the evaluation?
The firm should attempt to construct a chart showing the risk-return characteristics for every possible set of 20,By using a procedure similar to that indicated in Figure 13-11,the best risk-return trade-offs or efficient frontier can be determined,We then can decide where we wish to be along this line.
13-8.
Explain the effect of the risk-return trade-off on the market value of common stock.
High profits alone will not necessarily lead to a high market value for common stock,To the extent large or unnecessary risks are taken,a higher discount rate and lower valuation may be assigned to our stock,Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market.
13-9.
What is the purpose of using simulation analysis?
Simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions,A Monte Carlo simulation model uses random variables for inputs,By programming the computer to randomly select inputs from probability distributions,the outcomes generated by a simulation are distributed about a mean and instead of generating one return or net present value,a range of outcomes with standard deviations are provided.
Problems
13-1.
Myers Business Systems is evaluating the introduction of a new product,The possible levels of unit sales and the probabilities of their occurrence are given below.
Possible
Market Reaction
Sales
in Units
Probabilities
Low response
20
.10
Moderate response
40
.30
High response
55
.40
Very high response
70
.20
a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?
Solution:
Myers Business Systems
a.
D
20
40
55
70
P
.10
.30
.40
.20
DP
2
12
22
14
50 =
b.
20
50
–30
900
.10
90
40
50
–10
100
.30
30
55
50
+5
25
.40
10
70
50
+20
400
.20
80
210
13-2.
Monarck King Size Beds,Inc.,is evaluating a new promotional campaign that could increase sales,Possible outcomes and probabilities of the outcomes are shown below,Compute the coefficient of variation.
Possible Outcomes
Additional
Sales in Units
Probabilities
Ineffective campaign
20
.20
Normal response
30
.50
Extremely effective
70
.30
Solution:
Monarck King Size Beds,Inc.
Coefficient of variation (V) = standard deviation/expected value.
D
20
30
70
P
.20
.50
.30
DP
4
15
21
40 =
20
40
–20
400
.20
80
30
40
–10
100
.50
50
70
40
+30
900
.30
270
400
13-3.
Al Bundy is evaluating a new advertising program that could increase shoe sales,Possible outcomes and probabilities of the outcomes are shown below,Compute the coefficient of variation.
Possible Outcomes
Additional
Sales in Units
Probabilities
Ineffective campaign
40
.20
Normal response
60
.50
Extremely effective
140
.30
Solution:
Al Bundy
Coefficient of variation (V) = standard deviation/expected value.
D
40
60
140
P
.20
.50
.30
DP
8
30
42
80 =
40
80
–40
1,600
.20
320
60
80
–20
400
.50
200
140
80
+60
3,600
.30
1,080
1,600
13-4.
Possible outcomes for three investment alternatives and their probabilities of occurrence are given below.
Alternative 1
Alternative 2
Alternative 3
Outcomes
Probability
Outcomes
Probability
Outcomes
Probability
Failure
50
.2
90
.3
80
.4
Acceptable
80
.4
160
.5
200
.5
Successful
120
.4
200
.2
400
.1
Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation).
Solution:
Alternative 1
D x P = DP
Alternative 2
D x P = DP
Alternative 3
D x P = DP
$ 50 .2 $10
80 .4 32
120 .4 48
= $90
$ 90 .3 $ 27
160 .5 80
200 .2 40
= $147
$ 80 .4 $ 32
200 .5 100
400 .1 40
= $172
Standard Deviation Alternative 1
$ 50
$90
$–40
$1,600
.2
$320
80
90
–10
100
.4
40
120
90
+30
900
.4
360
$720
13-4,Continued
Alternative 2
$ 90
$147
$–57
$3,249
.3
$ 974.70
160
147
+13
169
.5
84.50
200
147
+53
2,809
.2
561.80
$1,621.00
Alternative 3
$ 80
$172
$–92
$ 8,464
.4
$3,385.60
200
172
+28
784
.5
392.00
400
172
+228
51,984
.1
5,198.40
$8,976.00
Rank by Coefficient of Variation
Coefficient of Variation (V) = Standard Deviation/Expected Value
V
Alternative 2
Alternative 1
Alternative 3
13-5.
Five investment alternatives have the following returns and standard deviations of returns.
Alternative
Returns:
Expected Value
Standard
Deviation
A
$ 5,000
$1,200
B
4,000
600
C
4,000
800
D
8,000
3,200
E
10,000
900
Using the coefficient of variation,rank the five alternatives from lowest risk to highest risk.
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)
C
$800/$4,000 =,20
C (.20)
D
E
$3,200/$8,000 =,40
$900/$10,000 =,09
A (.24)
D (.40)
13-6.
In problem 5,if you were to choose between Alternative B and C only,would you need to use the coefficient of variation? Why?
Solution:
Since B and C have the same expected value,they can be evaluated based on their standard deviations of return,C has a larger standard deviation and so is riskier than B for the same expected return.
13-7.
Tom Fears is highly risk-averse while Sonny Outlook actually enjoys taking a risk.
a. Which one of the four investments should Tom choose? Compute the coefficients of variation to help you in your choice.
b. Which one of the four investments should Sonny choose?
Investments
Returns –
Expected Value
Standard
Deviation
Buy stocks
$ 7,000
$ 4,000
Buy bonds
5,000
1,560
Buy commodity futures
12,000
15,100
Buy options
8,000
8,850
Solution:
Coefficient of variation (V) = standard deviation/expected value.
Buy stocks
$4,000/$7,000 =,571
Buy bonds
$1,560/$5,000 =,312
Buy commodity futures
$15,100/$12,000 = 1.258
Buy options
$8,850/$8,000 = 1.106
a. Tom should buy the bonds because bonds have the lowest coefficient of variation.
b. Sonny should buy the commodity futures because they have the highest coefficient of variation.
13-8.
Bridget’s Modeling Studios is considering opening a new location in Miami,An aftertax cash flow of $120 per day (expected value) is projected for each of the two locations being evaluated..
Which of these sites 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
.15
$ 80
.10
$ 50
.50
110
.20
80
.30
140
.40
120
.05
220
.20
160
Expected value
$120
.10
Expected Value
190
$120
Solution:
Bridget’s Modeling Studios
Standard Deviations of Sites A and B
Site A
$ 80
$120
$–40
$ 1,600
.15
$240
110
120
–10
100
.50
50
140
120
+20
400
.30
120
220
120
+100
10,000
.05
500
$910
13-8,Continued
Site B
$ 50
$120
$–70
$4,900
.10
$ 490
80
120
–40
1,600
.20
320
120
120
–0–
–0–
.40
–0–
160
120
+40
1,600
.20
320
190
120
+70
4,900
.10
490
$1,620
VA = $30.17/$120 =,2514
VB = $40.25/$120 =,3354
Site A is the preferred site since it has the smallest coefficient of variation,Because both alternatives have the same expected value,the standard deviation alone would have been enough for a decision,A will be just as profitable as B but with less risk.
13-9.
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
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
5
30,000
.519
15,570
PV of Inflows
$65,904
Investment
70,000
NPV
$(4,096)
Based on the positive net present value,the project should not be undertaken.
13-10.
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 below,Which method should be selected using net present value analysis?
Year
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
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
4
26,000
.636
16,536
28,000
.552
15,456
5
14,000
.597
7,938
15,000
.476
7,140
PV of Inflows $83,884
$80,846
Investment –75,000
–75,000
NPV $ 8,884
Select Method 1
$ 5,846
13-11.
Fill in the table below 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 ______ ______
Solution:
Discount Rate
Years 5% 20%
1 .952 .833
10 .614 .162
20 .377 .026
The impact of a high discount rate is much greater on long-term value,For example,after the first year,the high rate discount value produce an answer that is 87.5% of the low discount rate (.833/.952),However,after the 20th year,the high rate discount rate is only 6.90% of the low discount rate (.026/.377).
13-12.
Larry’s Athletic Lounge is planning an expansion program to increase the sophistication of its exercise equipment,Larry is considering some new equipment priced at $20,000 with an estimated life of five years,Larry is not sure how many members the new equipment will attract,but he estimates his increased yearly cash flows for each of the next five years will have the following probability distribution,Larry’s cost of capital is 14 percent.
P
(Probability)
Cash Flow
.2
$2,400
.4
4,800
.3
6,000
.1
7,200
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 Larry buy the new equipment?
Solution:
Larry’s Athletic Lounge
a. Expected Cash Flow
$2,400
x
.2
$ 480
4,800
x
.4
1,920
6,000
x
.3
1,800
7,200
x
.1
720
Expected cash flow
$4,920
b. $4,920 x 3.433 (PVIFA @ 14%,n = 5) = (Appendix D)
$16,890 Present value of inflows
20,000 Present value of outflows
$(3,110) Net present value
c. Larry should not buy this equipment because the net present value is negative.
13-13.
Silverado Mining Company is analyzing the purchase of two silver mines,Only one investment will be made,The Alaska mine will cost $2,000,000 and will produce $400,000 per year in years 5 through 15 and $800,000 per year in years 16 through 25,The Montana mine will cost $2,400,000 and will produce $300,000 per year for the next 25 years,The cost of capital is 10 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 Alaska 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 Alaska mine justifies an extra 5 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of flows,does the investment decision change?
Solution:
Silverado Mining Company
a. Calculate the net present value for each project.
The Alaska Mine
Years
Cash Flow
n Factor
PVIFA @ 10%
Present Value
5-15
$400,000
(15 – 4)
(7.606 – 3.170)
$1,774,400
16-25
$800,000
(25 – 15)
(9.077 – 7.606)
$1,176,800
Present value of inflows
$2,951,200
Present value of outflows
$2,000,000
Net present value
$ 951,200
13-13,Continued
The Montana Mine
Years
Cash Flow
n Factor
PVIFA @ 10%
Present Value
1-25
$300,000
9.077
$2,723,100
Present value of inflows
$2,723,100
Present value of outflows
$2,400,100
Net present value
$ 323,100
Select the Alaska Mine.
b. Recalculate the net present value of the Alaska Mine at a 15 percent discount rate.
Years
Cash Flow
n Factor
PVIFA @ 15%
Present Value
5-15
$400,000
(15 – 4)
(5.847 – 2.855)
$1,196,800
16-25
$800,000
(25 – 15)
(6.464 – 5.847)
$ 493,600
Present value of inflows
$1,690,000
Present value of outflows
$2,000,000
Net present value
$(309,600)
Now the decision should be made to reject the purchase of the Alaska Mine and purchase the Montana Mine.
13-14.
Mr,Monty Terry,a real estate investor,is trying to decide between two potential small shopping center purchases,His choices are the Wrigley Village and Crosley Square,The anticipated annual cash inflows from each are as follows:
Wrigley Village
Crosley Square
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
$10
.1
$20
.1
30
.2
30
.3
40
.3
35
.4
50
.3
40
.2
60
.1
50
a. Find the expected value of the cash flow from each shopping center.
b. What is the coefficient of variation for each shopping center?
c. Which shopping center has more risk?
Solution:
Mr,Monty Terry
a.
Wrigley Village
Crosley Square
D
P
DP
D
P
DP
10
0.1
$ 1
20
0.1
$ 2
30
0.2
6
30
0.3
9
40
0.3
12
35
0.4
14
50
0.3
15
50
0.2
10
60
0.1
6
Expected Cash Flow
$35
Expected Cash Flow
$40
13-14,Continued
b. First find the standard deviation and then the coefficient of variation.
Wrigley Village
$10
$40
$–30
$900
.1
$ 90
30
40
–10
100
.2
20
40
40
0
0
.3
0
50
40
+10
100
.3
30
60
40
+20
400
.1
40
$180
V = $13.42/$40 =,336
Crosley Square
$20
$35
$–15
$225
.1
$22.5
30
35
–5
25
.3
7.5
35
35
0
0
.4
0
50
35
+15
225
.2
45.0
$75.0
V = $8.66/$35 =,247
c. Based on the coefficient of variation,Wrigley Village has more risk (.336 vs.,247).
13-15.
Referring to Problem 14,Mr,Terry is likely to hold the shopping center of his choice for 25 years and will use this period for decision-making purposes,Either shopping center can be purchased for $300,000,Mr,Terry uses a risk-adjusted discount rate when evaluating investments,His scale is related to the coefficient of variation presented below.
Coefficient
of Variation
Discount
Rate
0-0.30
8%
0.31-0.60
11
(cost of capital)
0.61-0.90
14
Over 0.90
18
a. Compute the risk-adjusted net present values for Wrigley Village and Crosley Square,You can get the coefficient of variation and cash flow figures (in thousands) from the previous problem.
b. Which investment should Mr,Terry accept if the two investments are mutually exclusive? If the investments are not mutually exclusive and no capital rationing is involved,how would your decision be affected?
Solution:
Mr,Monty Terry (Continued)
a. Risk-adjusted net present value
Wrigley Village
Crosley Square
(with V =,336,
discount rate = 11%
(with V =,247,
discount rate = 8%
Expected Cash Flow
$ 40,000
$ 35,000
IFPVA (n = 25)
8,422
10.675
Present Value of
Inflows
$336,880
$373,625
Present Value of
Outflows
300,000
$300,000
Net Present Value
$ 36,880
$ 73,625
13-15,Continued
b. If these two investments are mutually exclusive,he should accept Crosley Village because it has a higher net present value.
If the investments are non-mutually exclusive and no capital rationing is involved,they both should be undertaken.
13-16.
Roper Fashions is preparing a product strategy for the fall season,One option is to go to a highly imaginative new,four-gold-button sport coat with special emblems on the front pocket,The all-wool product would be available for both males and females,A second option would be to produce a traditional blue blazer line,The marketing research department has determined that the new,four-gold-button coat and traditional blue blazer line offer the probabilities of outcomes and related cash flows shown at the top of page ___.
New Coat
Blazer
Expected
Sales
Probability
Present Value
of Cash Flows
from Sales
Probability
Present Value
of Cash Flows
from Sales
Fantastic
.5
$130,000
.3
$65,000
Moderate
.2
70,000
.4
50,000
Dismal
.3
0
.3
35,000
The initial cost to get into the new coat line is $50,000 in designs,equipment,and inventory,The blazer line would carry an initial cost of $30,000.
a. Diagram a complete decision tree of possible outcomes similar to Figure 13-8 on page ___,Take the analysis all the way through the process of computing expected NPV (last column) for each investment.
b. Given the analysis in part a,would you automatically make the investment indicated?
13-16,Continued
Solution:
Roper Fashions
a.
(1)
(2)
(3)
(4)
(5)
(6)
Expected Sales
Probability
Present Value of Cash Flows From Sales
Initial Cost
NPV
(3) – (4)
Expected
NPV
(2) x (5)
Enter
Fantastic
.5
$130,000
$50,000
$80,000
$40,000
New Coat
Moderate
.2
70,000
50,000
20,000
4,000
Market
Dismal
.3
0
50,000
(50,000)
(15,000)
Expected
NPV
$29,000
Enter
Fantastic
.3
$65,000
$30,000
$35,000
$10,500
Blazer
Moderate
.4
50,000
30,000
30,000
8,000
Market
Dismal
.3
35,000
30,000
5,000
1,500
Expected
NPV
$20,000
b. The indicated investment,based on the expected NPV,is in the new coat market,However,there is more risk in this alternative so further analysis may be necessary,It is not an automatic decision.
Copyright? 2005 by The McGraw-Hill Companies,Inc.
13-17.
When returns from a project can be assumed to be normally distributed,such as those shown in Figure 13-6 (represented by a symmetrical,bell-shaped curve),the areas under the curve can be determined from statistical tables based on standard deviations,For example,68.26 percent of the distribution will fall within one standard deviation of the expected value (D ± 1σ),Similarly 95.44 percent will fall within two standard deviations (D ± 2σ),and so on,An abbreviated table of areas under the normal curve is shown here.
Number of σ's
from Expected Value
+ or –
+ and –
0.5
0.1915
0.3830
1.0
0.3413
0.6826
1.5
0.4332
0.8664
1.96
0.4750
0.9500
2.0
0.4772
0.9544
Assume Project A has an expected value of $40,000 and a standard deviation (σ) of $8,000.
a. What is the probability the outcome will be between $32,000 and $48,000?
b. What is the probability the outcome will be between $28,000 and $52,000?
c. What is the probability the outcome will be greater than $32,000?
d. What is the probability the outcome will be less than $55,680?
e. What is the probability that the outcome will be less than $32,000 or greater than $52,000?
Solution:
a. Expected value = $40,000,σ = $8,000
$32,000 – $48,000
expected value ± 1 σ
.6826
b. $28,000 – $52,000
expected value ± 1.5 σ
.8664
13-17,Continued
c. Greater than $32,000
,3413
Distribution
under the curve
d. Less than $55,680
,4750
Distribution
under the curve
13-17,Continued
e. Less than $32,000 or greater than $52,000
Area
+
Distribution under the curve is,2255
13-18.
The Palo Alto Microchip Corporation projects a pattern of inflows from the investment shown at the top of page ____,The inflows are spread over time to reflect delayed benefits,Each year is independent of the others.
Year 1
Year 5
Year 10
Cash Inflow
Probability
Cash Inflow
Probability
Cash Inflow
Probability
$50 ,20
$40 ,25
$30 ,30
60 ,60
60 ,50
60 ,40
70 ,20
80 ,25
90 ,30
The expected value for all three years is $60.
a. Compute the standard deviation for each of the three years.
b. Diagram the expected values and standard deviations for each of the three years in a manner similar to Figure 13-6.
c. Assuming a 5 percent and a 10 percent discount rate,complete the table for present value factors.
13-18,Continued
Year
PVIF
5 Percent
PVIF
10 Percent
Difference
1
0.952
0.909
0.043
5
___
___
___
10
___
___
___
d. Is the increasing risk over time,as diagrammed in part b,consistent with the larger differences in PVIFs over time as computed in part c?
e. Assume the initial investment is $110,What is the net present value of the expected values of $60 for the investment at a 10 percent discount rate? Should the investment be accepted?
Solution:
The Palo Alto Microchip Corporation
a. Standard deviation—year 1
50
60
–10
100
.20
20
60
60
0
0
.60
0
70
60
+10
100
.20
20
40
Standard deviation—year 5
40
60
–20
400
.25
100
60
60
0
0
.50
0
80
60
+20
400
.25
100
200
13-18,Continued
Standard deviation—year 10
30
60
–30
900
.30
270
60
60
0
0
.40
0
90
60
+30
900
.30
270
540
b. Risk over time
13-18,Continued
c.
(1)
(2)
(3)
Year
PVIF
5%
PVIF
10%
PVIF
Difference
1
.952
.909
.043
5
.784
.621
.163
10
.614
.386
.228
d. Yes,The larger risk over time is consistent with the larger differences in PVIFAS over time,In effect,future uncertainty is being penalized by a lower IFPV,This is one of the consequences of using progressively higher discount rates to penalize for risk.
e.
Year
Inflow
PVIF (10%)
PV
1
$60
.909
$ 54.5
5
60
.621
$ 37.3
10
60
.386
$ 23.2
PV of inflows
$115.0
Investment
$110.0
NPV
$ 5.0
Accept the investment.
13-19.
Gifford Western Wear makes blue jeans and cowboy shirts,It has seven manufacturing outlets in Texas,Oklahoma,and New Mexico,It is seeking to diversity its business and lower its risk,It is examining three companies—a toy company,a boot company,and a highly exclusive jewelry store chain,Each of these companies can be bought at the same multiple of earnings,The following represents information about all the companies.
Company
Correlation
with Gifford Sales
Western Wear ($ millions)
Average
Earnings
($ millions)
Standard
Deviation
in Earnings
($ millions)
Gifford Western
Wear +1.0
$150
$10
$3
Toy Company +,2
150
10
6
Boot Company +,9
150
10
5
Jewelry Company –,6
150
10
7
a. Discuss what would happen to Gifford Western Wear’s portfolio risk-return if it bought the toy company? the boot company? the jewelry company? Pay particular attention to the first column of correlation data.
b. If you were going to buy one company,which would you choose? Why?
c. If you wanted to buy two companies,which would you choose? Why?
Solution:
Gifford Western Wear
a. Purchase of the Toy Company would provide some reduction in risk because of the low correlation with Gifford Western Wear,while purchase of Boot Company would do very little to reduce portfolio risk because of the high correlation coefficient,A combination with the Jewelry Company would provide a fairly large degree of risk reduction.
Students may or may not calculate the coefficient of variation to get some idea about the riskiness of each project,If they do,they will find the following:
VGWW = $3/$10 =,3 VB = $5/$10 =,5
VTOY = $6/$10 =,6 VJC = $7/$10 =,7
13-19,Continued
Although the Jewelry Company has the highest risk as measured by the coefficient of variation,its negative correlation coefficient of –.6 should provide the best risk reduction for Gifford Western Wear,This is an example of a risky company being added to a portfolio but reducing total risk,Buy the Jewelry Company.
c. Since the Boot Company is most like Gifford Western Wear,its selection would provide the least amount of risk reduction,Therefore add the Toy Company to the Jewelry Company selected in part (b),The Toy Company offers the next best risk reduction after the Jewelry Company because of its low positive correlation coefficient,You might also want to know more about the relationship of the other companies to each other.
13-20.
Hooper Chemical Company,a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process,is examining a plastics firm to add to its operations,Before the acquisition,the normal expected outcomes for the firm were as follows:
Outcomes
($ 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
$10
.30
Normal economy
40
.40
Strong economy
80
.30
13-20,Continued
a. Compute the expected value,standard deviation,a coefficient of variation before the acquisition.
After the acquisition,these values are as follows:
Expected value 43.0 ($ millions)
Standard deviation 27.2 ($ millions)
Coefficient of variation .633
b. 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 were 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
Solution:
Hooper Chemical Co.
a.
D
$20
40
60
P
.30
.40
.30
PD
6
16
18
$40 ($ million)
13-20,Continued
$20
40
–20
400
.30
120
40
40
0
0
.40
0
60
40
+20
400
.30
120
240
V = $15.5/$40 =,388
b. No,it does not appear to be desirable,Although the expected value is $3 million higher,the coefficient of variation is more than twice as high (.633 vs.,388),The slightly added return probably does not adequately compensate for the added risk.
c. Probably not,There may be a higher discount rate applied to the firm's earnings to compensate for the additional risk,The stock price may actually go down.
d. The oil company may provide the best risk reduction benefits,Since petroleum is used as part of the firm’s production process,an increase in the price of oil would normally hurt the chemical company,but this would be offset by the increased profits for the oil company,The same type of offsetting risk reduction benefits would take place if the price of oil were going down.
13-21.
Mr,Boone is looking at a number of different types of investments for his portfolio,He identifies eight possible investments.
Return
Risk
Return
Risk
A
10%
1.5%
E
14%
4.0%
B
11
3.0
F
14
5.0
C
13
3.5
G
15
5.5
D
13
4.0
H
17
7.0
a. Graph the data in a manner similar to Figure 13-11,Use the following axes 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?
13-21,Continued
Solution:
Mr,Boone
a.,b.
c. Achieve the highest possible return for a given risk level,Allow the lowest possible risk at a given return level.
d. No,Each investor must assess his or her own preferences about their risk and return trade-off.
Comprehensive Problems
CP 13-1.
Tobacco Company of America is a very stable billion-dollar company with sales growth of about 5 percent per year in good or bad economic conditions,Because of this stability (a correlation coefficient with the economy of +,3,and a standard deviation of sales of about 5 percent from the mean),Mr,Weed,the vice president of finance,thinks the company could absorb some 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,Tobacco Company of America’s cost of capital is 10 percent.
Computer Whiz Company (CWC)
(cost $75 million)
American Micro-Technology (AMT)
(cost $75 million)
Probability
Aftertax Cash Flows for
10 years
($ millions)
Probability
Aftertax Cash Flows for
10 years
($ millions)
.3
$ 6
.2
$ (1)
.3
10
.2
3
.2
16
.2
10
.2
25
.3
25
.1
31
a. What is the expected cash flow for each company?
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 net present values?
e. Would you change your mind if you added the risk dimensions to the problem? Explain.
f. What if Computer Whiz Company had a correlation coefficient with the economy of +,5 and American Micro-Technology had one of –,1? Which of the 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 Tobacco Company’s stock?
CP 13-1,Continued
Solution:
Portfolio Effect of a Merger
Tobacco Company of America
a.
Computer Whiz Company
American Micro-Technology
P x Cash Flow Millions
P x Cash Flow Millions
.3
$6.0
$1.8
.2
($1.0)
($2.0)
.3
10.0
3.0
.2
3.0
.6
.2
16.0
3.2
.2
10.0
2.0
.2
25.0
5.0
.3
25.0
7.5
.1
31.0
3.1
Expected Value of
$13.0
Expected Value of $13.0
Cash Flows (million)
Cash Flows (million)
b. Coefficient of variation for Computer Whiz Company
$ 6
$13
$–7
$ 49
.3
$14.7
10
13
–3
9
.3
2.7
16
13
3
9
.2
1.8
25
13
12
144
.2
28.8
$48.0
Coefficient of variation = $6.93/$13 =,533
CP 13-1,Continued
Coefficient of variation for American Micro-Technology
$ –1
$13
$–14
$196
.2
$ 39.2
3
13
–10
100
.2
20.0
10
13
–3
9
.2
1.8
25
13
12
144
.3
43.2
31
13
18
324
.1
2.4
$136.6
Coefficient of variation = $11.69/$13 =,899
Computer Whiz has a lower coefficient of variation,.533 <,899
c. $13 million x 6.145
PVIF @ 10%,n = 10 yrs,=
$79.885 PV of inflows
75.000 PV of outflows
$ 4.885 Net Present Value (millions)
The net present value is the same for both companies since they each have the same expected cash flow of $13 million.
d. Based on net present values,you could pick either company.
CP 13-1,Continued
e. The only way one will win over the other is if risk factors are considered,Since American Micro-Technology has the higher coefficient of variation,we would select the lower risk company of Computer Whiz,If Tobacco Company of America uses risk-adjusted cost of capital concepts,it would use a higher cost of capital for the cash flows generated by AMT and this would reduce its NPV.
f. Since Tobacco Company of America has a correlation coefficient with the economy of +.3,the selection of AMT would offer the most risk reduction because its correlation coefficient with the economy is –1.
g. Since Tobacco Company of America is a stable billion-dollar company,this investment of $75 million would probably not have a great impact on the stock price in the short run,There could be some positive movement in the stock price if investors perceive less risk from portfolio diversification,You can use this question to discuss risk-return trade-offs and market reactions.
CP 13-2.
Ace Trucking Company is considering buying 50 new diesel trucks that are 15 percent more fuel-efficient than the ones the firm is now using,Mr,King,the president,has found that the company uses an average of 10 million gallons of diesel fuel per year at a price of $1.20 per gallon,If he can cut fuel consumption by 15 percent,he will save $1,800,000 per year (1,500,000 gallons times $1.20).
Mr,King assumes the price of diesel fuel is an external market force he cannot control and 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 $1.30 per gallon,he would save $1,950,000 in total if he buys the new trucks),
Mr,King has come up with two possible forecasts as shown below and at the top of page ___—each of which he believes has about a 50 percent chance of coming true,Under assumption one,diesel prices will stay relatively low; under assumption two,diesel prices will rise considerably,
Fifty new trucks will cost AceTrucking $5 million,Under a special provision from the Interstate Commerce Commission,the allowable deprecation will be 25 percent in year one,38 percent in year two,and 37 percent in year three,The firm has a tax rate of 40 percent and a cost of capital of 11 percent.
a. First compute the yearly expected costs of diesel fuel for both assumption one (relatively low prices) and assumption two (high prices) from the following forecasts.
Forecast for assumption one:
Probability
(same for
each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$,70
$,90
$1.00
.2
.90
1.10
1.20
.3
1.00
1.20
1.30
.2
1.20
1.45
1.50
.2
1.30
1.55
1.70
CP 13-2,Continued
Forecast for assumption two:
Probability
(same for
each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$1.30
$1.50
$1.90
.3
1.40
1.70
2.20
.4
1.90
2.30
2.70
.2
2.30
2.50
3.00
b. What will be the dollar savings in diesel expenses each year for assumption one and for assumption two?
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 NPVs by,5).
e. If you were Mr,King,would you go ahead with this capital investment?
f. How sensitive to fuel prices is this capital investment?
Solution:
Investment Decision Based on Probability Analysis
Ace Trucking Company
a. Assumption One:
Yr,1
Yr,2
Yr,3
Probability
D
DP
D
DP
D
DP
.1
$0.70
.07
$0.90
.09
$1.00
.10
.2
.90
.18
1.10
.22
1.20
.24
.3
1.00
.30
1.20
.36
1.30
.39
.2
1.20
.24
1.45
.29
1.50
.30
.2
1.30
.26
1.55
.31
1.70
.34
Expected value $1.05/gallon $1.27/gallon $1.37/gallon
CP 13-2,Continued
Assumption Two:
Yr,1
Yr,2
Yr,3
Probability
D
DP
D
DP
D
DP
.1
$1.30
.13
$1.50
.15
$1.90
.19
.3
1.40
.42
1.70
.51
2.20
.66
.4
1.90
.76
2.30
.92
2.70
1.08
.2
2.30
.46
2.50
.50
3.00
,60
Expected value $1.77/gallon $2.08/gallon $2.53/gallon
b. Assumption One:
Yr.
Expected
Cost/gal.
# of Gals.
without
Efficiency =
Cost
% Savings
with
Efficiency
Total
$ Saved
1
$1.05
10 million
$10,500,000
15%
$1,525,000
2
1.27
12,700,000
1,905,000
3
1.37
13,700,000
2,055,000
Assumption Two:
1
$1.77
10 million
$17,700,000
15%
$2,655,000
2
2.08
20,800,000
3,120,000
3
2.53
25,300,000
3,795,000
CP 13-2,Continued
c. First compute annual depreciation,Then proceed to the analysis.
Year 1 25% x 5 mil. = 1.25 mil.
Year 2 38% x 5 mil. = 1.90 mil.
Year 3 37% x 5 mil. = 1.85 mil.
Total saved equals increase in EBDT.
Assumption One:
Year 1
Year 2
Year 3
Increase in EBDT
$1,575,000
$1,905,000
$2,055,000
– Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
325,000
5,000
205,000
– Taxes 40 percent
130,000
2,000
82,000
Increase in EAT
195,000
3,000
123,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$1,445,000
$1,903,000
$1,973,000
Assumption Two:
Increase in EBDT
$2,655,000
$3,120,000
$3,795,000
– Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
1,405,000
1,220,000
1,945,000
– Taxes 40 percent
562,000
488,000
778,000
Increase in EAT
843,000
732,000
1,167,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$2,093,000
$2,632,000
$3,017,000
CP 13-2,Continued
d. Present Value:
Assumption One:
Year
Cash Flow
PVIF @ 11%
Present Value
1
$1,445,000
.901
$1,301,945
2
1,903,000
.812
1,545,236
3
1,973,000
.731
1,442,263
PV of inflows
$4,289,444
PV of outflows
5,000,000
NPV
$(710,556)
Assumption Two:
Year
Cash Flow
PVIF @ 11%
Present Value
1
$2,093,000
.901
$1,885,793
2
2,632,000
.812
2,137,184
3
3,017,000
.731
2,205,427
PV of inflows
$6,228,404
PV of outflows
5,000,000
NPV
$1,228,404
Combined NPV:
Outcome
NPV
Probability
Assumption One
Assumption Two
Expected Outcome
–710,556
1,228,404
.5
.5
–335,278
614,202
$258,924
e. Yes – The combined expected value of the outcomes is positive.
f. Quite sensitive when that many gallons are used per year.
Discussion Questions
13-1.
If corporate managers are risk-averse,does this mean they will not take risks? Explain.
Risk-averse corporate managers are not unwilling to take risks,but will require a higher return from risky investments,There must be a premium or additional compensation for risk taking.
13-2.
Discuss the concept of risk and how it might be measured.
Risk may be defined in terms of the variability of outcomes from a given investment,The greater the variability,the greater the risk,Risk may be measured in terms of the coefficient of variation,in which we divide the standard deviation (or measure of dispersion) by the mean,We also may measure risk in terms of beta,in which we determine the volatility of returns on an individual stock relative to a stock market index.
13-3.
When is the coefficient of variation a better measure of risk than the standard deviation?
The standard deviation is an absolute measure of dispersion while the coefficient of variation is a relative measure and allows us to relate the standard deviation to the mean,The coefficient of variation is a better measure of dispersion when we wish to consider the relative size of the standard deviation or compare two or more investments of different size.
13-4.
Explain how the concept of risk can be incorporated into the capital budgeting process.
Risk may be introduced into the capital budgeting process by requiring higher returns for risky investments,One method of achieving this is to use higher discount rates for riskier investments,This risk-adjusted discount rate approach specifies different discount rates for different risk categories as measured by the coefficient of variation or some other factor,Other methods,such as the certainty equivalent approach,also may be used.
13-5.
If risk is to be analyzed in a qualitative way,place the following investment decisions in order from the lowest risk to the highest risk:
New equipment.
New market.
Repair of old machinery.
New product in a foreign market.
New product in a related market.
Addition to a new product line.
Referring to Table 13-3,the following order would be correct:
repair old machinery (c)
new equipment (a)
addition to normal product line (f)
new product in related market (e)
completely new market (b)
new product in foreign market (d)
13-6.
Assume a company,correlated with the economy,is evaluating six projects,of which two are positively correlated with the economy,two are negatively correlated,and two are not correlated with it at all,Which two projects would you select to minimize the company's overall risk?
In order to minimize risk,the firm that is positively correlated with the economy should select the two projects that are negatively correlated with the economy.
13-7.
Assume a firm has several hundred possible investments and that it wants to analyze the risk-return trade-off for portfolios of 20 projects,How should it proceed with the evaluation?
The firm should attempt to construct a chart showing the risk-return characteristics for every possible set of 20,By using a procedure similar to that indicated in Figure 13-11,the best risk-return trade-offs or efficient frontier can be determined,We then can decide where we wish to be along this line.
13-8.
Explain the effect of the risk-return trade-off on the market value of common stock.
High profits alone will not necessarily lead to a high market value for common stock,To the extent large or unnecessary risks are taken,a higher discount rate and lower valuation may be assigned to our stock,Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market.
13-9.
What is the purpose of using simulation analysis?
Simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions,A Monte Carlo simulation model uses random variables for inputs,By programming the computer to randomly select inputs from probability distributions,the outcomes generated by a simulation are distributed about a mean and instead of generating one return or net present value,a range of outcomes with standard deviations are provided.
Problems
13-1.
Myers Business Systems is evaluating the introduction of a new product,The possible levels of unit sales and the probabilities of their occurrence are given below.
Possible
Market Reaction
Sales
in Units
Probabilities
Low response
20
.10
Moderate response
40
.30
High response
55
.40
Very high response
70
.20
a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?
Solution:
Myers Business Systems
a.
D
20
40
55
70
P
.10
.30
.40
.20
DP
2
12
22
14
50 =
b.
20
50
–30
900
.10
90
40
50
–10
100
.30
30
55
50
+5
25
.40
10
70
50
+20
400
.20
80
210
13-2.
Monarck King Size Beds,Inc.,is evaluating a new promotional campaign that could increase sales,Possible outcomes and probabilities of the outcomes are shown below,Compute the coefficient of variation.
Possible Outcomes
Additional
Sales in Units
Probabilities
Ineffective campaign
20
.20
Normal response
30
.50
Extremely effective
70
.30
Solution:
Monarck King Size Beds,Inc.
Coefficient of variation (V) = standard deviation/expected value.
D
20
30
70
P
.20
.50
.30
DP
4
15
21
40 =
20
40
–20
400
.20
80
30
40
–10
100
.50
50
70
40
+30
900
.30
270
400
13-3.
Al Bundy is evaluating a new advertising program that could increase shoe sales,Possible outcomes and probabilities of the outcomes are shown below,Compute the coefficient of variation.
Possible Outcomes
Additional
Sales in Units
Probabilities
Ineffective campaign
40
.20
Normal response
60
.50
Extremely effective
140
.30
Solution:
Al Bundy
Coefficient of variation (V) = standard deviation/expected value.
D
40
60
140
P
.20
.50
.30
DP
8
30
42
80 =
40
80
–40
1,600
.20
320
60
80
–20
400
.50
200
140
80
+60
3,600
.30
1,080
1,600
13-4.
Possible outcomes for three investment alternatives and their probabilities of occurrence are given below.
Alternative 1
Alternative 2
Alternative 3
Outcomes
Probability
Outcomes
Probability
Outcomes
Probability
Failure
50
.2
90
.3
80
.4
Acceptable
80
.4
160
.5
200
.5
Successful
120
.4
200
.2
400
.1
Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation).
Solution:
Alternative 1
D x P = DP
Alternative 2
D x P = DP
Alternative 3
D x P = DP
$ 50 .2 $10
80 .4 32
120 .4 48
= $90
$ 90 .3 $ 27
160 .5 80
200 .2 40
= $147
$ 80 .4 $ 32
200 .5 100
400 .1 40
= $172
Standard Deviation Alternative 1
$ 50
$90
$–40
$1,600
.2
$320
80
90
–10
100
.4
40
120
90
+30
900
.4
360
$720
13-4,Continued
Alternative 2
$ 90
$147
$–57
$3,249
.3
$ 974.70
160
147
+13
169
.5
84.50
200
147
+53
2,809
.2
561.80
$1,621.00
Alternative 3
$ 80
$172
$–92
$ 8,464
.4
$3,385.60
200
172
+28
784
.5
392.00
400
172
+228
51,984
.1
5,198.40
$8,976.00
Rank by Coefficient of Variation
Coefficient of Variation (V) = Standard Deviation/Expected Value
V
Alternative 2
Alternative 1
Alternative 3
13-5.
Five investment alternatives have the following returns and standard deviations of returns.
Alternative
Returns:
Expected Value
Standard
Deviation
A
$ 5,000
$1,200
B
4,000
600
C
4,000
800
D
8,000
3,200
E
10,000
900
Using the coefficient of variation,rank the five alternatives from lowest risk to highest risk.
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)
C
$800/$4,000 =,20
C (.20)
D
E
$3,200/$8,000 =,40
$900/$10,000 =,09
A (.24)
D (.40)
13-6.
In problem 5,if you were to choose between Alternative B and C only,would you need to use the coefficient of variation? Why?
Solution:
Since B and C have the same expected value,they can be evaluated based on their standard deviations of return,C has a larger standard deviation and so is riskier than B for the same expected return.
13-7.
Tom Fears is highly risk-averse while Sonny Outlook actually enjoys taking a risk.
a. Which one of the four investments should Tom choose? Compute the coefficients of variation to help you in your choice.
b. Which one of the four investments should Sonny choose?
Investments
Returns –
Expected Value
Standard
Deviation
Buy stocks
$ 7,000
$ 4,000
Buy bonds
5,000
1,560
Buy commodity futures
12,000
15,100
Buy options
8,000
8,850
Solution:
Coefficient of variation (V) = standard deviation/expected value.
Buy stocks
$4,000/$7,000 =,571
Buy bonds
$1,560/$5,000 =,312
Buy commodity futures
$15,100/$12,000 = 1.258
Buy options
$8,850/$8,000 = 1.106
a. Tom should buy the bonds because bonds have the lowest coefficient of variation.
b. Sonny should buy the commodity futures because they have the highest coefficient of variation.
13-8.
Bridget’s Modeling Studios is considering opening a new location in Miami,An aftertax cash flow of $120 per day (expected value) is projected for each of the two locations being evaluated..
Which of these sites 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
.15
$ 80
.10
$ 50
.50
110
.20
80
.30
140
.40
120
.05
220
.20
160
Expected value
$120
.10
Expected Value
190
$120
Solution:
Bridget’s Modeling Studios
Standard Deviations of Sites A and B
Site A
$ 80
$120
$–40
$ 1,600
.15
$240
110
120
–10
100
.50
50
140
120
+20
400
.30
120
220
120
+100
10,000
.05
500
$910
13-8,Continued
Site B
$ 50
$120
$–70
$4,900
.10
$ 490
80
120
–40
1,600
.20
320
120
120
–0–
–0–
.40
–0–
160
120
+40
1,600
.20
320
190
120
+70
4,900
.10
490
$1,620
VA = $30.17/$120 =,2514
VB = $40.25/$120 =,3354
Site A is the preferred site since it has the smallest coefficient of variation,Because both alternatives have the same expected value,the standard deviation alone would have been enough for a decision,A will be just as profitable as B but with less risk.
13-9.
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
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
5
30,000
.519
15,570
PV of Inflows
$65,904
Investment
70,000
NPV
$(4,096)
Based on the positive net present value,the project should not be undertaken.
13-10.
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 below,Which method should be selected using net present value analysis?
Year
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
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
4
26,000
.636
16,536
28,000
.552
15,456
5
14,000
.597
7,938
15,000
.476
7,140
PV of Inflows $83,884
$80,846
Investment –75,000
–75,000
NPV $ 8,884
Select Method 1
$ 5,846
13-11.
Fill in the table below 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 ______ ______
Solution:
Discount Rate
Years 5% 20%
1 .952 .833
10 .614 .162
20 .377 .026
The impact of a high discount rate is much greater on long-term value,For example,after the first year,the high rate discount value produce an answer that is 87.5% of the low discount rate (.833/.952),However,after the 20th year,the high rate discount rate is only 6.90% of the low discount rate (.026/.377).
13-12.
Larry’s Athletic Lounge is planning an expansion program to increase the sophistication of its exercise equipment,Larry is considering some new equipment priced at $20,000 with an estimated life of five years,Larry is not sure how many members the new equipment will attract,but he estimates his increased yearly cash flows for each of the next five years will have the following probability distribution,Larry’s cost of capital is 14 percent.
P
(Probability)
Cash Flow
.2
$2,400
.4
4,800
.3
6,000
.1
7,200
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 Larry buy the new equipment?
Solution:
Larry’s Athletic Lounge
a. Expected Cash Flow
$2,400
x
.2
$ 480
4,800
x
.4
1,920
6,000
x
.3
1,800
7,200
x
.1
720
Expected cash flow
$4,920
b. $4,920 x 3.433 (PVIFA @ 14%,n = 5) = (Appendix D)
$16,890 Present value of inflows
20,000 Present value of outflows
$(3,110) Net present value
c. Larry should not buy this equipment because the net present value is negative.
13-13.
Silverado Mining Company is analyzing the purchase of two silver mines,Only one investment will be made,The Alaska mine will cost $2,000,000 and will produce $400,000 per year in years 5 through 15 and $800,000 per year in years 16 through 25,The Montana mine will cost $2,400,000 and will produce $300,000 per year for the next 25 years,The cost of capital is 10 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 Alaska 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 Alaska mine justifies an extra 5 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of flows,does the investment decision change?
Solution:
Silverado Mining Company
a. Calculate the net present value for each project.
The Alaska Mine
Years
Cash Flow
n Factor
PVIFA @ 10%
Present Value
5-15
$400,000
(15 – 4)
(7.606 – 3.170)
$1,774,400
16-25
$800,000
(25 – 15)
(9.077 – 7.606)
$1,176,800
Present value of inflows
$2,951,200
Present value of outflows
$2,000,000
Net present value
$ 951,200
13-13,Continued
The Montana Mine
Years
Cash Flow
n Factor
PVIFA @ 10%
Present Value
1-25
$300,000
9.077
$2,723,100
Present value of inflows
$2,723,100
Present value of outflows
$2,400,100
Net present value
$ 323,100
Select the Alaska Mine.
b. Recalculate the net present value of the Alaska Mine at a 15 percent discount rate.
Years
Cash Flow
n Factor
PVIFA @ 15%
Present Value
5-15
$400,000
(15 – 4)
(5.847 – 2.855)
$1,196,800
16-25
$800,000
(25 – 15)
(6.464 – 5.847)
$ 493,600
Present value of inflows
$1,690,000
Present value of outflows
$2,000,000
Net present value
$(309,600)
Now the decision should be made to reject the purchase of the Alaska Mine and purchase the Montana Mine.
13-14.
Mr,Monty Terry,a real estate investor,is trying to decide between two potential small shopping center purchases,His choices are the Wrigley Village and Crosley Square,The anticipated annual cash inflows from each are as follows:
Wrigley Village
Crosley Square
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
Yearly Aftertax
Cash Inflow
(in thousands)
Probability
$10
.1
$20
.1
30
.2
30
.3
40
.3
35
.4
50
.3
40
.2
60
.1
50
a. Find the expected value of the cash flow from each shopping center.
b. What is the coefficient of variation for each shopping center?
c. Which shopping center has more risk?
Solution:
Mr,Monty Terry
a.
Wrigley Village
Crosley Square
D
P
DP
D
P
DP
10
0.1
$ 1
20
0.1
$ 2
30
0.2
6
30
0.3
9
40
0.3
12
35
0.4
14
50
0.3
15
50
0.2
10
60
0.1
6
Expected Cash Flow
$35
Expected Cash Flow
$40
13-14,Continued
b. First find the standard deviation and then the coefficient of variation.
Wrigley Village
$10
$40
$–30
$900
.1
$ 90
30
40
–10
100
.2
20
40
40
0
0
.3
0
50
40
+10
100
.3
30
60
40
+20
400
.1
40
$180
V = $13.42/$40 =,336
Crosley Square
$20
$35
$–15
$225
.1
$22.5
30
35
–5
25
.3
7.5
35
35
0
0
.4
0
50
35
+15
225
.2
45.0
$75.0
V = $8.66/$35 =,247
c. Based on the coefficient of variation,Wrigley Village has more risk (.336 vs.,247).
13-15.
Referring to Problem 14,Mr,Terry is likely to hold the shopping center of his choice for 25 years and will use this period for decision-making purposes,Either shopping center can be purchased for $300,000,Mr,Terry uses a risk-adjusted discount rate when evaluating investments,His scale is related to the coefficient of variation presented below.
Coefficient
of Variation
Discount
Rate
0-0.30
8%
0.31-0.60
11
(cost of capital)
0.61-0.90
14
Over 0.90
18
a. Compute the risk-adjusted net present values for Wrigley Village and Crosley Square,You can get the coefficient of variation and cash flow figures (in thousands) from the previous problem.
b. Which investment should Mr,Terry accept if the two investments are mutually exclusive? If the investments are not mutually exclusive and no capital rationing is involved,how would your decision be affected?
Solution:
Mr,Monty Terry (Continued)
a. Risk-adjusted net present value
Wrigley Village
Crosley Square
(with V =,336,
discount rate = 11%
(with V =,247,
discount rate = 8%
Expected Cash Flow
$ 40,000
$ 35,000
IFPVA (n = 25)
8,422
10.675
Present Value of
Inflows
$336,880
$373,625
Present Value of
Outflows
300,000
$300,000
Net Present Value
$ 36,880
$ 73,625
13-15,Continued
b. If these two investments are mutually exclusive,he should accept Crosley Village because it has a higher net present value.
If the investments are non-mutually exclusive and no capital rationing is involved,they both should be undertaken.
13-16.
Roper Fashions is preparing a product strategy for the fall season,One option is to go to a highly imaginative new,four-gold-button sport coat with special emblems on the front pocket,The all-wool product would be available for both males and females,A second option would be to produce a traditional blue blazer line,The marketing research department has determined that the new,four-gold-button coat and traditional blue blazer line offer the probabilities of outcomes and related cash flows shown at the top of page ___.
New Coat
Blazer
Expected
Sales
Probability
Present Value
of Cash Flows
from Sales
Probability
Present Value
of Cash Flows
from Sales
Fantastic
.5
$130,000
.3
$65,000
Moderate
.2
70,000
.4
50,000
Dismal
.3
0
.3
35,000
The initial cost to get into the new coat line is $50,000 in designs,equipment,and inventory,The blazer line would carry an initial cost of $30,000.
a. Diagram a complete decision tree of possible outcomes similar to Figure 13-8 on page ___,Take the analysis all the way through the process of computing expected NPV (last column) for each investment.
b. Given the analysis in part a,would you automatically make the investment indicated?
13-16,Continued
Solution:
Roper Fashions
a.
(1)
(2)
(3)
(4)
(5)
(6)
Expected Sales
Probability
Present Value of Cash Flows From Sales
Initial Cost
NPV
(3) – (4)
Expected
NPV
(2) x (5)
Enter
Fantastic
.5
$130,000
$50,000
$80,000
$40,000
New Coat
Moderate
.2
70,000
50,000
20,000
4,000
Market
Dismal
.3
0
50,000
(50,000)
(15,000)
Expected
NPV
$29,000
Enter
Fantastic
.3
$65,000
$30,000
$35,000
$10,500
Blazer
Moderate
.4
50,000
30,000
30,000
8,000
Market
Dismal
.3
35,000
30,000
5,000
1,500
Expected
NPV
$20,000
b. The indicated investment,based on the expected NPV,is in the new coat market,However,there is more risk in this alternative so further analysis may be necessary,It is not an automatic decision.
Copyright? 2005 by The McGraw-Hill Companies,Inc.
13-17.
When returns from a project can be assumed to be normally distributed,such as those shown in Figure 13-6 (represented by a symmetrical,bell-shaped curve),the areas under the curve can be determined from statistical tables based on standard deviations,For example,68.26 percent of the distribution will fall within one standard deviation of the expected value (D ± 1σ),Similarly 95.44 percent will fall within two standard deviations (D ± 2σ),and so on,An abbreviated table of areas under the normal curve is shown here.
Number of σ's
from Expected Value
+ or –
+ and –
0.5
0.1915
0.3830
1.0
0.3413
0.6826
1.5
0.4332
0.8664
1.96
0.4750
0.9500
2.0
0.4772
0.9544
Assume Project A has an expected value of $40,000 and a standard deviation (σ) of $8,000.
a. What is the probability the outcome will be between $32,000 and $48,000?
b. What is the probability the outcome will be between $28,000 and $52,000?
c. What is the probability the outcome will be greater than $32,000?
d. What is the probability the outcome will be less than $55,680?
e. What is the probability that the outcome will be less than $32,000 or greater than $52,000?
Solution:
a. Expected value = $40,000,σ = $8,000
$32,000 – $48,000
expected value ± 1 σ
.6826
b. $28,000 – $52,000
expected value ± 1.5 σ
.8664
13-17,Continued
c. Greater than $32,000
,3413
Distribution
under the curve
d. Less than $55,680
,4750
Distribution
under the curve
13-17,Continued
e. Less than $32,000 or greater than $52,000
Area
+
Distribution under the curve is,2255
13-18.
The Palo Alto Microchip Corporation projects a pattern of inflows from the investment shown at the top of page ____,The inflows are spread over time to reflect delayed benefits,Each year is independent of the others.
Year 1
Year 5
Year 10
Cash Inflow
Probability
Cash Inflow
Probability
Cash Inflow
Probability
$50 ,20
$40 ,25
$30 ,30
60 ,60
60 ,50
60 ,40
70 ,20
80 ,25
90 ,30
The expected value for all three years is $60.
a. Compute the standard deviation for each of the three years.
b. Diagram the expected values and standard deviations for each of the three years in a manner similar to Figure 13-6.
c. Assuming a 5 percent and a 10 percent discount rate,complete the table for present value factors.
13-18,Continued
Year
PVIF
5 Percent
PVIF
10 Percent
Difference
1
0.952
0.909
0.043
5
___
___
___
10
___
___
___
d. Is the increasing risk over time,as diagrammed in part b,consistent with the larger differences in PVIFs over time as computed in part c?
e. Assume the initial investment is $110,What is the net present value of the expected values of $60 for the investment at a 10 percent discount rate? Should the investment be accepted?
Solution:
The Palo Alto Microchip Corporation
a. Standard deviation—year 1
50
60
–10
100
.20
20
60
60
0
0
.60
0
70
60
+10
100
.20
20
40
Standard deviation—year 5
40
60
–20
400
.25
100
60
60
0
0
.50
0
80
60
+20
400
.25
100
200
13-18,Continued
Standard deviation—year 10
30
60
–30
900
.30
270
60
60
0
0
.40
0
90
60
+30
900
.30
270
540
b. Risk over time
13-18,Continued
c.
(1)
(2)
(3)
Year
PVIF
5%
PVIF
10%
PVIF
Difference
1
.952
.909
.043
5
.784
.621
.163
10
.614
.386
.228
d. Yes,The larger risk over time is consistent with the larger differences in PVIFAS over time,In effect,future uncertainty is being penalized by a lower IFPV,This is one of the consequences of using progressively higher discount rates to penalize for risk.
e.
Year
Inflow
PVIF (10%)
PV
1
$60
.909
$ 54.5
5
60
.621
$ 37.3
10
60
.386
$ 23.2
PV of inflows
$115.0
Investment
$110.0
NPV
$ 5.0
Accept the investment.
13-19.
Gifford Western Wear makes blue jeans and cowboy shirts,It has seven manufacturing outlets in Texas,Oklahoma,and New Mexico,It is seeking to diversity its business and lower its risk,It is examining three companies—a toy company,a boot company,and a highly exclusive jewelry store chain,Each of these companies can be bought at the same multiple of earnings,The following represents information about all the companies.
Company
Correlation
with Gifford Sales
Western Wear ($ millions)
Average
Earnings
($ millions)
Standard
Deviation
in Earnings
($ millions)
Gifford Western
Wear +1.0
$150
$10
$3
Toy Company +,2
150
10
6
Boot Company +,9
150
10
5
Jewelry Company –,6
150
10
7
a. Discuss what would happen to Gifford Western Wear’s portfolio risk-return if it bought the toy company? the boot company? the jewelry company? Pay particular attention to the first column of correlation data.
b. If you were going to buy one company,which would you choose? Why?
c. If you wanted to buy two companies,which would you choose? Why?
Solution:
Gifford Western Wear
a. Purchase of the Toy Company would provide some reduction in risk because of the low correlation with Gifford Western Wear,while purchase of Boot Company would do very little to reduce portfolio risk because of the high correlation coefficient,A combination with the Jewelry Company would provide a fairly large degree of risk reduction.
Students may or may not calculate the coefficient of variation to get some idea about the riskiness of each project,If they do,they will find the following:
VGWW = $3/$10 =,3 VB = $5/$10 =,5
VTOY = $6/$10 =,6 VJC = $7/$10 =,7
13-19,Continued
Although the Jewelry Company has the highest risk as measured by the coefficient of variation,its negative correlation coefficient of –.6 should provide the best risk reduction for Gifford Western Wear,This is an example of a risky company being added to a portfolio but reducing total risk,Buy the Jewelry Company.
c. Since the Boot Company is most like Gifford Western Wear,its selection would provide the least amount of risk reduction,Therefore add the Toy Company to the Jewelry Company selected in part (b),The Toy Company offers the next best risk reduction after the Jewelry Company because of its low positive correlation coefficient,You might also want to know more about the relationship of the other companies to each other.
13-20.
Hooper Chemical Company,a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process,is examining a plastics firm to add to its operations,Before the acquisition,the normal expected outcomes for the firm were as follows:
Outcomes
($ 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
$10
.30
Normal economy
40
.40
Strong economy
80
.30
13-20,Continued
a. Compute the expected value,standard deviation,a coefficient of variation before the acquisition.
After the acquisition,these values are as follows:
Expected value 43.0 ($ millions)
Standard deviation 27.2 ($ millions)
Coefficient of variation .633
b. 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 were 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
Solution:
Hooper Chemical Co.
a.
D
$20
40
60
P
.30
.40
.30
PD
6
16
18
$40 ($ million)
13-20,Continued
$20
40
–20
400
.30
120
40
40
0
0
.40
0
60
40
+20
400
.30
120
240
V = $15.5/$40 =,388
b. No,it does not appear to be desirable,Although the expected value is $3 million higher,the coefficient of variation is more than twice as high (.633 vs.,388),The slightly added return probably does not adequately compensate for the added risk.
c. Probably not,There may be a higher discount rate applied to the firm's earnings to compensate for the additional risk,The stock price may actually go down.
d. The oil company may provide the best risk reduction benefits,Since petroleum is used as part of the firm’s production process,an increase in the price of oil would normally hurt the chemical company,but this would be offset by the increased profits for the oil company,The same type of offsetting risk reduction benefits would take place if the price of oil were going down.
13-21.
Mr,Boone is looking at a number of different types of investments for his portfolio,He identifies eight possible investments.
Return
Risk
Return
Risk
A
10%
1.5%
E
14%
4.0%
B
11
3.0
F
14
5.0
C
13
3.5
G
15
5.5
D
13
4.0
H
17
7.0
a. Graph the data in a manner similar to Figure 13-11,Use the following axes 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?
13-21,Continued
Solution:
Mr,Boone
a.,b.
c. Achieve the highest possible return for a given risk level,Allow the lowest possible risk at a given return level.
d. No,Each investor must assess his or her own preferences about their risk and return trade-off.
Comprehensive Problems
CP 13-1.
Tobacco Company of America is a very stable billion-dollar company with sales growth of about 5 percent per year in good or bad economic conditions,Because of this stability (a correlation coefficient with the economy of +,3,and a standard deviation of sales of about 5 percent from the mean),Mr,Weed,the vice president of finance,thinks the company could absorb some 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,Tobacco Company of America’s cost of capital is 10 percent.
Computer Whiz Company (CWC)
(cost $75 million)
American Micro-Technology (AMT)
(cost $75 million)
Probability
Aftertax Cash Flows for
10 years
($ millions)
Probability
Aftertax Cash Flows for
10 years
($ millions)
.3
$ 6
.2
$ (1)
.3
10
.2
3
.2
16
.2
10
.2
25
.3
25
.1
31
a. What is the expected cash flow for each company?
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 net present values?
e. Would you change your mind if you added the risk dimensions to the problem? Explain.
f. What if Computer Whiz Company had a correlation coefficient with the economy of +,5 and American Micro-Technology had one of –,1? Which of the 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 Tobacco Company’s stock?
CP 13-1,Continued
Solution:
Portfolio Effect of a Merger
Tobacco Company of America
a.
Computer Whiz Company
American Micro-Technology
P x Cash Flow Millions
P x Cash Flow Millions
.3
$6.0
$1.8
.2
($1.0)
($2.0)
.3
10.0
3.0
.2
3.0
.6
.2
16.0
3.2
.2
10.0
2.0
.2
25.0
5.0
.3
25.0
7.5
.1
31.0
3.1
Expected Value of
$13.0
Expected Value of $13.0
Cash Flows (million)
Cash Flows (million)
b. Coefficient of variation for Computer Whiz Company
$ 6
$13
$–7
$ 49
.3
$14.7
10
13
–3
9
.3
2.7
16
13
3
9
.2
1.8
25
13
12
144
.2
28.8
$48.0
Coefficient of variation = $6.93/$13 =,533
CP 13-1,Continued
Coefficient of variation for American Micro-Technology
$ –1
$13
$–14
$196
.2
$ 39.2
3
13
–10
100
.2
20.0
10
13
–3
9
.2
1.8
25
13
12
144
.3
43.2
31
13
18
324
.1
2.4
$136.6
Coefficient of variation = $11.69/$13 =,899
Computer Whiz has a lower coefficient of variation,.533 <,899
c. $13 million x 6.145
PVIF @ 10%,n = 10 yrs,=
$79.885 PV of inflows
75.000 PV of outflows
$ 4.885 Net Present Value (millions)
The net present value is the same for both companies since they each have the same expected cash flow of $13 million.
d. Based on net present values,you could pick either company.
CP 13-1,Continued
e. The only way one will win over the other is if risk factors are considered,Since American Micro-Technology has the higher coefficient of variation,we would select the lower risk company of Computer Whiz,If Tobacco Company of America uses risk-adjusted cost of capital concepts,it would use a higher cost of capital for the cash flows generated by AMT and this would reduce its NPV.
f. Since Tobacco Company of America has a correlation coefficient with the economy of +.3,the selection of AMT would offer the most risk reduction because its correlation coefficient with the economy is –1.
g. Since Tobacco Company of America is a stable billion-dollar company,this investment of $75 million would probably not have a great impact on the stock price in the short run,There could be some positive movement in the stock price if investors perceive less risk from portfolio diversification,You can use this question to discuss risk-return trade-offs and market reactions.
CP 13-2.
Ace Trucking Company is considering buying 50 new diesel trucks that are 15 percent more fuel-efficient than the ones the firm is now using,Mr,King,the president,has found that the company uses an average of 10 million gallons of diesel fuel per year at a price of $1.20 per gallon,If he can cut fuel consumption by 15 percent,he will save $1,800,000 per year (1,500,000 gallons times $1.20).
Mr,King assumes the price of diesel fuel is an external market force he cannot control and 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 $1.30 per gallon,he would save $1,950,000 in total if he buys the new trucks),
Mr,King has come up with two possible forecasts as shown below and at the top of page ___—each of which he believes has about a 50 percent chance of coming true,Under assumption one,diesel prices will stay relatively low; under assumption two,diesel prices will rise considerably,
Fifty new trucks will cost AceTrucking $5 million,Under a special provision from the Interstate Commerce Commission,the allowable deprecation will be 25 percent in year one,38 percent in year two,and 37 percent in year three,The firm has a tax rate of 40 percent and a cost of capital of 11 percent.
a. First compute the yearly expected costs of diesel fuel for both assumption one (relatively low prices) and assumption two (high prices) from the following forecasts.
Forecast for assumption one:
Probability
(same for
each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$,70
$,90
$1.00
.2
.90
1.10
1.20
.3
1.00
1.20
1.30
.2
1.20
1.45
1.50
.2
1.30
1.55
1.70
CP 13-2,Continued
Forecast for assumption two:
Probability
(same for
each year)
Price of Diesel Fuel per Gallon
Year 1
Year 2
Year 3
.1
$1.30
$1.50
$1.90
.3
1.40
1.70
2.20
.4
1.90
2.30
2.70
.2
2.30
2.50
3.00
b. What will be the dollar savings in diesel expenses each year for assumption one and for assumption two?
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 NPVs by,5).
e. If you were Mr,King,would you go ahead with this capital investment?
f. How sensitive to fuel prices is this capital investment?
Solution:
Investment Decision Based on Probability Analysis
Ace Trucking Company
a. Assumption One:
Yr,1
Yr,2
Yr,3
Probability
D
DP
D
DP
D
DP
.1
$0.70
.07
$0.90
.09
$1.00
.10
.2
.90
.18
1.10
.22
1.20
.24
.3
1.00
.30
1.20
.36
1.30
.39
.2
1.20
.24
1.45
.29
1.50
.30
.2
1.30
.26
1.55
.31
1.70
.34
Expected value $1.05/gallon $1.27/gallon $1.37/gallon
CP 13-2,Continued
Assumption Two:
Yr,1
Yr,2
Yr,3
Probability
D
DP
D
DP
D
DP
.1
$1.30
.13
$1.50
.15
$1.90
.19
.3
1.40
.42
1.70
.51
2.20
.66
.4
1.90
.76
2.30
.92
2.70
1.08
.2
2.30
.46
2.50
.50
3.00
,60
Expected value $1.77/gallon $2.08/gallon $2.53/gallon
b. Assumption One:
Yr.
Expected
Cost/gal.
# of Gals.
without
Efficiency =
Cost
% Savings
with
Efficiency
Total
$ Saved
1
$1.05
10 million
$10,500,000
15%
$1,525,000
2
1.27
12,700,000
1,905,000
3
1.37
13,700,000
2,055,000
Assumption Two:
1
$1.77
10 million
$17,700,000
15%
$2,655,000
2
2.08
20,800,000
3,120,000
3
2.53
25,300,000
3,795,000
CP 13-2,Continued
c. First compute annual depreciation,Then proceed to the analysis.
Year 1 25% x 5 mil. = 1.25 mil.
Year 2 38% x 5 mil. = 1.90 mil.
Year 3 37% x 5 mil. = 1.85 mil.
Total saved equals increase in EBDT.
Assumption One:
Year 1
Year 2
Year 3
Increase in EBDT
$1,575,000
$1,905,000
$2,055,000
– Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
325,000
5,000
205,000
– Taxes 40 percent
130,000
2,000
82,000
Increase in EAT
195,000
3,000
123,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$1,445,000
$1,903,000
$1,973,000
Assumption Two:
Increase in EBDT
$2,655,000
$3,120,000
$3,795,000
– Depreciation
1,250,000
1,900,000
1,850,000
Increase in EBT
1,405,000
1,220,000
1,945,000
– Taxes 40 percent
562,000
488,000
778,000
Increase in EAT
843,000
732,000
1,167,000
+ Depreciation
1,250,000
1,900,000
1,850,000
Increased Cash Flow
$2,093,000
$2,632,000
$3,017,000
CP 13-2,Continued
d. Present Value:
Assumption One:
Year
Cash Flow
PVIF @ 11%
Present Value
1
$1,445,000
.901
$1,301,945
2
1,903,000
.812
1,545,236
3
1,973,000
.731
1,442,263
PV of inflows
$4,289,444
PV of outflows
5,000,000
NPV
$(710,556)
Assumption Two:
Year
Cash Flow
PVIF @ 11%
Present Value
1
$2,093,000
.901
$1,885,793
2
2,632,000
.812
2,137,184
3
3,017,000
.731
2,205,427
PV of inflows
$6,228,404
PV of outflows
5,000,000
NPV
$1,228,404
Combined NPV:
Outcome
NPV
Probability
Assumption One
Assumption Two
Expected Outcome
–710,556
1,228,404
.5
.5
–335,278
614,202
$258,924
e. Yes – The combined expected value of the outcomes is positive.
f. Quite sensitive when that many gallons are used per year.
