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340
Integrated Case
Chapter 12: Cash Flow Estimation and Risk Analysis
E. (1) What three levels, or types, of project risk are normally considered?
Answer: [Show S12-16 through S12-19 here.] Here are the three types of
project risk:
1. Stand-alone risk is the project's total risk if it were operated
independently. Stand-alone risk ignores both the firm's
E. (2) Which type is most relevant?
Answer: [Show S12-20 here.] Because management's primary goal is
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E. (3) Which type is easiest to measure?
Answer: [Show S12-21 here.] By far the easiest type of risk to measure is a
project's stand-alone risk. Thus, firms often focus primarily on this
E. (4) Are the three types of risk generally highly correlated?
Answer: [Show S12-22 here.] Because most projects that a firm undertakes
F. (1) What is sensitivity analysis?
Answer: [Show S12-23 here.] Sensitivity analysis measures the effect of
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Chapter 12: Cash Flow Estimation and Risk Analysis
F. (2) How would you perform a sensitivity analysis on the unit sales,
salvage value, and WACC for the project? Assume that each of
these variables deviates from its base-case, or expected, value by
plus or minus 10%, 20%, and 30%. Explain how you would
calculate the NPV, IRR, MIRR, and payback for each case; but don’t
do the analysis unless your instructor asks you to.
Answer: The base case value for unit sales was 100; therefore, if you were to
assume that this value deviated by plus and minus 10%, 20%, and
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70
60
50
40
30
NPV
(Thousands of Dollars)
Unit Sales
Sensitivity Graph
⚫
⚫
⚫
⚫
⚫
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The sensitivity data are given here in tabular form (in thousands of
dollars):
Change from Resulting NPV after the Indicated Change in:
Base Level Unit Sales Salvage Value WACC
-30% ($36.4) $11.9 $34.1
F. (3) What is the primary weakness of sensitivity analysis? What are its
primary advantages?
Answer: [Show S12-24 here.] The two primary disadvantages of sensitivity
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345
G. Unrelated to the lemon juice project, Allied is upgrading its plant
and must choose between two machines that are mutually
exclusive. The plant is highly successful, so whichever machine is
chosen will be repurchased after its useful life is over. Both
machines cost $50,000; however, Machine A provides after-tax
savings of $17,500 per year for 4 years, while Machine B provides
after-tax savings of $34,000 in Year 1 and $27,500 in Year 2.
(1) Using the replacement chain method, what is the NPV of the better
machine?
Answer: [Show S12-25 through S12-27 here.]
Machine A: 0 1 2 3 4
10%
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Chapter 12: Cash Flow Estimation and Risk Analysis
G. (2) Using the EAA method, what is the EAA of the better machine?
Answer: [Show S12-28 here.]
Machine A:
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H. Assume that inflation is expected to average 5% over the next 4
years and that this expectation is reflected in the WACC. Moreover,
inflation is expected to increase revenues and variable costs by this
same 5%. Does it appear that inflation has been dealt with
properly in the initial analysis to this point? If not, what should be
done and how would the required adjustment affect the decision?
Answer: [Show S12-29 through S12-31 here.] It is apparent from the data
in the previous table that inflation has not been reflected in the
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Table IC 12.2. Allied’s Lemon Juice Project Considering 5% Inflation
(in Thousands)
Inputs: Price: $2.00 WACC: 10% Infl: 5.0%
VC rate: 60.0% T-rate: 40%
End of Year: 0 1 2 3 4
Investment Outlays:
CAPEX ($240)
NOWC (20)
Project Operating Cash Flows:
Unit sales (thousands) 100 100 100 100
Terminal Cash Flows:
Salvage value 25.0
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349
I. The expected cash flows, considering inflation (in thousands of
dollars), are given in Table IC 12.2. Allied’s WACC is 10%. Assume
that you are confident about the estimates of all the variables that
affect the cash flows except unit sales. If product acceptance is poor,
sales would be only 75,000 units a year, while a strong consumer
response would produce sales of 125,000 units. In either case, cash
costs would still amount to 60% of revenues. You believe that there
is a 25% chance of poor acceptance, a 25% chance of excellent
acceptance, and a 50% chance of average acceptance (the base
case). Provide numbers only if you are using a computer model.
(1) What is the worst-case NPV? The best-case NPV?
Answer: [Show S12-32 and S12-33 here.] We used a spreadsheet model to
develop the scenarios (in thousands of dollars), which are
I. (2) Use the worst-case, most likely case (or base-case), and best-case
NPVs with their probabilities of occurrence, to find the project's
expected NPV, standard deviation, and coefficient of variation.
Answer: [Show S12-34 here.] The expected NPV is $14,968 (rounded to the
nearest thousand below).
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J. Assume that Allied's average project has a coefficient of variation
(CV) in the range of 1.25 to 1.75. Would the lemon juice project be
classified as high risk, average risk, or low risk? What type of risk is
being measured here?
Answer: [Show S12-35 here.] The project has a CV of 2.0, which is much
K. Based on common sense, how highly correlated do you think the
project would be with the firm's other assets? (Give a correlation
coefficient or range of coefficients, based on your judgment.)
Answer: [Show S12-36 here.] It is reasonable to assume that if the
economy is strong and people are buying a lot of lemon juice, then
L. How would the correlation coefficient and the previously calculated
combine to affect the project's contribution to corporate, or
within-firm, risk? Explain.
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Answer: [Show S12-37 here.] If the project's cash flows are likely to be
highly correlated with the firm's aggregate cash flows, which is
M. Based on your judgment, what do you think the project's
correlation coefficient would be with respect to the general
economy and thus with returns on "the market"? How would
correlation with the economy affect the project’s market risk?
Answer: In all likelihood, this project would have a positive correlation with
returns on other assets in the economy, and specifically with the
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N. Allied typically adds or subtracts 3% to its WACC to adjust for risk.
After adjusting for risk, should the lemon juice project be accepted?
Should any subjective risk factors be considered before the final
decision is made? Explain.
Answer: [Show S12-38 and S12-39 here.] Since the project is judged to
have above-average risk, its differential risk-adjusted, or project,
