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Chapter 12
Risk and Refinements in Capital Budgeting
Instructor’s Resources
Overview
Chapters 10 and 11 developed the major decision-making aspects of capital budgeting. Cash flows and budgeting
models have been integrated and discussed in providing the principles of capital budgeting. However, there are
more complex issues beyond those presented. Chapter 12 expands capital budgeting to consider risk with such
methods as scenario analysis and simulation. Capital budgeting techniques used to evaluate international projects,
as well as the special risks multinational companies face, are also presented. In addition, two basic risk-adjustment
techniques are examined: certainty equivalents and risk-adjusted discount rates. The chapter presents students with
several examples of the application of risk-based refinements when capital budgeting in their professional and
personal life.
Suggested Answer to Opener-in-Review Question
The chapter opener describes the expropriation of a Spanish company’s investment in an Argentinian oil
and gas company, as well as the decision by Chevron to undertake a major new investment in that country.
If you were a financial analyst at Chevron, how might you use scenario analysis to evaluate the risk of
entering into a joint venture in Argentina with YPF?
A 50% decrease in the share price meant that the market discounted YPF’s cash flows at a higher rate. As the
commentators note, Chevron must take into account risks related to oil and gas exploration and the political risks
of doing business in Argentina. As an analyst at Chevron, one must perform a scenario analysis assuming the worst
possible outcomes relating to risks associated with both exploration and political stability. This will help the
management understand the worst possible outcomes. Knowing this will help the management take steps to reduce
the probability of the worst outcome. For example, Chevron ensured that there were no price guarantees in the
YPF-Chevron agreement.
Answers to Review Questions
1. There is usually a signicant degree of uncertainty associated with capital budgeng projects. There is the usual
2. Risk, in terms of cash inows from a project, is the variability of expected cash ows, hence the expected returns, of the
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Chapter 12 Risk and Refinements in Capital Budgeting 254
3. a. Scenario analysis uses a number of possible inputs (cash inows) to assess their impact on the rm’s net present
b. Simulation is a statistically based approach using random numbers to simulate various cash flows
4. Answers will vary for queson because values are algorithmically generated in MyFinanceLab.
5. a. Mulnaonal companies (MNCs) must consider the e!ect of exchange rate risk, the risk that the exchange rate
b. Political risk, the risk that a foreign government’s actions will adversely affect the project, makes
c. Tax laws differ from country to country. Because only after-tax cash flows are relevant for capital budgeting
d. Transfer pricing refers to the prices charged by a corporation’s subsidiaries for goods and services traded
e. MNCs cannot evaluate international capital projects from only a financial perspective. The strategic
6. Risk-adjusted discount rates (RADRs) reect the return that must be earned on a given project in order to adequately
7. A rm whose stock is traded acvely in security markets generally does not increase in value through diversicaon.
8. RADRs are most o&en used in pracce for two reasons: (1) nancial decision makers prefer using rate of return-based
9. A comparison of NPVs of unequal-lived, mutually exclusive projects is inappropriate because it may lead to an incorrect
10. Real opons are opportunies embedded in real assets that are part of the capital budgeng process. Managers have
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Chapter 12 Risk and Refinements in Capital Budgeting 255
Abandonment—the opon to abandon or terminate a project prior to the end of its planned life.
11. Strategic NPV incorporates the value of the real opons associated with the project, while tradional NPV includes only
NPVstrategic NPVtraditional Value of real options
12. Capital raoning is a situaon where a rm has only a limited amount of funds available for capital investments. In
most cases, implementaon of the acceptable projects would require more capital than is available. Capital raoning is
13. The IRR approach and the NPV approach to capital raoning both involve ranking projects on the basis of IRRs. Using
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Chapter 12 Risk and Refinements in Capital Budgeting 256
Suggested Answer to Focus on Practice Box: The Monte Carlo Method:
The Forecast Is for Less Uncertainty
A Monte Carlo simulation program requires the user to first build an Excel spreadsheet model that captures
the input variables for the proposed project. What issues and what benefits can the user derive from this
process?
A good Monte Carlo simulation requires reasonably accurate estimates of data, including projected sales figures,
Suggested Answer to Focus on Ethics Box:
Ethics and the Cost of Capital
Is the ultimate goal of the firm, to maximize the wealth of the owners for whom the firm is being operated,
ethical?
Why might ethical companies benefit from a lower cost of capital than less ethical companies?
Answers to Warm-Up Exercises
E12-1. Sensivity analysis
Answer: Using the 12% cost of capital to discount all of the cash flows for each scenario to yield the following
NPVs, resulting in a NPV range of $19,109.78:
Pessimistic Most Likely Optimistic
E12-2. Using IRR as selecon criteria
Answer: The minimum amount of annual cash inflow needed to earn 8% is $11,270.54
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Chapter 12 Risk and Refinements in Capital Budgeting 257
E12-3. Risk-adjusted discount rates
Answer: Project Sourdough RADR 7.0%
Project Greek Salad RADR 8.0%
Yeastime should select Project Sourdough.
E12-4. ANPV
Answer: You may use a financial calculator to determine the IRR of each project. Choose the project with the
higher IRR.
Project M
Step 1: Find the NPV of the project
Step 2: Find the ANPV
Project N
Step 1: Find the NPV of the project
Step 2: Find the ANPV
E12-5. NPV proles
Answer:
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Chapter 12 Risk and Refinements in Capital Budgeting 258
Solutions to Problems
P12-1. Recognizing risk
LG 1; Basic
a. and b.
Project Risk Reason
A Low The cash flows from the project can be easily determined because this
B Medium The competitive nature of the industry makes it so that Caradine will need to
C Medium Because the firm is only preparing a proposal, their commitment at this time is
D High Although this purchase is in the industry in which Caradine normally
P12-2. Breakeven cash flows
LG 2; Intermediate
a. We need to find the 10-year annuity that has a PV (using a 9% discount rate) equal to $750,000, the
b. We need to find the 10-year annuity that has a PV (using a 12% discount rate) equal to $750,000, the
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Chapter 12 Risk and Refinements in Capital Budgeting 259
P12-3. Breakeven cash inflows and risk
LG 2; Intermediate
a. Standard Plant Custom Plant
b. Breakeven cash inflow:
Standard Plant Custom Plant
c. The standard plant has a breakeven cash flow of a little more than $8.3 million. It appears that this
d. There is a greater chance that the company will earn a negative NPV if they build the custom plant
e. If the goal is to minimize losses, the traditional plant appears to be the safer choice. However, the
P12-4. Basic scenario analysis
LG 2; Intermediate
a. Range A $1,800 $200 $1,600;Range B $1,100 $900 $200
b.
NPVs
Outcome Project A Project B
c. Although the “most likely” outcome is identical for Project A and B, the NPV range varies
d. Project selection would depend upon the risk disposition of the management. (A is more risky than B
P12-5. Scenario analysis
LG 2; Intermediate
a. Range – Soft drinks $1,000 $500 $500
b.
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Chapter 12 Risk and Refinements in Capital Budgeting 260
NPVs
Outcome Soft drinks Snack foods
Pessimistic $72.28 $542.17
c. Range Soft drinks $3,144.57 $72.28 $3,072.29
P12-6. Personal Finance: Impact of inflation on investments
LG 2; Easy
a. c.
Year
Investment
Cash Flows Current
NPV (a)
Higher
Inaon NPV
(b)
Lower
Inaon
NPV (c)
0
(40,000)
(40,000)
(40,000)
(40,000)
d. If inflation’s primary effect is to raise the discount rate, then the NPV will fall. Of course, for many
P12-7. Simulation
LG 2; Intermediate
a. Ogden Corporation could use a computer simulation to generate the respective profitability
b. The advantages to computer simulations include the decision maker’s ability to view a continuum of
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P12-8. Risk-adjusted discount rates—Basic
LG 4; Intermediate
a. Project E
N 4, I 15%, PMT $6,000
Project F
Project G
b. RADRE 0.10 (1.80 (0.15 0.10)) 0.19
c. Project E
N 4, I 19%, PMT $6,000
Project F
Same as in part a, $1,673.05
Project G
Rank Project
d. After adjusting the discount rate, even though all projects are still acceptable, the ranking changes.
Project G has the highest NPV and should be chosen.
P12-9. Risk-adjusted discount rates—Tabular
LG 4; Intermediate
a. Project A
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Chapter 12 Risk and Refinements in Capital Budgeting 262
Project B
b. Project A is preferable to Project B because the NPV of A is greater than the NPV of B.
P12-10. Personal Finance: Mutually exclusive investment and risk
LG 4; Intermediate
b. N 6, I 10.5%, PMT $3,800
c. Using NPV as her guide, Lara should select the second investment. It has a higher NPV.
d. The second investment is riskier. The higher required return implies a higher risk factor.
P12-11. Risk-adjusted rates of return using CAPM
LG 4; Challenge
a. rX 7% 1.2(12% 7%) 7% 6% 13%
b. The RADR approach prefers Project Y over Project X. The RADR approach combines the risk
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