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Chapter 12
Risk and Refinements in Capital Budgeting
Instructor Resources
Chapter Overview
Chapters 10 and 11 introduced the building blocks of capital budgeting; Chapter 12 expands the
discussion to include complications that often arise in real-world project evaluation. The first
complication is risk. To this point, all firm projects were assumed equally risky. In actual practice,
however, project risk can vary considerably , and project acceptance can raise or lower the firm’s
overall risk. The chapter explores three “behavioral” approaches to integrating risk into capital
budgeting: breakeven analysis, scenario analysis, and simulation. After reviewing risks peculiar to
multinational operations, the discussion turns to risk-adjusted discount rates or RADR—a more
quantitative approach to incorporating risk differences into capital budgeting. The chapter concludes
by presenting several additional refinements in capital budgeting—assessing mutually exclusive
projects with unequal lives, incorporating real options into NPV analysis, and selecting projects under
capital rationing.
Suggested Answer to Opener-in-Review
The opener describes Venezuela’s expropriation of a General Motors factory. As a GM financial analyst,
how might you use scenario analysis to evaluate the risk of investing Venezuela?
Investing in Venezuela presents serious risks for GM. Adverse exchange-rate movements could eat into
profits, and corporate resources in the country are subject to expropriation. Venezuela has an extremely
unfavorable business climate to say the least—a recent Heritage Foundation ranking by degree of economic
well as NPVs for potential new projects in various economic/political states of the country (better, the same,
take steps to reduce firm exposure in the worst-case scenario.
Answers to Review Questions
12-1 Mutually exclusive projects are “either or” projects; pursuing one precludes pursuit of the
other. An example is a sports team choosing a location for a new stadium. Cash inflows
from different projects—mutually exclusive as well as independent ones—are generally
carries more risk than the average risk of the firm’s current assets, overall risk will rise.
12-2 Risk, in a capital-budgeting context, refers to the uncertainty surrounding the cash flows
that a project will generate. The breakeven cash inflowthe sequence of cash inflows that
makes project NPV equal zero (for a given project cost, project life, and project cost of
12-3 a. Scenario analysis provides insight into the sensitivity of project cash flows
and NPVs to a range of assumptions about economic and competitive conditions.
Specifically, NPVs are estimated for a range of scenarios (such as the pessimistic,
b. Simulation is a statistically based approach using probability distributions and random
dispersion of potential project outcomes.
12-4 Student answers will vary because values are algorithmically generated in MyFinanceLab.
12-5 a. Multinational companies (MNCs) must consider the effect of exchange
rate risk, the risk an adverse movement in exchange rates will reduce dollar cash flows
minimize this risk.
b. Political risk is the risk foreign-government actions (such as asset expropriation) will
adversely affect project NPVs. It is particularly tricky to manage because such actions are
c. Tax laws differ from country to country. Because only after-tax cash flows are relevant for
capital budgeting decisions, managers must account for all taxes paid to foreign governments
and consider the effect of any foreign tax payments on the firm’s U.S. tax liability.
d. Transfer pricing refers to the prices charged by a corporation’s subsidiaries for goods and
e. MNCs should not evaluate international projects from a narrow financial perspective; strategic
considerations often dominate. For example, a project with negative NPV in purely financial
12-6 Risk-adjusted discount rates (RADRs) reflect the return that must be earned on a given
project in order to adequately compensate the firm’s owners. The relationship between
RADRs and the capital asset pricing model (CAPM) is a purely theoretical concept. The
12-7 A firm whose stock is actively traded in deep security markets will generally not create
value for shareholders through diversification because they can cheaply diversify on their
own by adding other stocks with imperfectly correlated returns to their investment portfolios.
12-8 RADRs are most often used in practice for two reasons: (1) financial decision makers
prefer using rate of return-based criteria, and (2) they are easy to estimate and apply. In
12-9 A comparison of NPVs of unequal-lived, mutually exclusive projects is inappropriate
12-10 Real options are opportunities embedded in real assets that are part of the capital budgeting
process. Managers have the option of implementing some of these opportunities to alter the
cash flow and risk of a given project. Examples of real options include:
Abandonment: Option to abandon or terminate a project prior to the end of its planned
life.
12-11 Strategic NPV incorporates the value of the real options associated with the project, while
traditional NPV includes only the identifiable relevant cash flows. Using strategic NPV
12-12 Capital rationing occurs when a firm has only a limited amount of funds available for
capital investments. In theory, the firm will maximize shareholder value by accepting all
12-13 The IRR and NPV approaches to capital rationing both involve ranking projects on the
basis of IRRs. Using the IRR approach, a cut-off rate and a budget constraint are imposed.
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 build an Excel spreadsheet model capturing the
input variables for the proposed project. What issues and what benefits can the user derive from this
process?
As in any type of modeling, good output requires good input. Accordingly, good Monte Carlo simulation
starts with reasonably accurate data series for key variables, such as sales, production costs, associated
overhead, and marketing costs. Gathering historical data (and adjusting those data for changes in output or
the range of project NPVs quickly is the discipline Monte Carlo simulation brings to the capital-budgeting
process. Thinking hard about the relevant data and needed adjustments to the data will bring fresh insights
Suggested Answer to Focus on Ethics Box:
“Remain Calm—All Is Well”
Suppose you are a CEO and market turmoil from a shock unrelated to your company has your shareholders
nervous. Nonetheless, you believe everything will blow over, leaving the company unaffected. What is your
responsibility to shareholders?
Your foremost responsibility under all circumstances is to maximize shareholder wealth. So if you have
good reason to believe market turmoil will not affect factors relevant to your firm’s capital budget (like
Answers to Warm-Up Exercises
E12-1 Sensitivity analysis
Answer: Net present value, (NPV) = Present value of cash inflows – upfront project cost. The present
value of cash inflows may be found in Excel with the NPV command. Start by arranging cash
inflows in adjacent cells in a row or column. If, for example, cash inflows for the pessimistic
For all three cases:
E12-2 Using IRR as selection criteria
Answer: To find the minimum annual cash inflows in Excel, use the PMT command with this syntax:
=PMT(discount rate, number of periods,-cash outflow) = PMT(0.087,7,-59500) = $11,703.34.
E12-3 Risk-adjusted discount rates
Answer:
Project Pita
RADR 7.0% (for risk index of 6)
Number of periods 7
Project Grape Leaf
RADR 8.0% (for risk index of 8)
Number of periods 7
Culinary Cafe should select Project Pita as it has the higher NPV.
E12-4 ANPV
Answer: ANPV may be obtained in two steps: (1) find NPV for projects S and T, and (ii) find the annual
cash payment (annuity) that would generate those NPVs for the two projects over their
Both projects have positive NPVs. If the two were independent—that is, Fiftycent had the
option of accepting projects S and T– the firm would maximize shareholder wealth by
E12-5 NPV profiles
Answer: The Investment Opportunity Schedule (IOS) and cost of capital are sketched in the
figure below. The IRR decision rule dictates all projects with IRRs exceeding the cost of
capital should be accepted. Here, that would mean projects 4, 2, 5, and 1 (the firm would
Another issue is project rankings by NPV do not necessary correspond to rankings by
IRR. Project 1, for example, has the lowest IRR of the four acceptable projects (with no
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
expenditure is all outflows. The amount is also relatively small.
B Medium The nature of the industry will compel Spin Corp. to make this expenditure
exchange risk of operating in a foreign country add to the uncertainty.
Note: Other answers are possible depending on student assumptions. Too little information is given
about the firm and industry to establish a definitive risk analysis.
P12-2 Breakeven cash flows (LG 2; Intermediate)
a. Breakeven annual cash inflow is the cash inflow that, for the given project life, upfront cost,
and cost of capital, makes NPV equal zero. To find that cash inflow in Excel, use the PMT
in the Excel equation above:
P12-3 Breakeven cash inflows and risk (LG 2; Intermediate)
a. To find NPV for the standard and custom plants, first recognize NPV is given by:
Present value of cash inflows from project – Upfront project cost.
The present value of cash inflows for the standard plant may be found in Excel with the PV
command with this syntax:
b. The breakeven annual cash inflow is the cash inflow that, for the given life of the project,
upfront cost of the project, and cost of capital, makes project NPV equal zero. To find that
cash inflow in Excel, use the PMT command with the following syntax:
c. To find the probability cash flows will meet/exceed the breakeven level, sum the probabilities
for ranges greater than or equal to the specific range where breakeven cash flows lie for each
project:
d. Relative project risk can be evaluated in several ways. For example, cash flows for the
standard plant are distributed relatively tightly around the breakeven level; there is a 60%
chance annual cash flows will be $8 to $11 million and a 100% chance they will be $5 and $14
e. A firm wishing to minimize the likelihood of negative NPV should opt for the standard plant
because of the lower cumulative probability cash flows will fall below the breakeven level
P12-4 Basic scenario analysis (LG 2; Basic)
a. and b.
c. Both projects offer the same NPVs for the most likely scenario. If the three scenarios are
equally likely, then the average or expected NPV is the same for both projects too. But project
d. Recall from earlier chapters the typical investor is risk averse. As noted both projects have the
same NPV in the most likely scenario and the same average NPV. But in all scenarios, cash
P12-5 Scenario analysis (LG 2; Basic)
a. and b.
c. Both projects offer the same NPV in the most likely scenario. But the range of NPVs for the
snack food machines is 1.6 times larger than the range for soft drink machines. Moreover,
snack food machines have a much larger downside—in the pessimistic scenario the negative
NPV is 1.8 times larger than the negative NPV for soft drink machines.
d. The risk averse financial manager is, therefore, likely to opt for soft-drink machines.
P12-6 Scenario Analysis (LG 2; Intermediate)
a., b., c., and d.
To find NPVs for all gold prices, first calculate the present value of operating cash flows
associated with each price over five years at a discount rate of 11.2%. Then subtract the $67.8
project cost. Operating cash flows and project NPV are highlighted in bold font in the table
below. Internal rate of return (IRR) is the discount rate that makes project NPV equal zero for
a given discount rate, number of periods, and set of operating cash flows. IRR may be found in
Excel with the IRR command. Begin by arranging the cash outflow and inflows in adjacent
cells in a row or column with the outflow (project cost) expressed as a negative. If, for
example, the cash flows appear in column A, rows 1-6, proper syntax is: =IRR(A1:A6). The
IRR for each gold price is highlighted in bold font at the bottom of the table below.
e. The minimum acceptable price of gold is the price at which project NPV equals zero. This
price may be found in a few steps:
(i) Find the breakeven cash flows for the project in Excel with the PMT command and the
following syntax:
=PMT(discount rate,number of periods,-initial investment) = PMT(0.1120,5,-67800000)
= $18,437,051.
(ii) Next, work backwards from operating cash flow to annual revenue:
Operating Cash Flow $18,437,051
– Annual Depreciation –$13,560,000
= Net Profit After Taxes = $4,877,051
(1 – Tax Rate) (1 – 0.2104 = 0.7896]
=Net Profit Before Taxes $6,176,610
+ Depreciation + $13,560,000
+ Operating Expenses +$19,420,000
Annual Revenue (at which NPV = 0) = $39,156,610
(iii) Now, to find the gold price that makes NPV = 0, divide the annual revenue figure just
obtained by annual projected gold sales (174,000 expected sales over five years 5 years
= 34,800). So, the minimum acceptable gold price = $39,156,610 34,800 = $1,125.19
(rounded from $1,125.189932).
