978-0134476315 Chapter 12 Solution Manual Part 1

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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 inflowthe 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).