Chapter 10 Risk and Refinements in Capital Budgeting.

Chapter 10

Risk and Refinements in Capital Budgeting

Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 10-2

Learning Goals

1. Understand the importance of recognizing risk in the analysis of capital budgeting projects.

2. Discuss breakeven cash flow, sensitivity and scenario analysis, and simulation as behavioral approaches for dealing with risk.

3. Discuss the unique risks that multinational companies face.


Learning Goals (cont.)

4. Describe the determination and use of risk-adjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs.

5. Select the best of a group of mutually exclusive projects using annualized net present values (ANPVs).

6. Explain the role of real options and the objective and procedures for selecting projects under capital rationing.


Introduction to Risk in Capital Budgeting

• Thus far in our exploration of capital budgeting, all projects were assumed to be equally risky.

• The acceptance of any project would not alter the firm’s overall risk.

• In actuality, these situations are rare—project cash flows typically have different levels of risk and the acceptance of a project does affect the firm’s overall risk.

• This chapter will focus on how to handle risk.


Introduction to Risk in Capital Budgeting (cont.)


Behavioral Approaches for Dealing with Risk

• In the context of the capital budgeting projects discussed in this chapter, risk results almost entirely from the uncertainty about future cash inflows, because the initial cash outflow is generally known.

• These risks result from a variety of factors including uncertainty about future revenues, expenditures and taxes.

• Therefore, to asses the risk of a potential project, the analyst needs to evaluate the riskiness of the cash inflows.


Treadwell Tire, a tire retailer with a 10% cost of capital, is considering investing in either of two mutually exclusive projects, A and B. Each requires a $10,000 initial investment, and both are expected to provide equal annual cash inflows over their 15-year lives. For either project to be acceptable, NPV must be greater than zero. We can solve for CF using the following:

Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows


Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows (cont.)


Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows (cont.)


The risk of Treadwell Tire Company’s investments can be

evaluated using sensitivity analysis as shown in Table 10.2

on the following slide. For this example, assume that the

financial manager made pessimistic, most likely, and

optimistic estimates of the cash inflows for each project.

Behavioral Approaches for Dealing with Risk: Sensitivity Analysis


Behavioral Approaches for Dealing with Risk: Sensitivity Analysis (cont.)


Behavioral Approaches for Dealing with Risk: Scenario Analysis

• Scenario analysis is a behavioral approach similar to sensitivity analysis but is broader in scope.

• This method evaluates the impact on the firm’s return of simultaneous changes in a number of variables, such as cash inflows, outflows, and the cost of capital.

• NPV is then calculated under each different set of variable assumptions.


Behavioral Approaches for Dealing with Risk: Simulation

• Simulation is a statistically-based behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes.

• Figure 10.1 presents a flowchart of the simulation of the NPV of a project.

• The use of computers has made the use of simulation economically feasible, and the resulting output provides an excellent basis for decision-making.


Behavioral Approaches for Dealing with Risk


International Risk Considerations

• Exchange rate risk is the risk that an unexpected change in the exchange rate will reduce NPV of a project’s cash flows.

• In the short term, much of this risk can be hedged by using financial instruments such as foreign currency futures and options.

• Long-term exchange rate risk can best be minimized by financing the project in whole or in part in the local currency.


International Risk Considerations (cont.)

• Political risk is much harder to protect against once a project is implemented.

• A foreign government can block repatriation of profits and even seize the firm’s assets.

• Accounting for these risks can be accomplished by adjusting the rate used to discount cash flows—or better—by adjusting the project’s cash flows.


• Since a great deal of cross-border trade among MNCs takes place between subsidiaries, it is also important to determine the net incremental impact of a project’s cash flows overall.

• As a result, it is important to approach international capital projects from a strategic viewpoint rather than from a strictly financial perspective.

International Risk Considerations (cont.)


Risk-Adjusted Discount Rates

• Risk-adjusted discount rates are rates of return that must be earned on given projects to compensate the firm’s owners adequately—that is, to maintain or improve the firm’s share price.

• The higher the risk of a project, the higher the RADR—and thus the lower a project’s NPV.


Risk-Adjusted Discount Rates: Review of CAPM


Risk-Adjusted Discount Rates: Using CAPM to Find RADRs


Bennett Company wishes to apply the Risk-Adjusted

Discount Rate (RADR) approach to determine whether to

implement Project A or B. In addition to the data

presented earlier, Bennett’s management assigned a

“risk index” of 1.6 to project A and 1.0 to project B as

indicated in the following table. The required rates of

return associated with these indexes are then applied as

the discount rates to the two projects to determine NPV.

Risk-Adjusted Discount Rates: Applying RADRs


Risk-Adjusted Discount Rates: Applying RADRs (cont.)








Risk-Adjusted Discount Rates: RADRs in Practice


Risk-Adjustment Techniques: Portfolio Effects

• As noted earlier, individual investors must hold diversified portfolios because they are not rewarded for assuming diversifiable risk.

• Because business firms can be viewed as portfolios of assets, it would seem that it is also important that they too hold diversified portfolios.

• Surprisingly, however, empirical evidence suggests that firm value is not affected by diversification.

• In other words, diversification is not normally rewarded and therefore is generally not necessary.


Risk-Adjustment Techniques: Portfolio Effects (cont.)

• It turns out that firms are not rewarded for diversification because investors can do so themselves.

• An investor can diversify more readily, easily, and costlessly simply by holding portfolios of stocks.


Capital Budgeting Refinements: Comparing Projects With Unequal Lives

• If projects are independent, comparing projects with unequal lives is not critical.

• But when unequal-lived projects are mutually exclusive, the impact of differing lives must be considered because they do not provide service over comparable time periods.

• This is particularly important when continuing service is needed from the projects under consideration.


The AT Company, a regional cable-TV firm, is evaluating two projects, X and Y. The projects’ cash flows and resulting NPVs at a cost of capital of 10% is given below.

Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)











Ignoring the difference in their useful lives, both projects are

acceptable (have positive NPVs). Furthermore, if the projects

were mutually exclusive, project Y would be preferred over

project X. However, it is important to recognize that at the end

of its 3 year life, project Y must be replaced, or renewed.

Although a number of approaches are available for

dealing with unequal lives, we will present the most

efficient technique -- the annualized NPV approach.



The ANPV approach converts the NPV of unequal-lived mutually exclusive projects into an equivalent (in NPV terms) annual amount that can be used to select the best project.

1. Calculate the NPV of each project over its live using the appropriate cost of capital.

2. Divide the NPV of each positive NPV project by the PVIFA at the given cost of capital and the project’s live

to get the ANPV for each project.

3. Select the project with the highest ANPV.

Annualized NPV (ANPV)



1. Calculate the NPV for projects X and Y at 10%.

NPVX = $11,248; NPVY = $18,985.

2. Calculate the ANPV for Projects X and Y.

ANPVX = $11,248/PVIFA10%,3 years = $4,523

ANPVY = $18,985/PVIFA10%,6 years = $4,359

3. Choose the project with the higher ANPV.

Pick project X.










Recognizing Real Options

• Real options are opportunities that are embedded in capital projects that enable managers to alter their cash flows and risk in a way that affects project acceptability (NPV).

• Real options are also sometimes referred to as strategic options.

• Some of the more common types of real options are described in the table on the following slide.


Recognizing Real Options (cont.)


Assume that a strategic analysis of Bennett Company’s projects A and B (see Table 10.1) finds no real options embedded in Project A but two real options embedded in B:

1. During it’s first two years, B would have downtime that results in unused production capacity that could be used to perform contract manufacturing;

2. Project B’s computerized control system could control two other machines, thereby reducing labor costs.

NPVstrategic = NPVtraditional + Value of Real Options



Bennett’s management estimated the NPV of the contract manufacturing option to be $1,500 and the NPV of the computer control sharing option to be $2,000. Furthermore, they felt there was a 60% chance that the contract manufacturing option would be exercised and a 30% chance that the computer control sharing option would be exercised.

Value of Real Options for B = (60% x $1,500) + (30% x $2,000)

$900 + $600 = $1,500

NPVstrategic = $10,924 + $1,500 = $12,424

NPVA = $12,424; NPVB = $11,071; Now choose A over B.



Capital Rationing

• Firm’s often operate under conditions of capital rationing—they have more acceptable independent projects than they can fund.

• In theory, capital rationing should not exist—firms should accept all projects that have positive NPVs.

• However, research has found that management internally imposes capital expenditure constraints to avoid what it deems to be “excessive” levels of new financing, particularly debt.

• Thus, the objective of capital rationing is to select the group of projects within the firm’s budget that provides the highest overall NPV or IRR.


Tate Company, a fast growing plastics company with a

cost of capital of 10%, is confronted with six projects

competing for its fixed budget of $250,000. The initial

investment and IRR for each project are shown below:

Capital Rationing


Capital Rationing: IRR Approach


Capital Rationing: NPV Approach

Chapter 10 Risk and Refinements in Capital Budgeting.

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