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Principles of Managerial Finance 9th Edition

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Principles of Managerial Finance9th Edition

Chapter 10

Risk & Refinements

in Capital Budgeting

- Understand the importance of explicitly recognizing risk in the analysis of capital budgeting projects.
- Discuss breakeven cash flow, sensitivity and scenario analysis, and simulation as behavioral approaches for dealing with risk, and the unique risks facing multinational companies.
- Describe the two basic risk-adjustment techniques in terms of NPV and the procedures for applying the certainty equivalent (CE) approach.

Learning Objectives

- Review the use of risk-adjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs relative to CEs.
- Recognize the problem caused by unequal-lived mutually exclusive projects and the use of annualized net present values (ANPVs) to resolve it.
- Explain the objective of capital rationing and the two basic approaches to project selection under it.

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.

Behavioral Approaches for Dealing with Risk

Sensitivity Analysis

Treadwell Tire has a 10% cost of capital and is considering investing in one of two mutually exclusive projects A or B. Each project has a $10,000 initial cost and a useful life of 15 years.

As financial manager, you have provided pessimistic, most-likely, and optimistic estimates of the equal annual cash inflows for each project as shown in the following table.

Behavioral Approaches for Dealing with Risk

Sensitivity

Analysis

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

Simulation

Behavioral Approaches for Dealing with Risk

International Risk Consideration

- 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.

Behavioral Approaches for Dealing with Risk

International Risk Considerations

- 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.

Behavioral Approaches for Dealing with Risk

International Risk Considerations

- 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.

Risk-Adjustment Techniques

Certainty Equivalents

Bennett Company is currently evaluating two projects, A and B.

The firm’s cost of capital is 10% and the initial investment and operating cash flows are shown on the following slide.

Risk-Adjustment Techniques

Certainty Equivalents

Risk-Adjustment Techniques

Certainty Equivalents

Assume that it is determined that Project A is actually more risky than B.

To adjust for this risk, you decide to apply certainty equivalents (CEs) to the cash flows, where CEs represent the percentage of the cash flows that you would be satisfied to receive for certain rather than the original (possible) cash flows.

Risk-Adjustment Techniques

Certainty Equivalents

Risk-Adjustment Techniques

Certainty Equivalents

Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Bennett Company also wishes to apply the Risk-Adjusted Discount Rate (RADR) approach to determine whether to implement Project A or B.

To do so, Bennett has developed the following Risk Index to assist them in their endeavor.

Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Project B has been assigned a Risk Index Value of 1.0 (average risk) with a RADR of 11%, and Project A has been assigned a Risk Index Value of 1.6 (above average risk) with a RADR of 14%.

These rates are then applied as the discount rates to the two projects to determine NPV as shown on the following slide.

Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Risk-Adjustment Techniques

Risk-Adjusted Discount Rates

Risk-Adjustment Techniques

Portfolio Effects

- As noted in Chapter 6, 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

- 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.

Risk-Adjustment Techniques

CE Versus RADR in Practice

- In general, CEs are the theoretically preferred approach for project risk adjustment because they separately adjust for risk and time.
- The first eliminate risk from the cash flows and then discount the certain cash flows at a risk-free rate.
- RADRs on the other hand, have a major theoretical problem: they combine the risk and time adjustments in a single discount rate adjustment.

Risk-Adjustment Techniques

CE Versus RADR in Practice

- Because of the mathematics of discounting, the RADR approach implicitly assumes that risk is an increasing function of time.
- However, because of the complexity in developing CEs, RADRs are more often used in practice.
- More specifically, firms often establish a number of risk classes, with an RADR assigned to each.
- Projects are then placed in the appropriate risk class and the corresponding RADR is then applied.

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.

Capital Budgeting Refinements

Comparing Projects With Unequal Lives

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

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.

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.

Capital Budgeting Refinements

Comparing Projects With Unequal Lives

Annualized NPV (ANPV)

The ANPV approach converts the NPV of unequal-lived 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.

Capital Budgeting Refinements

Comparing Projects With Unequal Lives

Annualized NPV (ANPV)

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

NPVX = $11,277; NPVY = $19,013.

2. Calculate the ANPV for Projects X and Y.

ANPVX = $11,277/PVIFA10%,3 years = $4,534

ANPVY = $19,013/PVIFA10%,6 years = $4,366

3. Choose the project with the higher ANPV.

Pick project X.

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

Capital Rationing

Example

Capital Rationing

IRR Approach

Capital Rationing

IRR Approach

Assume the firm’s

cost of capital

is 10% and has

a maximum of

$250,000 available

for investment.

Ranking the

projects according

to IRR, the

optimal set of

projects for

Gould is B, C,

and E.

Capital Rationing

NPV Approach

If we ration

capital using the

NPV approach

and maintain the

rankings provided

by IRR, the total

PV of inflows and

NPV would be

$336,000 and

$106,000

respectively.

Capital Rationing

NPV Approach

However, if we

rank them such

that NPV is

maximized, then

we can use our

entire budget and

raise the PV of

inflows and NPV to

$357,000 and

$107,000

respectively.