chapter 9 capital budgeting techniques: certainty and risk

Chapter 9

Capital Budgeting Techniques: Certainty and Risk

Copyright © 2006 Pearson Addison-Wesley. All rights reserved. 9-2

Learning Goals

1. Understand the role of capital budgeting techniques in the capital budgeting process.

2. Calculate, interpret, and evaluate the payback period.

3. Calculate, interpret, and evaluate the net present value (NPV).


Learning Goals (cont.)

4. Calculate, interpret, and evaluate the internal rate of return (IRR).

5. Use net present value profiles to compare NPV and IRR techniques.

6. Discuss NPV and IRR in terms of conflicting rankings and the theoretical and practical strengths of each approach.



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

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

9. Discuss the unique risks that multinational companies face.



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

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

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


Bennett Company is a medium sized metal fabricator

that is currently contemplating two projects: Project A

requires an initial investment of $42,000, project B an

initial investment of $45,000. The relevant operating

cash flows for the two projects are presented in Table

9.1 and depicted on the time lines in Figure 9.1.

Capital Budgeting Techniques

• Chapter Problem


Capital Budgeting Techniques (cont.)


Payback Period

• The payback method simply measures how long (in years and/or months) it takes to recover the initial investment.

• The maximum acceptable payback period is determined by management.

• If the payback period is less than the maximum acceptable payback period, accept the project.

• If the payback period is greater than the maximum acceptable payback period, reject the project.


Net Present Value (NPV)

• Net Present Value (NPV): Net Present Value is found by subtracting the present value of the after-tax outflows from the present value of the after-tax inflows.


Decision Criteria

If NPV > 0, accept the project

If NPV < 0, reject the project

If NPV = 0, technically indifferent

Net Present Value (NPV) (cont.)

• Net Present Value (NPV): Net Present Value is found by subtracting the present value of the after-tax outflows from the present value of the after-tax inflows.


Using the Bennett Company data from Table 9.1,

assume the firm has a 10% cost of capital. Based on the

given cash flows and cost of capital (required return), the

NPV can be calculated as shown in Figure 9.2



Internal Rate of Return (IRR)

• The Internal Rate of Return (IRR) is the discount rate that will equate the present value of the outflows with the present value of the inflows.

• The IRR is the project’s intrinsic rate of return.


Decision Criteria

If IRR > k, accept the project

If IRR < k, reject the project

If IRR = k, technically indifferent

Internal Rate of Return (IRR) (cont.)

• The Internal Rate of Return (IRR) is the discount rate that will equate the present value of the outflows with the present value of the inflows.

• The IRR is the project’s intrinsic rate of return.


To prepare NPV profiles for Bennett Company’s

projects A and B, the first step is to develop a number

of discount rate-NPV coordinates and then graph

them as shown in the following table and figure.

Net Present Value Profiles

• NPV Profiles are graphs that depict project NPVs for various discount rates and provide an excellent means of making comparisons between projects.


Net Present Value Profiles (cont.)


Conflicting Rankings

• Conflicting rankings between two or more projects using NPV and IRR sometimes occurs because of differences in the timing and magnitude of cash flows.

• This underlying cause of conflicting rankings is the implicit assumption concerning the reinvestment of intermediate cash inflows—cash inflows received prior to the termination of the project.

• NPV assumes intermediate cash flows are reinvested at the cost of capital, while IRR assumes that they are reinvested at the IRR.


A project requiring a $170,000 initial investment is

expected to provide cash inflows of $52,000, $78,000

and $100,000. The NPV of the project at 10% is

$16,867 and it’s IRR is 15%. Table 9.5 on the following

slide demonstrates the calculation of the project’s future

value at the end of it’s 3-year life, assuming both a 10%

(cost of capital) and 15% (IRR) interest rate.

Conflicting Rankings (cont.)


If the future value in each case in Table 9.5 were

viewed as the return received 3 years from today from

the $170,000 investment, then the cash flows would be

those given in Table 9.6 on the following slide.



Bennett Company’s projects A and B were found to have

conflicting rankings at the firm’s 10% cost of capital as

depicted in Table 9.4. If we review the project’s cash inflow

pattern as presented in Table 9.1 and Figure 9.1, we see

that although the projects require similar investments, they

have dissimilar cash flow patterns. Table 9.7 on the

following slide indicates that project B, which has higher

early-year cash inflows than project A, would be preferred

over project A at higher discount rates.



Which Approach is Better?

• On a purely theoretical basis, NPV is the better approach because:– NPV assumes that intermediate cash flows are

reinvested at the cost of capital whereas IRR assumes they are reinvested at the IRR,

– Certain mathematical properties may cause a project with non-conventional cash flows to have zero or more than one real IRR.

• Despite its theoretical superiority, however, financial managers prefer to use the IRR because of the preference for rates of return.


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


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.)


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

chapter 9 capital budgeting techniques: certainty and risk

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