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9

Why This Chapter Matters To You

Accounting: You need to understand cap-

ital budgeting techniques in order to

develop good estimates of the relevant

cash flows associated with a proposed

capital expenditure and to appreciate how

Capital risk may affect the variability of cash

flows.

Information systems: You need to under-

Budgeting stand capital budgeting techniques,

including how risk is measured in those

techniques, in order to design decision

Techniques: modules that help reduce the amount of

work required in analyzing proposed capi-

tal projects.

Certainty and Risk Management: You need to understand

capital budgeting techniques in order to

understand the decision criteria used to

accept or reject proposed projects; how to

apply capital budgeting techniques when

capital must be rationed; and behavioral

LEARNING GOALS and risk-adjustment approaches for deal-

ing with risk, including international risk.

Calculate, interpret, and evaluate the

LG1

payback period. Marketing: You need to understand capi-

tal budgeting techniques in order to

Apply net present value (NPV) and

LG2

understand how proposals for new prod-

internal rate of return (IRR) to relevant

ucts and expansion of existing product

cash flows to choose acceptable

capital expenditures. lines will be evaluated by the firmâ€™s deci-

sion makers and how risk of proposed pro-

Use net present value profiles to

LG3 jects is treated in capital budgeting.

compare the NPV and IRR techniques

in light of conflicting rankings. Operations: You need to understand capi-

tal budgeting techniques in order to

Discuss two additional considerations

LG4

understand how proposals for the acquisi-

in capital budgetingâ€”recognizing

tion of new equipment and plants will be

real options and choosing projects

evaluated by the firmâ€™s decision makers,

under capital rationing.

especially when capital must be rationed.

Recognize sensitivity analysis and

LG5

scenario analysis, decision trees, and

simulation as behavioral approaches

for dealing with project risk, and the

unique risks that multinational

companies face.

Understand the calculation and

LG6

practical aspects of risk-adjusted

discount rates (RADRs).

340

341

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

F irms use the relevant cash flows to make decisions about proposed capital

expenditures. These decisions can be expressed in the form of project accep-

tance or rejection or of project rankings. A number of techniques are used in such

decision making, some more sophisticated than others. These techniques are the

topic of this chapter, wherein we describe the assumptions on which capital bud-

geting techniques are based, show how they are used in both certain and risky sit-

uations, and evaluate their strengths and weaknesses.

Capital Budgeting Techniques

LG1 LG2

When firms have developed relevant cash flows, as demonstrated in Chapter 8,

they analyze them to assess whether a project is acceptable or to rank projects. A

number of techniques are available for performing such analyses. The preferred

approaches integrate time value procedures, risk and return considerations, and

valuation concepts to select capital expenditures that are consistent with the

firmâ€™s goal of maximizing ownersâ€™ wealth. This section and the following one

focus on the use of these techniques in an environment of certainty. Later in the

chapter, we will look at capital budgeting under uncertain circumstances.

We will use one basic problem to illustrate all the techniques described in this

chapter. The problem concerns Bennett Company, a medium-sized metal fabrica-

tor that is currently contemplating two projects: Project A requires an initial

investment of $42,000, project B an initial investment of $45,000. The projected

relevant operating cash inflows for the two projects are presented in Table 9.1

and depicted on the time lines in Figure 9.1.1 The projects exhibit conventional

TABLE 9.1 Capital Expenditure

Data for Bennett

Company

Project A Project B

Initial investment $42,000 $45,000

Year Operating cash inflows

1 $14,000 $28,000

2 14,000 12,000

3 14,000 10,000

4 14,000 10,000

5 14,000 10,000

1. For simplification, these 5-year-lived projects with 5 years of cash inflows are used throughout this chapter. Proj-

ects with usable lives equal to the number of years of cash inflows are also included in the end-of-chapter problems.

Recall from Chapter 8 that under current tax law, MACRS depreciation results in n 1 years of depreciation for an

n-year class asset. This means that projects will commonly have at least 1 year of cash flow beyond their recovery

period. In actual practice, the usable lives of projects (and the associated cash inflows) may differ significantly from

their depreciable lives. Generally, under MACRS, usable lives are longer than depreciable lives.

342 PART 3 Long-Term Investment Decisions

FIGURE 9.1

Project A

$14,000 $14,000 $14,000 $14,000 $14,000

Bennett Companyâ€™s

Projects A and B

Time lines depicting the

conventional cash flows of

projects A and B 0

1 2 3 4 5

$42,000

End of Year

Project B

$28,000 $12,000 $10,000 $10,000 $10,000

0

1 2 3 4 5

$45,000

End of Year

cash flow patterns, which are assumed throughout the text. In addition, we ini-

tially assume that all projectsâ€™ cash flows have the same level of risk, that projects

being compared have equal usable lives, and that the firm has unlimited funds.

Because very few decisions are actually made under such conditions, some of

these simplifying assumptions are relaxed in later sections of this chapter. Here

we begin with a look at the three most popular capital budgeting techniques: pay-

back period, net present value, and internal rate of return.2

Payback Period

payback period

The amount of time required for a

Payback periods are commonly used to evaluate proposed investments. The

firm to recover its initial invest-

payback period is the amount of time required for the firm to recover its initial

ment in a project, as calculated

investment in a project, as calculated from cash inflows. In the case of an annuity,

from cash inflows.

2. Two other, closely related techniques that are sometimes used to evaluate capital budgeting projects are the aver-

age (or accounting) rate of return (ARR) and the profitability index (PI). The ARR is an unsophisticated technique

that is calculated by dividing a projectâ€™s average profits after taxes by its average investment. Because it fails to con-

sider cash flows and the time value of money, it is ignored here. The PI, sometimes called the benefitâ€“cost ratio, is

calculated by dividing the present value of cash inflows by the initial investment. This technique, which does con-

sider the time value of money, is sometimes used as a starting point in the selection of projects under capital

rationing; the more popular NPV and IRR methods are discussed here.

343

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

the payback period can be found by dividing the initial investment by the annual

cash inflow. For a mixed stream of cash inflows, the yearly cash inflows must be

accumulated until the initial investment is recovered. Although popular, the pay-

back period is generally viewed as an unsophisticated capital budgeting tech-

nique, because it does not explicitly consider the time value of money.

The Decision Criteria

When the payback period is used to make acceptâ€“reject decisions, the decision

criteria are as follows:

â€˘ If the payback period is less than the maximum acceptable payback period,

accept the project.

â€˘ If the payback period is greater than the maximum acceptable payback

period, reject the project.

The length of the maximum acceptable payback period is determined by manage-

ment. This value is set subjectively on the basis of a number of factors, including

the type of project (expansion, replacement, renewal), the perceived risk of the

project, and the perceived relationship between the payback period and the share

value. It is simply a value that management feels, on average, will result in value-

creating investment decisions.

We can calculate the payback period for Bennett Companyâ€™s projects A and B

EXAMPLE

using the data in Table 9.1. For project A, which is an annuity, the payback

period is 3.0 years ($42,000 initial investment $14,000 annual cash inflow).

Because project B generates a mixed stream of cash inflows, the calculation of its

payback period is not as clear-cut. In year 1, the firm will recover $28,000 of its

$45,000 initial investment. By the end of year 2, $40,000 ($28,000 from year 1

$12,000 from year 2) will have been recovered. At the end of year 3, $50,000 will

have been recovered. Only 50% of the year 3 cash inflow of $10,000 is needed to

complete the payback of the initial $45,000. The payback period for project B is

therefore 2.5 years (2 years 50% of year 3).

If Bennettâ€™s maximum acceptable payback period were 2.75 years, project A

would be rejected and project B would be accepted. If the maximum payback were

2.25 years, both projects would be rejected. If the projects were being ranked, B

would be preferred over A, because it has a shorter payback period.

Pros and Cons of Payback Periods

The payback period is widely used by large firms to evaluate small projects and

by small firms to evaluate most projects. Its popularity results from its computa-

tional simplicity and intuitive appeal. It is also appealing in that it considers cash

flows rather than accounting profits. By measuring how quickly the firm recovers

its initial investment, the payback period also gives implicit consideration to the

timing of cash flows and therefore to the time value of money. Because it can be

viewed as a measure of risk exposure, many firms use the payback period as a

decision criterion or as a supplement to other decision techniques. The longer the

344 PART 3 Long-Term Investment Decisions

firm must wait to recover its invested funds, the greater the possibility of a

calamity. Therefore, the shorter the payback period, the lower the firmâ€™s expo-

sure to such risk.

The major weakness of the payback period is that the appropriate payback

period is merely a subjectively determined number. It cannot be specified in light

of the wealth maximization goal because it is not based on discounting cash flows

to determine whether they add to the firmâ€™s value. Instead, the appropriate pay-

back period is simply the maximum acceptable period of time over which man-

agement decides that a projectâ€™s cash flows must break even (that is, just equal

the initial investment). A second weakness is that this approach fails to take fully

into account the time factor in the value of money.3 This weakness can be illus-

trated by an example.

DeYarman Enterprises, a small medical appliance manufacturer, is considering

EXAMPLE

two mutually exclusive projects, which it has named projects Gold and Silver.

The firm uses only the payback period to choose projects. The relevant cash flows

and payback period for each project are given in Table 9.2. Both projects have 3-

year payback periods, which would suggest that they are equally desirable. But

comparison of the pattern of cash inflows over the first 3 years shows that more

of the $50,000 initial investment in project Silver is recovered sooner than is

recovered for project Gold. For example, in year 1, $40,000 of the $50,000

invested in project Silver is recovered, whereas only $5,000 of the $50,000 invest-

ment in project Gold is recovered. Given the time value of money, project Silver

would clearly be preferred over project Gold, in spite of the fact that they both

have identical 3-year payback periods. The payback approach does not fully

TABLE 9.2 Relevant Cash Flows and

Payback Periods for

DeYarman Enterprisesâ€™

Projects

Project Gold Project Silver

Initial investment $50,000 $50,000

Year Operating cash inflows

1 $ 5,000 $40,000

2 5,000 2,000

3 40,000 8,000

4 10,000 10,000

5 10,000 10,000

Payback period 3 years 3 years

3. To consider differences in timing explicitly in applying the payback method, the present value payback period is

sometimes used. It is found by first calculating the present value of the cash inflows at the appropriate discount rate

and then finding the payback period by using the present value of the cash inflows.

345

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

TABLE 9.3 Calculation of the

Payback Period for

Rashid Companyâ€™s

Two Alternative

Investment Projects

Project X Project Y

Initial investment $10,000 $10,000

Year Operating cash inflows

1 $5,000 $3,000

2 5,000 4,000

3 1,000 3,000

4 100 4,000

5 100 3,000

Payback period 2 years 3 years

account for the time value of money, which, if recognized, would cause project

Silver to be preferred over project Gold.

A third weakness of payback is its failure to recognize cash flows that occur

after the payback period.

Rashid Company, a software developer, has two investment opportunities, X and

EXAMPLE

Y. Data for X and Y are given in Table 9.3. The payback period for project X is 2

years; for project Y it is 3 years. Strict adherence to the payback approach sug-

gests that project X is preferable to project Y. However, if we look beyond the

payback period, we see that project X returns only an additional $1,200 ($1,000

in year 3 $100 in year 4 $100 in year 5), whereas project Y returns an addi-

tional $7,000 ($4,000 in year 4 $3,000 in year 5). On the basis of this informa-

tion, project Y appears preferable to X. The payback approach ignored the cash

inflows occurring after the end of the payback period.4

Net Present Value (NPV)

Because net present value (NPV) gives explicit consideration to the time value of

money, it is considered a sophisticated capital budgeting technique. All such tech-

niques in one way or another discount the firmâ€™s cash flows at a specified rate.

4. To get around this weakness, some analysts add a desired dollar return to the initial investment and then calculate

the payback period for the increased amount. For example, if the analyst wished to pay back the initial investment

plus 20% for projects X and Y in Table 9.3, the amount to be recovered would be $12,000 [$10,000 (0.20

$10,000)]. For project X, the payback period would be infinite because the $12,000 would never be recovered; for

project Y, the payback period would be 3.50 years [3 years ($2,000 $4,000) years]. Clearly, project Y would be

preferred.

346 PART 3 Long-Term Investment Decisions

This rateâ€”often called the discount rate, required return, cost of capital, or

opportunity costâ€”is the minimum return that must be earned on a project to

leave the firmâ€™s market value unchanged. In this chapter, we take this rate as a

â€śgiven.â€ť In Chapter 10 we will explore how it is calculated.

The net present value (NPV) is found by subtracting a projectâ€™s initial invest-

net present value (NPV)

A sophisticated capital budget- ment (CF0) from the present value of its cash inflows (CFt) discounted at a rate

ing technique; found by subtract-

equal to the firmâ€™s cost of capital (k).

ing a projectâ€™s initial investment

from the present value of its cash NPV Present value of cash inflows Initial investment

inflows discounted at a rate n

CFt

equal to the firmâ€™s cost of capital. NPV CF0 (9.1)

t 1 (1 k)t

n

(CFt PVIFk,t) CF0 (9.1a)

t1

When NPV is used, both inflows and outflows are measured in terms of present

dollars. Because we are dealing only with investments that have conventional

cash flow patterns, the initial investment is automatically stated in terms of

todayâ€™s dollars. If it were not, the present value of a project would be found by

subtracting the present value of outflows from the present value of inflows.

The Decision Criteria

When NPV is used to make acceptâ€“reject decisions, the decision criteria are as

follows:

â€˘ If the NPV is greater than $0, accept the project.

â€˘ If the NPV is less than $0, reject the project.

If the NPV is greater than $0, the firm will earn a return greater than its cost of

capital. Such action should enhance the market value of the firm and therefore

the wealth of its owners.

We can illustrate the net present value (NPV) approach by using Bennett

EXAMPLE

Company data presented in Table 9.1. If the firm has a 10% cost of capital, the

net present values for projects A (an annuity) and B (a mixed stream) can be cal-

culated as shown on the time lines in Figure 9.2. These

calculations result in net present values for projects A

Project A Project B and B of $11,071 and $10,924, respectively. Both proj-

ects are acceptable, because the net present value of each

Input Function

Input Function

is greater than $0. If the projects were being ranked,

45000

42000 CF0

CF0

however, project A would be considered superior to B,

28000 CF1

14000 CF1

because it has a higher net present value ($11,071 versus

CF2

12000

5 N

$10,924).

CF3

I 10000

10

NPV 3 Calculator Use The preprogrammed NPV function in a

N

financial calculator can be used to simplify the NPV cal-

10 I

Solution

culation. The keystrokes for project Aâ€”the annuityâ€”

11071.01 NPV

typically are as shown at left. Note that because project

Solution

A is an annuity, only its first cash inflow, CF1 14000, is

10924.40

input, followed by its frequency, N 5.

347

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

FIGURE 9.2 Calculation of NPVs for Bennett Companyâ€™s Capital Expenditure Alternatives

Time lines depicting the cash flows and NPV calculations for projects A and B

Project A End of Year

0 1 2 3 4 5

$42,000 $14,000 $14,000 $14,000 $14,000 $14,000

k = 10%

53,071

NPVA = $11,071

Project B End of Year

0 1 2 3 4 5

$45,000 $28,000 $12,000 $10,000 $10,000 $10,000

k = 10%

25,455

k = 10%

9,917

k = 10%

7,513

$55,924

k = 10%

6,830

k = 10%

6,209

NPVB = $10,924

The keystrokes for project Bâ€”the mixed streamâ€”are

as shown on page 346. Because the last three cash inflows

for project B are the same (CF3 CF4 CF5 10000),

after inputting the first of these cash inflows, CF3, we

merely input its frequency, N 3.

The calculated NPVs for projects A and B of $11,071

and $10,924, respectively, agree with the NPVs cited

above.

Spreadsheet Use The NPVs can be calculated as shown

on the Excel spreadsheet at the left.

348 PART 3 Long-Term Investment Decisions

Internal Rate of Return (IRR)

The internal rate of return (IRR) is probably the most widely used sophisticated

capital budgeting technique. However, it is considerably more difficult than NPV

to calculate by hand. The internal rate of return (IRR) is the discount rate that

internal rate of return (IRR)

A sophisticated capital equates the NPV of an investment opportunity with $0 (because the present value

budgeting technique; the of cash inflows equals the initial investment). It is the compound annual rate of

discount rate that equates the

return that the firm will earn if it invests in the project and receives the given cash

NPV of an investment opportunity

inflows. Mathematically, the IRR is the value of k in Equation 9.1 that causes

with $0 (because the present

NPV to equal $0.

value of cash inflows equals the

initial investment); it is the n

CFt

compound annual rate of return

$0 (9.2)

CF0

(1 IRR)t

that the firm will earn if it invests t1

in the project and receives the

n

given cash inflows. CFt

(9.2a)

CF0

(1 IRR)t

t1

The Decision Criteria

When IRR is used to make acceptâ€“reject decisions, the decision criteria are as

follows:

â€˘ If the IRR is greater than the cost of capital, accept the project.

â€˘ If the IRR is less than the cost of capital, reject the project.

These criteria guarantee that the firm earns at least its required return. Such an

outcome should enhance the market value of the firm and therefore the wealth of

its owners.

Calculating the IRR

The actual calculation by hand of the IRR from Equation 9.2a is no easy chore. It

WW involves a complex trial-and-error technique that is described and demonstrated

W

on this textâ€™s Web site: www.aw.com/gitman. Fortunately, many financial calcu-

lators have a preprogrammed IRR function that can be used to simplify the IRR

calculation. With these calculators, you merely punch in all cash flows just as if

to calculate NPV and then depress IRR to find the internal rate of return. Com-

puter software, including spreadsheets, is also available for simplifying these cal-

culations. All NPV and IRR values presented in this and subsequent chapters are

obtained by using these functions on a popular financial calculator.

We can demonstrate the internal rate of return (IRR) approach using Bennett

EXAMPLE

Company data presented in Table 9.1. Figure 9.3 uses time lines to depict the

framework for finding the IRRs for Bennettâ€™s projects A and B, both of which

have conventional cash flow patterns. It can be seen in the figure that the IRR is

the unknown discount rate that causes the NPV just to equal $0.

Calculator Use To find the IRR using the preprogrammed function in a finan-

cial calculator, the keystrokes for each project are the same as those shown on

349

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

FIGURE 9.3 Calculation of IRRs for Bennett Companyâ€™s Capital Expenditure Alternatives

Time lines depicting the cash flows and IRR calculations for projects A and B

Project A End of Year

0 1 2 3 4 5

$42,000 $14,000 $14,000 $14,000 $14,000 $14,000

IRR?

42,000

NPVA = $ 0

IRRA = 19.9%

Project B End of Year

0 1 2 3 4 5

$45,000 $28,000 $12,000 $10,000 $10,000 $10,000

IRR?

IRR?

IRR?

45,000

IRR?

IRR?

NPVB = $ 0

IRRB = 21.7%

page 346 for the NPV calculation, except that the last

two NPV keystrokes (punching I and then NPV) are

replaced by a single IRR keystroke.

Comparing the IRRs of projects A and B given in

Figure 9.3 to Bennett Companyâ€™s 10% cost of capital, we

can see that both projects are acceptable because

IRRA 19.9% 10.0% cost of capital

IRRB 21.7% 10.0% cost of capital

Comparing the two projectsâ€™ IRRs, we would prefer pro-

ject B over project A because IRRB 21.7% IRRA

19.9%. If these projects are mutually exclusive, the IRR

decision technique would recommend project B.

Spreadsheet Use The internal rate of return also can be

calculated as shown on the Excel spreadsheet at the left.

350 PART 3 Long-Term Investment Decisions

It is interesting to note in the preceding example that the IRR suggests that

project B, which has an IRR of 21.7%, is preferable to project A, which has an

IRR of 19.9%. This conflicts with the NPV rankings obtained in an earlier exam-

ple. Such conflicts are not unusual. There is no guarantee that NPV and IRR will

rank projects in the same order. However, both methods should reach the same

conclusion about the acceptability or nonacceptability of projects.

Review Questions

9â€“1 What is the payback period? How is it calculated? What weaknesses are

commonly associated with the use of the payback period to evaluate a

proposed investment?

9â€“2 How is the net present value (NPV) calculated for a project with a con-

ventional cash flow pattern? What are the acceptance criteria for NPV?

9â€“3 What is the internal rate of return (IRR) on an investment? How is it

determined? What are its acceptance criteria?

Comparing NPV and IRR Techniques

LG3

To understand the differences between the NPV and IRR techniques and decision

makersâ€™ preferences in their use, we need to look at net present value profiles,

conflicting rankings, and the question of which approach is better.

Net Present Value Profiles

Projects can be compared graphically by constructing net present value profiles that

net present value profile

depict the projectsâ€™ NPVs for various discount rates. These profiles are useful in

Graph that depicts a projectâ€™s

NPVs for various discount rates. evaluating and comparing projects, especially when conflicting rankings exist. They

are best demonstrated via an example.

To prepare net present value profiles for Bennett Companyâ€™s two projects, A and

EXAMPLE

B, the first step is to develop a number of â€śdiscount rateâ€“net present valueâ€ť

coordinates. Three coordinates can be easily obtained for each project; they are

at discount rates of 0%, 10% (the cost of capital, k), and the IRR. The net pres-

ent value at a 0% discount rate is found by merely adding all the cash inflows

and subtracting the initial investment. Using the data in Table 9.1 and Figure

9.1, we get

For project A:

($14,000 $14,000 $14,000 $14,000 $14,000) $42,000 $28,000

For project B:

($28,000 $12,000 $10,000 $10,000 $10,000) $45,000 $25,000

351

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

TABLE 9.4 Discount-Rateâ€“NPV

Coordinates for

Projects A and B

Net present value

Discount rate Project A Project B

0% $28,000 $25,000

10 11,071 10,924

19.9 0 â€”

21.7 â€” 0

FIGURE 9.4

NPV Profiles 40

Net present value profiles for Project A

30

NPV ($000)

Bennett Companyâ€™s projects

20

A and B IRRB = 21.7%

10 Project B

0

B

â€“10 A

IRRA = 19.9%

10.7%

â€“20

0 5 10 15 20 25 30 35

Discount Rate (%)

The net present values for projects A and B at the 10% cost of capital are

$11,071 and $10,924, respectively (from Figure 9.2). Because the IRR is the dis-

count rate for which net present value equals zero, the IRRs (from Figure 9.3) of

19.9% for project A and 21.7% for project B result in $0 NPVs. The three sets of

coordinates for each of the projects are summarized in Table 9.4.

Plotting the data from Table 9.4 results in the net present value profiles for

projects A and B shown in Figure 9.4. The figure indicates that for any discount

rate less than approximately 10.7%, the NPV for project A is greater than the

NPV for project B. Beyond this point, the NPV for project B is greater. Because

the net present value profiles for projects A and B cross at a positive NPV, the

IRRs for the projects cause conflicting rankings whenever they are compared to

NPVs calculated at discount rates below 10.7%.

Conflicting Rankings

Ranking is an important consideration when projects are mutually exclusive or

when capital rationing is necessary. When projects are mutually exclusive, ranking

enables the firm to determine which project is best from a financial standpoint.

352 PART 3 Long-Term Investment Decisions

When capital rationing is necessary, ranking projects will provide a logical starting

point for determining what group of projects to accept. As weâ€™ll see, conflicting

conflicting rankings

Conflicts in the ranking given a rankings using NPV and IRR result from differences in the magnitude and timing

project by NPV and IRR, resulting of cash flows.

from differences in the magnitude

The underlying cause of conflicting rankings is different implicit assumptions

and timing of cash flows.

about the reinvestment of intermediate cash inflowsâ€”cash inflows received prior

intermediate cash inflows to the termination of a project. NPV assumes that intermediate cash inflows are

Cash inflows received prior to

reinvested at the cost of capital, whereas IRR assumes that intermediate cash

the termination of a project.

inflows are invested at a rate equal to the projectâ€™s IRR.5

In general, projects with similar-size investments and lower cash inflows in

the early years tend to be preferred at lower discount rates. Projects that have

higher cash inflows in the early years tend to be preferred at higher discount

rates. Why? Because at high discount rates, later-year cash inflows tend to be

severely penalized in present value terms. For example, at a high discount rate,

say 20 percent, the present value of $1 received at the end of 5 years is about 40

cents, whereas for $1 received at the end of 15 years it is less than 7 cents.

Clearly, at high discount rates a projectâ€™s early-year cash inflows count most in

terms of its NPV. Table 9.5 summarizes the preferences associated with extreme

discount rates and dissimilar cash inflow patterns.

Bennett Companyâ€™s projects A and B were found to have conflicting rankings at

EXAMPLE

the firmâ€™s 10% cost of capital (as depicted in Figure 9.4). If we review each proj-

ectâ€™s cash inflow pattern as presented in Table 9.1 and Figure 9.1, we see that

although the projects require similar initial investments, they have dissimilar cash

inflow patterns. Table 9.5 indicates that project B, which has higher early-year

TABLE 9.5 Preferences Associated with

Extreme Discount Rates and

Dissimilar Cash Inflow

Patterns

Cash inflow pattern

Lower early-year Higher early-year

Discount rate cash inflows cash inflows

Low Preferred Not preferred

High Not preferred Preferred

5. To eliminate the reinvestment rate assumption of the IRR, some practitioners calculate the modified internal rate

of return (MIRR). The MIRR is found by converting each operating cash inflow to its future value measured at the

end of the projectâ€™s life and then summing the future values of all inflows to get the projectâ€™s terminal value. Each

future value is found by using the cost of capital, thereby eliminating the reinvestment rate criticism of the tradi-

tional IRR. The MIRR represents the discount rate that causes the terminal value just to equal the initial investment.

Because it uses the cost of capital as the reinvestment rate, the MIRR is generally viewed as a better measure of a

projectâ€™s true profitability than the IRR. Although this technique is frequently used in commercial real estate valua-

tion and is a preprogrammed function on some sophisticated financial calculators, its failure to resolve the issue of

conflicting rankings and its theoretical inferiority to NPV have resulted in the MIRR receiving only limited attention

and acceptance in the financial literature. For a thorough analysis of the arguments surrounding IRR and MIRR, see

D. Anthony Plath and William F. Kennedy, â€śTeaching Return-Based Measures of Project Evaluation,â€ť Financial

Practice and Education (Spring/Summer 1994), pp. 77â€“86.

353

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

cash inflows than project A, would be preferred over project A at higher discount

rates. Figure 9.4 shows that this is in fact the case. At any discount rate in excess

of 10.7%, project Bâ€™s NPV is above that of project A. Clearly, the magnitude and

timing of the projectsâ€™ cash inflows do affect their rankings.

Which Approach Is Better?

It is difficult to choose one approach over the other, because the theoretical and

practical strengths of the approaches differ. It is therefore wise to view both NPV

and IRR techniques in each of those dimensions.

Theoretical View

On a purely theoretical basis, NPV is the better approach to capital budgeting as

a result of several factors. Most important is that the use of NPV implicitly

assumes that any intermediate cash inflows generated by an investment are rein-

vested at the firmâ€™s cost of capital. The use of IRR assumes reinvestment at the

often high rate specified by the IRR. Because the cost of capital tends to be a rea-

sonable estimate of the rate at which the firm could actually reinvest intermediate

cash inflows, the use of NPV, with its more conservative and realistic reinvest-

ment rate, is in theory preferable.

In addition, certain mathematical properties may cause a project with a non-

conventional cash flow pattern to have zero or more than one real IRR; this

problem does not occur with the NPV approach.

Practical View

Evidence suggests that in spite of the theoretical superiority of NPV, financial

managers prefer to use IRR.6 The preference for IRR is due to the general dispo-

sition of businesspeople toward rates of return rather than actual dollar returns.

Because interest rates, profitability, and so on are most often expressed as annual

rates of return, the use of IRR makes sense to financial decision makers. They

tend to find NPV less intuitive because it does not measure benefits relative to the

amount invested. Because a variety of techniques are available for avoiding the

pitfalls of the IRR, its widespread use does not imply a lack of sophistication on

the part of financial decision makers.

Review Questions

9â€“4 Do the net present value (NPV) and internal rate of return (IRR) always

agree with respect to acceptâ€“reject decisions? With respect to ranking deci-

sions? Explain.

6. For example, see Harold Bierman, Jr., â€śCapital Budgeting in 1992: A Survey,â€ť Financial Management (Autumn

1993), p. 24, and Lawrence J. Gitman and Charles E. Maxwell, â€śA Longitudinal Comparison of Capital Budgeting

Techniques Used by Major U.S. Firms: 1986 versus 1976,â€ť Journal of Applied Business Research (Fall 1987), pp.

41â€“50, for discussions of evidence with respect to capital budgeting decision-making practices in major U.S. firms.

354 PART 3 Long-Term Investment Decisions

9â€“5 How is a net present value profile used to compare projects? What causes

conflicts in the ranking of projects via net present value and internal rate

of return?

9â€“6 Does the assumption concerning the reinvestment of intermediate cash

inflow tend to favor NPV or IRR? In practice, which technique is pre-

ferred and why?

Additional Considerations:

LG4

Real Options and Capital Rationing

A couple of important issues that often confront the financial manager when

making capital budgeting decisions are (1) the potential real options embedded in

capital projects and (2) the availability of only limited funding for acceptable

projects. Here we briefly consider each of these situations.

Recognizing Real Options

The procedures described in Chapter 8 and thus far in this chapter suggest that

to make capital budgeting decisions, we must (1) estimate relevant cash flows

and (2) apply an appropriate decision technique such as NPV or IRR to those

cash flows. Although this traditional procedure is believed to yield good deci-

sions, a more strategic approach to these decisions has emerged in recent years.

This more modern view considers any real optionsâ€”opportunities that are

real options

Opportunities that are embedded embedded in capital projects (â€śreal,â€ť rather than financial, asset investments)

in capital projects that enable

that enable managers to alter their cash flows and risk in a way that affects pro-

managers to alter their cash

ject acceptability (NPV). Because these opportunities are more likely to exist in,

flows and risk in a way that

and be more important to, large â€śstrategicâ€ť capital budgeting projects, they are

affects project acceptability

sometimes called strategic options.

(NPV). Also called strategic

options. Some of the more common types of real optionsâ€”abandonment, flexibility,

growth, and timingâ€”are briefly described in Table 9.6. It should be clear from

their descriptions that each of these types of options could be embedded in a

capital budgeting decision and that explicit recognition of them would probably

alter the cash flow and risk of a project and change its NPV.

By explicitly recognizing these options when making capital budgeting deci-

sions, managers can make improved, more strategic decisions that consider in

advance the economic impact of certain contingent actions on project cash flow

and risk. The explicit recognition of real options embedded in capital budgeting

projects will cause the projectâ€™s strategic NPV to differ from its traditional NPV

as indicated by Equation 9.3.

NPVstrategic NPVtraditional Value of real options (9.3)

Application of this relationship is illustrated in the following example.

Assume that a strategic analysis of Bennett Companyâ€™s projects A and B (see

EXAMPLE

cash flows and NPVs in Figure 9.2) finds no real options embedded in project A

355

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

TABLE 9.6 Major Types of Real Options

Option type Description

Abandonment option The option to abandon or terminate a project prior to the end of

its planned life. This option allows management to avoid or mini-

mize losses on projects that turn bad. Explicitly recognizing the

abandonment option when evaluating a project often increases

its NPV.

Flexibility option The option to incorporate flexibility into the firmâ€™s operations,

particularly production. It generally includes the opportunity to

design the production process to accept multiple inputs, use flexi-

ble production technology to create a variety of outputs by recon-

figuring the same plant and equipment, and purchase and retain

excess capacity in capital-intensive industries subject to wide

swings in output demand and long lead time in building new

capacity from scratch. Recognition of this option embedded in a

capital expenditure should increase the NPV of the project.

Growth option The option to develop follow-on projects, expand markets, expand

or retool plants, and so on, that would not be possible without

implementation of the project that is being evaluated. If a project

being considered has the measurable potential to open new doors if

successful, then recognition of the cash flows from such opportuni-

ties should be included in the initial decision process. Growth

opportunities embedded in a project often increase the NPV of the

project in which they are embedded.

Timing option The option to determine when various actions with respect to a

given project are taken. This option recognizes the firmâ€™s oppor-

tunity to delay acceptance of a project for one or more periods, to

accelerate or slow the process of implementing a project in

response to new information, or to shut down a project tem-

porarily in response to changing product market conditions or

competition. As in the case of the other types of options, the

explicit recognition of timing opportunities can improve the NPV

of a project that fails to recognize this option in an investment

decision.

and two real options embedded in project B. The two real options in project B

are as follows: (1) The project would have, during the first two years, some

downtime that would result in unused production capacity that could be used to

perform contract manufacturing for another firm, and (2) the projectâ€™s comput-

erized control system could, with some modification, control two other

machines, thereby reducing labor cost, without affecting operation of the new

project.

Bennettâ€™s management estimated the NPV of the contract manufacturing

over the 2 years following implementation of project B to be $1,500 and the

NPV of the computer control sharing to be $2,000. Management felt there was a

60% chance that the contract manufacturing option would be exercised and

only a 30% chance that the computer control sharing option would be exercised.

356 PART 3 Long-Term Investment Decisions

The combined value of these two real options would be the sum of their

expected values.

Value of real options for project B (0.60 $1,500) (0.30 $2,000)

$900 $600 $1,500

Substituting the $1,500 real options value along with the traditional NPV of

$10,924 for project B (from Figure 9.2) into Equation 9.3, we get the strategic

NPV for project B.

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

Bennett Companyâ€™s project B therefore has a strategic NPV of $12,424,

which is above its traditional NPV and now exceeds project Aâ€™s NPV of $11,071.

Clearly, recognition of project Bâ€™s real options improved its NPV (from $10,924

to $12,424) and causes it to be preferred over project A (NPV of $12,424 for B

NPV of $11,071 for A), which has no real options embedded in it.

It is important to realize that the recognition of attractive real options

when determining NPV could cause an otherwise unacceptable project -

(NPVtraditional $0) to become acceptable (NPVstrategic $0). The failure to rec-

ognize the value of real options could therefore cause management to reject pro-

jects that are acceptable. Although doing so requires more strategic thinking and

analysis, it is important for the financial manager to identify and incorporate real

options in the NPV process. The procedures for doing this efficiently are emerg-

ing, and the use of the strategic NPV that incorporates real options is expected to

become more commonplace in the future.

Choosing Projects under Capital Rationing

Firms commonly operate under capital rationingâ€”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 (or IRRs > the cost

of capital). However, in practice, most firms operate under capital rationing.

Generally, firms attempt to isolate and select the best acceptable projects subject

to a capital expenditure budget set by management. Research has found that

management internally imposes capital expenditure constraints to avoid what it

deems to be â€śexcessiveâ€ť levels of new financing, particularly debt. Although fail-

ing to fund all acceptable independent projects is theoretically inconsistent with

the goal of maximizing owner wealth, we will discuss capital rationing proce-

dures because they are widely used in practice.

The objective of capital rationing is to select the group of projects that pro-

vides the highest overall net present value and does not require more dollars than

are budgeted. As a prerequisite to capital rationing, the best of any mutually

exclusive projects must be chosen and placed in the group of independent proj-

ects. Two basic approaches to project selection under capital rationing are dis-

cussed here.

357

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

Internal Rate of Return Approach

internal rate of return approach

An approach to capital rationing

The internal rate of return approach involves graphing project IRRs in descend-

that involves graphing project

ing order against the total dollar investment. This graph, which is discussed in

IRRs in descending order against

the total dollar investment, to more detail in Chapter 10, is called the investment opportunities schedule

determine the group of accept-

(IOS). By drawing the cost-of-capital line and then imposing a budget con-

able projects.

straint, the financial manager can determine the group of acceptable projects.

investment opportunities

The problem with this technique is that it does not guarantee the maximum

schedule (IOS)

dollar return to the firm. It merely provides a satisfactory solution to capital-

The graph that plots project IRRs

rationing problems.

in descending order against total

dollar investment.

Tate Company, a fast-growing plastics company, is confronted with six projects

EXAMPLE

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

each project are as follows:

Project Initial investment IRR

A $ 80,000 12%

B 70,000 20

C 100,000 16

D 40,000 8

E 60,000 15

F 110,000 11

The firm has a cost of capital of 10%. Figure 9.5 presents the IOS that results

from ranking the six projects in descending order on the basis of their IRRs.

According to the schedule, only projects B, C, and E should be accepted.

FIGURE 9.5

Budget

Investment

Constraint

B

20%

Opportunities Schedule

Investment opportunities

C

schedule (IOS) for Tate E

Company projects

A

IRR

F Cost of

10% Capital

D

IOS

0 100 200 250 300 400 500

230

Total Investment ($000)

358 PART 3 Long-Term Investment Decisions

Together they will absorb $230,000 of the $250,000 budget. Projects A and F

are acceptable but cannot be chosen because of the budget constraint. Project D

is not worthy of consideration; its IRR is less than the firmâ€™s 10% cost of

capital.

The drawback of this approach is that there is no guarantee that the accep-

tance of projects B, C, and E will maximize total dollar returns and therefore

ownersâ€™ wealth.

Net Present Value Approach

The net present value approach is based on the use of present values to determine

net present value approach

An approach to capital rationing the group of projects that will maximize ownersâ€™ wealth. It is implemented by

that is based on the use of

ranking projects on the basis of IRRs and then evaluating the present value of the

present values to determine the

benefits from each potential project to determine the combination of projects

group of projects that will

with the highest overall present value. This is the same as maximizing net present

maximize ownersâ€™ wealth.

value, in which the entire budget is viewed as the total initial investment. Any

portion of the firmâ€™s budget that is not used does not increase the firmâ€™s value. At

best, the unused money can be invested in marketable securities or returned to the

owners in the form of cash dividends. In either case, the wealth of the owners is

not likely to be enhanced.

The group of projects described in the preceding example is ranked in Table 9.7 on

EXAMPLE

the basis of IRRs. The present value of the cash inflows associated with the proj-

ects is also included in the table. Projects B, C, and E, which together require

$230,000, yield a present value of $336,000. However, if projects B, C, and A

were implemented, the total budget of $250,000 would be used, and the present

value of the cash inflows would be $357,000. This is greater than the return

expected from selecting the projects on the basis of the highest IRRs. Implementing

B, C, and A is preferable, because they maximize the present value for the given

budget. The firmâ€™s objective is to use its budget to generate the highest present

value of inflows. Assuming that any unused portion of the budget does not gain

or lose money, the total NPV for projects B, C, and E would be $106,000

TABLE 9.7 Rankings for Tate Company

Projects

Initial Present value of

Project investment IRR inflows at 10%

B $170,000 20% $112,000

C 100,000 16 145,000

E 60,000 15 79,000

A 80,000 12 100,000

F 110,000 11 126,500 Cutoff point

(IRR 10%)

D 40,000 8 36,000

359

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

($336,000 $230,000), whereas for projects B, C, and A the total NPV would be

$107,000 ($357,000 $250,000). Selection of projects B, C, and A will therefore

maximize NPV.

Review Questions

9â€“7 What are real options? What are some major types of real options?

9â€“8 What is the difference between the strategic NPV and the traditional

NPV? Do they always result in the same acceptâ€“reject decisions?

9â€“9 What is capital rationing? In theory, should capital rationing exist? Why

does it frequently occur in practice?

9â€“10 Compare and contrast the internal rate of return approach and the net

present value approach to capital rationing. Which is better? Why?

Behavioral Approaches for Dealing with Risk

LG5

In the context of capital budgeting, the term risk refers to the chance that a proj-

risk (in capital budgeting)

The chance that a project will ect will prove unacceptableâ€”that is, NPV $0 or IRR cost of capital. More

prove unacceptable or, more formally, risk in capital budgeting is the degree of variability of cash flows. Pro-

formally, the degree of variability

jects with a small chance of acceptability and a broad range of expected cash

of cash flows.

flows are more risky than projects that have a high chance of acceptability and a

narrow range of expected cash flows.

In the conventional capital budgeting projects assumed here, risk stems

almost entirely from cash inflows, because the initial investment is generally

known with relative certainty. These inflows, of course, derive from a number of

variables related to revenues, expenditures, and taxes. Examples include the level

of sales, the cost of raw materials, labor rates, utility costs, and tax rates. We will

concentrate on the risk in the cash inflows, but remember that this risk actually

results from the interaction of these underlying variables.

Behavioral approaches can be used to get a â€śfeelâ€ť for the level of project risk,

whereas other approaches explicitly recognize project risk. Here we present a few

behavioral approaches for dealing with risk in capital budgeting: sensitivity and

scenario analysis, decision trees, and simulation. In addition, some international

risk considerations are discussed.

Sensitivity Analysis and Scenario Analysis

Two approaches for dealing with project risk to capture the variability of cash

inflows and NPVs are sensitivity analysis and scenario analysis. As noted in

Chapter 5, sensitivity analysis is a behavioral approach that uses several possible

values for a given variable, such as cash inflows, to assess that variableâ€™s impact

on the firmâ€™s return, measured here by NPV. This technique is often useful in get-

ting a feel for the variability of return in response to changes in a key variable. In

capital budgeting, one of the most common sensitivity approaches is to estimate

360 PART 3 Long-Term Investment Decisions

TABLE 9.8 Sensitivity Analysis

of Treadwellâ€™s

Projects A and B

Project A Project B

Initial investment $10,000 $10,000

Annual cash inflows

Outcome

Pessimistic $1,500 $ 0

Most likely 2,000 2,000

Optimistic 2,500 4,000

Range $1,000 $ 4,000

Net present valuesa

Outcome

Pessimistic $1,409 $10,000

Most likely 5,212 5,212

Optimistic 9,015 20,424

Range $7,606 $30,424

aThese values were calculated by using the correspond-

ing annual cash inflows. A 10% cost of capital and a

15-year life for the annual cash inflows were used.

the NPVs associated with pessimistic (worst), most likely (expected), and opti-

mistic (best) estimates of cash inflow. The range can be determined by subtract-

ing the pessimistic-outcome NPV from the optimistic-outcome NPV.

Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering

EXAMPLE

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. The firmâ€™s financial manager made pessimistic,

most likely, and optimistic estimates of the cash inflows for each project. The

cash inflow estimates and resulting NPVs in each case are summarized in Table

9.8. Comparing the ranges of cash inflows ($1,000 for project A and $4,000 for

B) and, more important, the ranges of NPVs ($7,606 for project A and $30,424

for B) makes it clear that project A is less risky than project B. Given that both

projects have the same most likely NPV of $5,212, the assumed risk-averse deci-

sion maker will take project A because it has less risk and no possibility of loss.

Scenario analysis is a behavioral approach similar to sensitivity analysis but

scenario analysis

A behavioral approach that broader in scope. It evaluates the impact on the firmâ€™s return of simultaneous

evaluates the impact on the

changes in a number of variables, such as cash inflows, cash outflows, and the

firmâ€™s return of simultaneous

cost of capital. For example, the firm could evaluate the impact of both high

changes in a number of

inflation (scenario 1) and low inflation (scenario 2) on a projectâ€™s NPV. Each sce-

variables.

nario will affect the firmâ€™s cash inflows, cash outflows, and cost of capital,

thereby resulting in different levels of NPV. The decision maker can use these

361

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

NPV estimates to assess the risk involved with respect to the level of inflation.

The widespread availability of computer and spreadsheets has greatly enhanced

the use of both scenario and sensitivity analysis.

Decision Trees

Decision trees are a behavioral approach that uses diagrams to map the various

decision trees

A behavioral approach that uses investment decision alternatives and payoffs, along with their probabilities of

diagrams to map the various occurrence. Their name derives from their resemblance to the branches of a tree

investment decision alternatives

(see Figure 9.6). Decision trees rely on estimates of the probabilities associated

and payoffs, along with their

with the outcomes (payoffs) of competing courses of action. The payoffs of each

probabilities of occurrence.

course of action are weighted by the associated probability; the weighted payoffs

are summed; and the expected value of each course of action is then determined.

The alternative that provides the highest expected value is preferred.

Convoy, Inc., a manufacturer of picture frames, wishes to choose between two

EXAMPLE

equally risky projects, I and J. To make this decision, Convoyâ€™s management has

gathered the necessary data, which are depicted in the decision tree in Figure 9.6.

Project I requires an initial investment of $120,000; a resulting expected present

value of cash inflows of $130,000 is shown in column 4. Project Iâ€™s expected net

present value, which is calculated below the decision tree, is therefore $10,000.

The expected net present value of project J is determined in a similar fashion.

Project J is preferred because it offers a higher NPVâ€”$15,000.

Weighted

FIGURE 9.6

Present Value Present Value

Decision Tree for NPV Initial of Cash Inflow of Cash Inflow

Decision Tree for Convoy, Investment Probablility (Payoff) [(2) (3)]

(1) (2) (3) (4)

Inc.â€™s choice between

projects I and J .40

$225,000 $ 90,000

$120,000 .50

$100,000 50,000

.10

Project I â€“$100,000 â€“10,000

Expected Present Value of Cash Inflows $130,000

Decision:

I or J ?

.30

Project J $280,000 $ 84,000

$140,000 .40

$200,000 80,000

.30

â€“$ 30,000 â€“9,000

Expected Present Value of Cash Inflows $155,000

Expected NPVI $130,000 $120,000 $10,000

Expected NPVJ $155,000 $140,000 $15,000

Because Expected NPVJ Expected NPVI , Choose J.

362 PART 3 Long-Term Investment Decisions

Simulation

Simulation is a statistics-based behavioral approach that applies predetermined

simulation

A statistics-based behavioral probability distributions and random numbers to estimate risky outcomes. By

approach that applies predeter- tying the various cash flow components together in a mathematical model and

mined probability distributions

repeating the process numerous times, the financial manager can develop a prob-

and random numbers to estimate

ability distribution of project returns. Figure 9.7 presents a flowchart of the simu-

risky outcomes.

lation of the net present value of a project. The process of generating random

numbers and using the probability distributions for cash inflows and cash out-

flows enables the financial manager to determine values for each of these vari-

ables. Substituting these values into the mathematical model results in an NPV.

By repeating this process perhaps a thousand times, one can create a probability

distribution of net present values.

Although only gross cash inflows and cash outflows are simulated in Figure

9.7, more sophisticated simulations using individual inflow and outflow compo-

nents, such as sales volume, sale price, raw material cost, labor cost, maintenance

expense, and so on, are quite common. From the distribution of returns, the deci-

sion maker can determine not only the expected value of the return but also the

probability of achieving or surpassing a given return. The use of computers has

made the simulation approach feasible. The output of simulation provides an

FIGURE 9.7

Repeat

NPV Simulation

Flowchart of a net present

value simulation

Generate Generate

Random Random

Number Number

Probability

Probability

Cash Inflows Cash Outflows

Mathematical Model

NPV = Present Value of Cash Inflows â€“ Present Value of Cash Outflows

Probability

Net Present Value (NPV)

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