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Chapter Across the Disciplines


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 firm’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 budgeting—recognizing
tion of new equipment and plants will be
real options and choosing projects
evaluated by the firm’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
firm’s goal of maximizing owners’ 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 Company’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 projects’ 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 project’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 benefit–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 accept–reject decisions, the decision
criteria are as follows:

• 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.

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 Company’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 Bennett’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 firm’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 firm’s value. Instead, the appropriate pay-
back period is simply the maximum acceptable period of time over which man-
agement decides that a project’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 Enterprises’
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 Company’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 firm’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 rate—often called the discount rate, required return, cost of capital, or
opportunity cost—is the minimum return that must be earned on a project to
leave the firm’s market value unchanged. In this chapter, we take this rate as a
“given.” In Chapter 10 we will explore how it is calculated.
The net present value (NPV) is found by subtracting a project’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 firm’s cost of capital (k).
ing a project’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 firm’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
today’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 accept–reject decisions, the decision criteria are as
follows:

• If the NPV is greater than $0, accept the project.
• 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 A—the annuity—
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 Company’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 B—the mixed stream—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 accept–reject decisions, the decision criteria are as
follows:

• If the IRR is greater than the cost of capital, accept the project.
• 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 text’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 Bennett’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 Company’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 Company’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 projects’ 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

9–1 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?
9–2 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?
9–3 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
makers’ 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 projects’ NPVs for various discount rates. These profiles are useful in
Graph that depicts a project’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 Company’s two projects, A and
EXAMPLE
B, the first step is to develop a number of “discount rate–net present value”
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-Rate–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 —
21.7 — 0




FIGURE 9.4
NPV Profiles 40
Net present value profiles for Project A
30
NPV ($000)




Bennett Company’s projects
20
A and B IRRB = 21.7%
10 Project B
0
B
–10 A
IRRA = 19.9%
10.7%
–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 we’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 inflows—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 project’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 project’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 Company’s projects A and B were found to have conflicting rankings at
EXAMPLE
the firm’s 10% cost of capital (as depicted in Figure 9.4). If we review each proj-
ect’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 project’s life and then summing the future values of all inflows to get the project’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
project’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, “Teaching Return-Based Measures of Project Evaluation,” Financial
Practice and Education (Spring/Summer 1994), pp. 77–86.
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 B’s NPV is above that of project A. Clearly, the magnitude and
timing of the projects’ 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 firm’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

9–4 Do the net present value (NPV) and internal rate of return (IRR) always
agree with respect to accept–reject decisions? With respect to ranking deci-
sions? Explain.



6. For example, see Harold Bierman, Jr., “Capital Budgeting in 1992: A Survey,” Financial Management (Autumn
1993), p. 24, and Lawrence J. Gitman and Charles E. Maxwell, “A Longitudinal Comparison of Capital Budgeting
Techniques Used by Major U.S. Firms: 1986 versus 1976,” Journal of Applied Business Research (Fall 1987), pp.
41–50, for discussions of evidence with respect to capital budgeting decision-making practices in major U.S. firms.
354 PART 3 Long-Term Investment Decisions


9–5 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?
9–6 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 options—opportunities that are
real options
Opportunities that are embedded embedded in capital projects (“real,” 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 “strategic” 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 options—abandonment, flexibility,
growth, and timing—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 project’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 Company’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 firm’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 firm’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 project’s comput-
erized control system could, with some modification, control two other
machines, thereby reducing labor cost, without affecting operation of the new
project.
Bennett’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 Company’s project B therefore has a strategic NPV of $12,424,
which is above its traditional NPV and now exceeds project A’s NPV of $11,071.
Clearly, recognition of project B’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 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 (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 “excessive” 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 firm’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
owners’ 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 owners’ 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 owners’ wealth.
value, in which the entire budget is viewed as the total initial investment. Any
portion of the firm’s budget that is not used does not increase the firm’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 firm’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

9–7 What are real options? What are some major types of real options?
9–8 What is the difference between the strategic NPV and the traditional
NPV? Do they always result in the same accept–reject decisions?
9–9 What is capital rationing? In theory, should capital rationing exist? Why
does it frequently occur in practice?
9–10 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 unacceptable—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 “feel” 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 variable’s impact
on the firm’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 Treadwell’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 firm’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 firm’s return of simultaneous
evaluates the impact on the
changes in a number of variables, such as cash inflows, cash outflows, and the
firm’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 project’s NPV. Each sce-
variables.
nario will affect the firm’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, Convoy’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 I’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 NPV—$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.’s choice between
projects I and J .40
$225,000 $ 90,000

$120,000 .50
$100,000 50,000

.10
Project I –$100,000 –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
–$ 30,000 –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 – Present Value of Cash Outflows
Probability




Net Present Value (NPV)

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