CHAPTER 10 The Fundamentals of Capital Budgeting Learning Objectives 1. Discuss why capital budgeting decisions are the most important decisions made by a firm’s management. 2. Explain the benefits of using the net present value (NPV) method to analyze capital expenditure decisions, and be able to calculate the NPV for a capital project. 3. Describe the strengths and weaknesses of the payback period as a capital expenditure decision-making tool, and be able to compute the payback period for a capital project. 4. Explain why the accounting rate of return (ARR) is not recommended for use as a capital expenditure decision-making tool. 5. Be able to compute the internal rate of return (IRR) for a capital project, and discuss the conditions under which the IRR technique and the NPV technique produce different results. 1
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CHAPTER 10The Fundamentals of Capital Budgeting
Learning Objectives
1. Discuss why capital budgeting decisions are the most important decisions made by a
firm’s management.
2. Explain the benefits of using the net present value (NPV) method to analyze capital
expenditure decisions, and be able to calculate the NPV for a capital project.
3. Describe the strengths and weaknesses of the payback period as a capital
expenditure decision-making tool, and be able to compute the payback period for a
capital project.
4. Explain why the accounting rate of return (ARR) is not recommended for use as a
capital expenditure decision-making tool.
5. Be able to compute the internal rate of return (IRR) for a capital project, and
discuss the conditions under which the IRR technique and the NPV technique
produce different results.
6. Explain the benefits of a postaudit review of a capital project.
I. Chapter Outline
10.1 An Introduction to Capital Budgeting
A. The Importance of Capital Budgeting
1
Capital budgeting decisions are the most important investment decisions made
by management.
The goal of these decisions is to select capital projects that will increase the
value of the firm.
Capital investments are important because they involve substantial cash
outlays and, once made, are not easily reversed.
Capital budgeting techniques help management to systematically analyze
potential business opportunities in order to decide which are worth
undertaking.
B. Sources of Information
Most of the information needed to make capital budgeting decisions is
generated internally, beginning likely with the sales force.
Then the production team is involved, followed by the accountants.
All this information is then reviewed by the financial managers, who evaluate
the feasibility of the project.
C. Classification of Investment Projects
Capital budgeting projects can be broadly classified into three types: (1)
independent projects; (2) mutually exclusive projects; and (3) contingent
projects.
1. Independent Projects
Projects are independent when their cash flows are unrelated.
If two projects are independent, accepting or rejecting one project has
no bearing on the decision on the other.
2
2. Mutually Exclusive Projects
When two projects are mutually exclusive, accepting one
automatically precludes the other.
Mutually exclusive projects typically perform the same function.
3. Contingent Projects
Contingent projects are those in which the acceptance of one project is
dependent on another project.
There are two types of contingency situations:
Projects that are mandatory
Projects that are optional
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D. Basic Capital Budgeting Terms
The cost of capital is the minimum return that a capital budgeting project
must earn for it to be accepted.
It is an opportunity cost since it reflects the rate of return investors can earn on
financial assets of similar risk.
Capital rationing implies that a firm does not have the resources necessary to
fund all of the available projects.
It implies that funding needs exceed funding resources.
Thus, the available capital will be allocated to the set of projects that will
benefit the firm and its shareholders the most.
10.2 Net Present Value
It is a capital budgeting technique that is consistent with the goal of maximizing
shareholder wealth.
The method estimates the amount by which the benefits or cash flows from a project
exceeds the cost of the project in present value terms.
A. Valuation of Real Assets
Valuing real assets calls for the same steps as valuing financial assets.
Estimate future cash flows.
Determine the investor’s cost of capital or required rate of return.
Calculate the present value of the future cash flows.
However, there are some practical difficulties in following the process for real
assets.
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First, cash flow estimates have to be prepared in-house and are not readily
available as they are for financial assets in legal contracts.
Second, estimates of required rates of return are more difficult than it is for
financial assets because no market data is available for real assets.
B. NPV—The Basic Concept
The present value of a project is the difference between the present value of the
expected future cash flows and the initial cost of the project.
Accepting a positive NPV project leads to an increase in shareholder wealth,
while accepting a negative NPV project leads to a decline in shareholder wealth.
Projects that have an NPV equal to zero imply that management will be
indifferent between accepting and rejecting the project.
C. Framework for Calculating NPV
The NPV technique uses the discounted cash flow technique.
Our goal is to compute the net cash flow (NCF) for each time period t, where NCFt =
(Cash inflows – Cash outflows) for the period t.
A five-step approach can be utilized to compute the NPV.
1. Determine the cost of the project.
Identify and add up all expenses related to the cost of the project.
While we are mostly looking at projects whose entire cost occurs at the start
of the project, we need to recognize that some projects may have costs
occurring beyond the first year also.
The cash flow in year 0 (NCF0) is negative, indicating a cost.
2. Estimate the project’s future cash flows over its expected life.
5
Betty Pessagno, 04/23/08,
More difficult than what? Please clarify from this point on the sentence.
Both cash inflows (CIF) and cash outflows are likely in each year of the
project. Estimate the net cash flow (NCFt) = CIFt – COFt for each year of the
project.
Remember to recognize any salvage value from the project in its terminal
year.
3. Determine the riskiness of the project and the appropriate cost of capital.
The cost of capital is the discount rate used in determining the present value of
the future expected cash flows.
The riskier the project, the higher the cost of capital for the project.
4. Compute the project’s NPV.
Determine the difference between the present value of the expected cash flows
from the project and the cost of the project.
5. Make a decision.
Accept the project if it produces a positive NPV or reject the project if NPV is
negative.
D. Concluding Comments on NPV
Beware of optimistic estimates of future cash flows.
Recognize that the estimates going into calculating NPV are estimates and not
market data. Estimates based on informed judgments are considered acceptable.
The NPV method of determining project viability is the recommended approach
for making capital investment decisions.
The NPV decision criteria can be summed up as follows:
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Summary of Net Present Value (NPV) Method
Decision Rule: NPV > 0: Accept the project.
NPV < 0: Reject the project.
Key Advantages Key Disadvantages
1. Uses the discounted cash flow
valuation technique.
2. Provides a direct measure of how much
a capital project will increase the value
of the firm.
3. Consistent with the goal of maximizing
shareholder wealth.
1. Difficult to understand without an
accounting and finance background.
10.3 The Payback Period
It is one of the most widely used tools for evaluating capital projects.
The payback period represents the number of years it takes for the cash flows from a
project to recover the project’s initial investment.
A project is accepted if its payback period is below some prespecified threshold.
This technique can serve as a risk indicator—the more quickly you recover the cash,
the less risky is the project.
A. Computing the Payback Period
To compute the payback period, we need to know the project’s cost and to
estimate its future net cash flows.
Equation 10.2 shows how to compute the payback period.
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There is no economic rationale that links the payback method to shareholder
wealth maximization.
If a firm has a number of projects that are mutually exclusive, the projects are
selected in order of their payback rank: projects with the lowest payback period
are selected first.
B. How the Payback Period Performs
The payback period analysis can lead to erroneous decisions because the rule does
not consider cash flows after the payback period.
A rapid payback does not necessarily mean a good investment. See Exhibit 10.6
—Projects D and E.
C. The Discounted Payback Period
One weakness of the ordinary payback period is that it does not take into account
the time value of money.
The discounted payback period calculation calls for the future cash flows to be
discounted by the firm’s cost of capital.
The major advantage of the discounted payback is that it tells management how
long it takes a project to reach a positive NPV.
However, this method still ignores all cash flows after the arbitrary cutoff period,
which is a major flaw.
D. Evaluating the Payback Rule
The standard payback period is widely used in business.
It provides a simple measure of an investment’s liquidity risk.
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The greatest advantage of the payback period is its simplicity.
It ignores the time value of money.
It does not adjust or account for differences in the overall, or total, risk for a
project, which could include operating, financing, and foreign exchange risk.
The biggest weakness of either the standard or discounted payback methods is
their failure to consider cash flows after the payback.
The following table summarizes this capital budgeting technique.
Summary of Payback Method
Decision Rule: Payback period ≤ Payback cutoff point ] Accept the project.
Payback period > Payback cutoff point ] Reject the project.
Key Advantages Key Disadvantages
1. Easy to calculate and understand for
people without strong finance
backgrounds.
2. A simple measure of a project’s
liquidity.
1. Most common version does not account
for time value of money.
2. Does not consider cash flows past the
payback period
3. Bias against long-term projects such as
research and development and new
product launches.
4. Arbitrary cutoff point.
10.4 The Accounting Rate of Return
It is sometimes called the book rate of return.
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This method computes the return on a capital project using accounting numbers—the
project’s net income (NI) and book value (BV) rather than cash flow data.
The most common definition is the one given in Equation 10.3:
It has a number of major flaws as a tool for evaluating capital expenditure decisions.
First, the ARR is not a true rate of return. ARR simply gives us a number based
on average figures from the income statement and balance sheet.
It ignores the time value of money.
There is no economic rationale that links a particular acceptance criterion to the
goal of maximizing shareholders’ wealth.
10.5 Internal Rate of Return
The IRR is an important and legitimate alternative to the NPV method.
The NPV and IRR techniques are similar in that both depend on discounting the cash
flows from a project.
When we use the IRR, we are looking for the rate of return associated with a project
so we can determine whether this rate is higher or lower than the firm’s cost of
capital.
The IRR is the discount rate that makes the NPV to equal zero.
A. Calculating the IRR
The IRR is an expected rate of return, much like the yield to maturity calculation
that was made on bonds.
We will need to apply the same trial-and-error method to compute the IRR.
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B. When the IRR and NPV Methods Agree
The two methods will always agree when the projects are independent and the
projects’ cash flows are conventional.
After the initial investment is made (cash outflow), all the cash flows in each
future year are positive (inflows).
C. When the IRR and NPV Methods Disagree
The IRR and NPV methods can produce different accept/reject decisions if a
project either has unconventional cash flows or the projects are mutually
exclusive.
1. Unconventional Cash Flows
Unconventional cash flows could follow several different patterns.
A positive initial cash flow followed by negative future cash flows.
Future cash flows from a project could include both positive and negative
cash flows.
A cash flow stream that looks similar to a conventional cash flow stream
except for a final negative cash flow.
In these circumstances, the IRR technique can provide more than one solution.
This makes the result unreliable and should not be used in deciding about
accepting or rejecting a project.
2. Mutually Exclusive Projects
When you are comparing two mutually exclusive projects, the NPVs of the
two projects will equal each other at a certain discount rate. This point at
which the NPVs intersect is called the crossover point. Depending on whether
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the required rate of return is above or below this crossover point, the ranking
of the projects will be different. While it is easy to identify the superior
project based on the NPV, one cannot do so based on the IRR. Thus, ranking
conflicts can arise.
A second situation arises when you compare projects with different costs.
While IRR gives you a return based on the dollar invested, it does not
recognize the difference in the size of the investments. NPV does!
D. Modified Internal Rate of Return (MIRR)
A major weakness of the IRR compared to the NPV method is the reinvestment
rate assumption.
IRR assumes that the cash flows from the project are reinvested at the IRR,
while the NPV assumes that they are invested at the firm’s cost of capital.
This optimistic assumption in the IRR method leads to some projects being
accepted when they should not be.
An alternative technique is the modified internal rate of return (MIRR). Here,
each operating cash flow is reinvested at the firm’s cost of capital.
The compounded values are summed up to get the project’s terminal value.
The MIRR is the interest rate that equates the project’s cost to the terminal value
at the end of the project.
Equation 10.5 shows how to calculate the MIRR.
E. IRR versus NPV: A Final Comment
While the IRR has an intuitive appeal to managers because the output is in the
form of a return, the technique has some critical problems.
12
Betty Pessagno, 04/23/08,
IPP? Did you mean IRR here? Just a typo? I will change it – pls verify.
On the other hand, decisions made based on the project’s NPV are consistent with
the goal of shareholder wealth maximization. In addition, the result shows
management the dollar amount by which each project is expected to increase the
value of the firm.
For these reasons, the NPV method should be used to make capital budgeting
decisions.
The following table summarizes the IRR decision-making criteria.
13
Review of Internal Rate of Return (IRR)
Decision Rule: IRR > Cost of capital ] Accept the project.
IRR < Cost of capital ] Reject the project.
Key Advantages Key Disadvantages
1. Intuitively easy to understand.
2. Based on the discounted cash flow
technique.
1. With nonconventional cash flows, IRR
approach can yield no or multiple answers.
2. A lower IRR can be better if a cash inflow is
followed by cash outflows.
3. With mutually exclusive projects, IRR can
lead to incorrect investment decisions.
10.6 Capital Budgeting in Practice
A. Practitioners’ Methods of Choice
Exhibit 10.12 summarizes surveys of practitioners on the capital budgeting
methods of choice.
In the late 1950s, less than 20 percent of managers used the NPV or IRR methods.
By 1981, over 65 percent of financial managers surveyed used the IRR, but only
16.5 percent of managers used the NPV.
In a recent study of Fortune 1000 managers, 85 percent of managers used the
NPV while 77 percent used the IRR. Surprisingly, over 50 percent of managers
used the payback method.
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B. Ongoing and Postaudit Reviews
Management should systematically review the status of all ongoing capital
projects and perform postaudits on all completed capital projects.
In a postaudit review, management compares the actual results of a project with
what was projected in the capital budgeting proposal.
A postaudit examination would determine why the project failed to achieve its
expected financial goals.
Managers should also conduct ongoing reviews of capital projects in progress.
The review should challenge the business plan, including the cash flow
projections and the operating cost assumptions.
Management must also evaluate people responsible for implementing a capital
project.
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II. Suggested and Alternative Approaches to the Material
This chapter is about capital budgeting, a topic we first visited in Chapter 1. We open the chapter
with a discussion of the types of capital projects that firms undertake and how the capital
budgeting process is managed within the firm. Next we examine some of the techniques financial
managers use to evaluate capital budgeting decisions. We first discuss the net present value
(NPV) method, which is the capital budgeting approach recommended in this book. We then
examine two other capital budgeting techniques that have some serious deficiencies with regard
to selecting capital projects—the payback period and the accounting rate of return. These
techniques do not consider the time value of money and can lead to decisions that decrease
stockholders’ wealth.
The fourth and last capital budgeting technique discussed in this chapter is the internal
rate of return (IRR), which is the expected rate of return for a capital project. We close the
chapter by looking at survey data that provide information on what capital budgeting techniques
financial managers actually use when making capital decisions.
The instructor can decide to take up the capital budgeting techniques in any order,
although the authors’ intent is to emphasize the net present value as the best possible approach to
capital budgeting decision making.
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III. Summary of Learning Objectives
1. Discuss why capital budgeting decisions are the most important decisions made by a
firm’s management.
Capital budgeting is the process by which management decides which productive assets
the firm should invest in. Because capital expenditures involve large amounts of money,
are critical to achieving the firm’s strategic plan, define the firm’s line of business over
the long term, and determine the firm’s profitability for years to come, they are
considered the most important investment decisions made by management.
2. Explain the benefits of using the net present value (NPV) method to analyze capital
expenditure decisions.
The net present value (NPV) method leads to better investment decisions than other
techniques because the NPV method does the following: (1) uses the discounted cash
flow valuation approach, which accounts for the time value of money, and (2) provides a
direct measure of how much a capital project is expected to increase the dollar value of
the firm. Thus, NPV is consistent with the top management goal of maximizing
stockholders’ wealth. NPV calculations are described in Section 10.2 and Learning by
Doing Application 10.1.
3. Describe the strengths and weaknesses of the payback period as a capital
expenditure decision-making tool, and be able to compute the payback period for a
capital project.
17
The payback period is the length of time it will take for the cash flows from a project to
recover the cost of the project. The payback period is widely used, mainly because it is
simple to apply and easy to understand. It also provides a simple measure of liquidity risk
because it tells management how quickly the firm will get its money back. The payback
period has a number of shortcomings, however. For one thing, the payback period, as
most commonly computed, ignores the time value of money. We can overcome this
objection by using discounted cash flows to calculate the payback period. Regardless of
how the payback period is calculated, it fails to take account of cash flows recovered after
the payback period. Thus, the payback period is biased in favor of short-lived projects.
Also, the hurdle rate used to identify what payback period is acceptable is arbitrarily
determined. Payback period calculations are described in Section 10.3 and Learning by
Doing Application 10.2.
4. Explain why the accounting rate of return (ARR) is not recommended as a capital
expenditure decision-making tool.
The ARR is based on accounting numbers, such as book value and net income, rather
than cash flow data. As such, it is not a true rate of return. Instead of discounting a
project’s cash flows over time, it simply gives us a number based on average figures from
the income statement and balance sheet. Furthermore, as with the payback method, there
is no economic rationale for establishing the hurdle rate. Finally, the ARR does not
account for the size of the projects when a choice between two projects of different sizes
must be made.
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5. Be able to compute the internal rate of return (IRR) for a capital project, and
discuss the conditions under which the internal rate of return (IRR) technique and
the NPV technique produce different results.
The IRR is the expected rate of return for an investment project; it is calculated as the
discount rate that equates the present value of a project’s expected cash inflows to the
present value of the project’s outflows—in other words, as the discount rate at which the
NPV is equal to zero. Calculations are shown in Section 10.5 and Learning by Doing
Application 10.3. If a project’s IRR is greater than the required rate of return, the cost of
capital, the project is accepted. The IRR rule often gives the same investment decision for
a project as the NPV rule. However, the IRR method does have operational pitfalls that
can lead to incorrect decisions. Specifically, when a project’s cash flows are
unconventional, the IRR calculation may yield no solution or more than one IRR. In
addition, the IRR technique cannot be used to rank projects that are mutually exclusive
because the project with the highest IRR may not be the project that would add the
greatest value to the firm if accepted—that is, the project with the highest NPV.
6. Explain the benefits of a postaudit review of a capital project.
Postaudit reviews of capital projects allow management to determine whether the
project’s goals were met and to quantify the benefits or costs of the project. By
conducting these reviews, managers can avoid similar mistakes and possibly better
recognize opportunities.
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IV. Summary of Key Equations
Equation Description Formula
10.1 Net present value
n
0tt
t
nn
22
11
0
)k1(
NCF
)k1(
NCF
)k1(
NCF
)k1(
NCFNCFNPV
10.2 Payback period
10.3 Average rate of returnValue Book Average
IncomeNet AverageARR
10.4 Internal rate of return NPV
10.5Modified internal rate of
returnPVCost = TV/ (1 + MIRR)n
20
V. Before You Go On Questions and Answers
Section 10.1
1. Why are capital investments considered the most important decisions made by a firm’s
management?
Capital investments are the most important decisions made by a firm’s management,
because they usually involve large cash outflows and once made are not easily reversed.
These are usually long-term projects that will define the firm’s line of business and
significantly contribute to the total revenue figure for years to come.
2. What are the differences between capital projects that are independent, mutually
exclusive, and contingent?
A project is independent if the decision to accept or reject it does not affect the decision
to accept or reject another project. On the other hand, projects are mutually exclusive if
the acceptance of one implies rejection of the other. Contingent projects are those in
which the acceptance of one project is dependent on another project.
Section 10.2
1. What is the NPV of a project?
21
NPV is simply the difference between the present value of a project’s expected future
cash flows and its cost. It is the recommended technique used to value capital
investments, as it takes into account both the timing of the cash flows and their risk.
2. If a firm accepts a project with a $10,000 NPV, what is the effect on the value of the firm?
If a firm accepts a project with a $10,000 NPV, it will increase its value by $10,000.
3. What are the five steps used in NPV analysis?
The five-step process used in the NPV analysis can be listed as follows:
(1) Determine the cost of the project.
(2) Estimate the project’s future cash flows over its expected life.
(3) Determine the riskiness of a project and the appropriate cost of capital.
(4) Compute the project’s NPV.
(5) Make a decision.
Section 10.3
1. What is the payback period?
The payback period is defined as the number of years it takes to recover the project’s
initial investment. All other things being equal, the project with the shortest payback
period is usually the optimal investment.
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2. Why does the payback period provide a measure of a project’s liquidity risk?
The payback period determines how quickly you recover your investment in a project.
Thus, it serves as a good measure of the project’s liquidity.
3. What are the main shortcomings of the payback method?
The payback method does not account for time value of money, nor does it distinguish
between high- and low-risk projects. In addition, there is no rationale behind choosing the
cutoff criteria. For all these reasons, the payback method is not the ideal capital decision
rule.
Section 10.4
1. What are the major shortcomings of using the ARR method as a capital budgeting
method?
The biggest shortcoming of using ARR as a capital budgeting tool is that it uses
historical, or book value data rather than cash flows and thus disregards the time value of
money principle. In addition, as in the payback method, it fails to establish a rationale
behind picking the appropriate hurdle rate.
Section 10.5
1. What is the IRR method?
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The IRR, or the internal rate of return, is the discount rate that makes the net present
value of the project’s future cash flows zero. The IRR determines whether the project’s
return rate is higher or lower than the required rate of return, which is the firm’s cost of
capital. As a rule, a project should be accepted if the IRR exceeds the firm’s cost of
capital; otherwise the project should be rejected.
2. In capital budgeting, what is a conventional cash flow?
A conventional project cash flow in capital budgeting is one in which an initial cash
outflow is followed by one or more future cash inflows.
3. Why should the NPV method be the primary decision tool used in making capital
investment decisions?
Given all the different methods to evaluate capital investment decisions, the NPV method
is the preferred valuation tool as it accounts for both time value of money and the
project’s risk. Furthermore, NPV is not sensitive to nonconventional projects, and
therefore it is superior to the IRR technique and it gives a measure of the value
increase/decrease to the firm by taking the project.
Section 10.6
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1. What shifts have taken place in the capital budgeting techniques used by U.S.
companies?
Over the years, there has been a shift from using payback and ARR as the primary capital
budgeting tools to using NPV and IRR instead. Managers nowadays understand the
importance of the time value of money and discounting and thus regard ARR as an
inaccurate and obsolete decision tool.
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VI. Self-Study Problems
10.1 Premium Manufacturing Company is evaluating two forklift systems to use in its plant that
produces the towers for a windmill power farm. The costs and the cash flows from these
systems are shown here. If the company uses a 12 percent discount rate for all projects,
determine which forklift system should be purchased using the net present value (NPV)
PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the
year)
= 6 + ($15,000 / $1,450,000) = 6.01 years
Discount PB = Years before Recovery + (Remaining Cost / Next Year’s CF)
= 8 + ($405,905 / $522,885) = 8.8 years
b. Cost of this project = $4,000,000
Required rate of return = 12%
Length of project = n = 9 years
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Since NPV > 0, the project should be accepted.
c. Given a positive NPV, to compute the IRR, one should try rates higher than 12
percent.
Try IRR = 12.5%.
The IRR is approximately 12.5 percent. Using the financial calculator, we find
that the IRR is 12.539 percent. Based on the IRR exceeding the cost of capital of
12 percent, the project should be accepted.
CFA Problems
10.36. Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent.YEAR 0 1 2 3 4 5CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000
The IRR, found with a financial calculator, is 10.88 percent.
10.37. Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent. The discounted payback period isYEAR 0 1 2 3 4 5CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000
A. 0.16 years longer than the payback period.B. 0.80 years longer than the payback period.C. 1.01 years longer than the payback period.D. 1.85 years longer than the payback period.
As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback period.
10.38. An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to
A. $42.22B. $58.33C. $68.52D. $98.95
95
SOLUTION:B is correct.
3
2 30
CF 40 80 120NPV 100
(1 ) 1.20 1.20 1.20t
tt r
= $58.33
10.39. An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return?
A. 28.19 percentB. 28.39 percentC. 28.59 percentD. 28.79 percent
SOLUTION:D is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent.
A more precise IRR of 28.7854 percent has a total PV closer to zero.
10.40. An investment has an outlay of 100 and after-tax cash flows of 40 annually for four years. A project enhancement increases the outlay by 15 and the annual after-tax cash flows by 5. As a result, the vertical intercept of the NPV profile of the enhanced project shifts
A. up and the horizontal intercept shifts left.B. up and the horizontal intercept shifts right.C. down and the horizontal intercept shifts left.D. down and the horizontal intercept shifts right.
SOLUTION:A is correct. The vertical intercept changes from 60 to 65, and the horizontal intercept changes from 21.86 percent to 20.68 percent.
Sample Test Problems
96
10.1 Net present value: Techno Corp. is considering developing new computer software. The
cost of development will be $675,000, and the company expects the revenue from the sale of
the software to be $195,000 for each of the next six years. If the company uses a discount rate
of 14 percent, what is the net present value of this project?
Solution:
Cost of this project = $675,000
Annual cash flows = $195,000
Required rate of return = 14%
Length of project = n = 6 years
10.2 Payback method: Parker Office Supplies is looking to replace its outdated inventory-
management software. The cost of the new software will be $168,000. Cost savings is
expected to be $43,500 for each of the first three years and then to drop off to $36,875 for the
next two years. What is the payback period for this project?
Solution:
Cumulative
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Year CF CF
0 $(168,000) $(168,000)
1 43,500 (124,500)
2 43,500 (81,000)
3 43,500 (37,500)
4 36,875 (625)
5 36,875 36,250
PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year)
= 4 + ($625 / $36,875) = 4.02 years
10.3 Accounting rate of return: Fresno, Inc., is expecting to generate after-tax income of
$156,435 over each of the next three years. The average book value of its equipment over
that period will be $322,500. If the firm’s acceptance decision on any project is based on
an ARR of 40 percent, should this project be accepted?
Solution:
Annual after-tax income = $156,435
Average after-tax income = $156,435
Average book value of equipment = $322,500
98
Since the project’s ARR is above the acceptance rate of 40 percent, the project should be
accepted.
10.4 Internal rate of return: Refer to Problem 10.1. What is the IRR on this project?
Solution:
Cost of this project = $675,000
Annual cash flows = $195,000
Required rate of return = 14%
Length of project = n = 6 years
Since NPV > 0, try IRR > k. Try IRR = 18%.
Try IRR = 18.4%.
99
The IRR is approximately 18.4 percent. Using the financial calculator, we find that the
IRR is 18.406 percent.
10.5 Net present value: Raycom, Inc., needs a new overhead crane and two alternatives are
available. Crane T costs $1.35 million and will produce cost savings of $765,000 for the
next three years. Crane R will cost the firm $1.675 million and will lead to cost savings
of $815,000 for the next three years. The firm’s required rate of return is 15 percent.
Which of the two options should Raycom choose based on NPV calculations and why?