CHAPTER 19
CAPITAL INVESTMENT
Capital investment decisions are concerned with the acquisition of long-term assets and usually involve a
significant outlay of funds. This chapter covers the basic capital budgeting models and decision making.
Taxes and inflation are considered later in the chapter. The focus of the chapter is on learning how to
apply the models.
LEARNING OBJECTIVES
After studying Chapter 19, students should be able to:
1. Describe the difference between independent and mutually exclusive capital investment decisions.
2. Explain the roles of the payback period and accounting rate of return in capital investment decisions.
3. Calculate the net present value (NPV) for independent projects.
4. Compute the internal rate of return (IRR) for independent projects.
5. Tell why NPV is better than IRR for choosing among mutually exclusive projects.
6. Convert gross cash flows to after-tax cash flows.
7. Describe capital investment for advanced technology and environmental impact settings.
KEY TOPICS
The following major topics are covered in this chapter (related learning objectives are listed for each
topic):
1. Capital Investment Decisions (LO 1)
2. Payback and Accounting Rate of Return: Nondiscounting Methods (LO 2)
3. The Net Present Value Method (LO 3)
4. Internal Rate of Return (LO 4)
5. NPV versus IRR: Mutually Exclusive Projects (LO 5)
6. Computing After-Tax Cash Flows (LO 6)
7. Capital Investment: Advanced Technology and Environmental Considerations (LO 7)
8. Appendix A: Present Value Concepts
I. CAPITAL INVESTMENT DECISIONS
Capital budgeting is the process of making capital investment decisions. Capital investment decisions are
concerned with the process of planning, setting goals and priorities, arranging financing, and using certain
criteria to select long-term assets. With the exception of land, many of the long-term assets acquired will
depreciate over their lives, and the original investment is used up as the assets are employed. In general
terms, a sound capital investment will earn back its original capital outlay over its life and, at the same
time, provide a reasonable return on the original investment.
Capital budgeting decisions are concerned with two types of projects: independent projects and mutually
exclusive projects. Independent projects are projects that, if accepted or rejected, do not affect the cash
flows of another project. Mutually exclusive projects are projects that, if accepted, preclude the
acceptance of all other competing projects.
To make a capital investment decision, a manager must estimate the quantity and timing of cash flows,
assess the risk of the investment, and consider the impact of the project on the firm’s profits. One of the
most difficult tasks is to estimate the cash flows. Projections must be made years into the future, and
forecasting is far from a perfect science.
II. PAYBACK AND ACCOUNTING RATE OF RETURN: NONDISCOUNTING METHODS
Managers must set goals and priorities for capital investments. They also must identify some basic criteria
for the acceptance or rejection of proposed investments. The text addresses four basic methods that can be
used by managers to assist in accepting or rejecting proposed investments. These methods can be
categorized as nondiscounting models and discounting models. Nondiscounting models ignore the time
value of money, whereas discounting models explicitly consider it. There are two methods for each
category.
A. Payback Period
The payback period is the time required for a firm to recover its original investment. When the cash flows
of a project are assumed to be even, the following formula can be used to compute the project’s payback
period:
Payback period = Original investment/Annual cash flow
If, however, the cash flows are uneven, the payback period is computed by adding the annual cash flows
until such time as the original investment is recovered. Cornerstone 19.1 (p. 984) illustrates payback
analysis for both even and uneven cash flows.
The payback period provides managers with information that can be used as follows:
1. To help to control the risks associated with the uncertainty of future cash flows.
2. To help to minimize the impact of an investment on a firm’s liquidity problems.
3. To help to control the risk of obsolescence.
4. To help to control the effect of the investment on performance measures.
However, the method suffers significant deficiencies: it ignores a project’s total profitability and the time
value of money.
B. Accounting Rate of Return
The accounting rate of return (ARR) measures the return on a project in terms of income, as opposed to
using the project’s cash flow. The accounting rate of return is computed by the following formula:
Accounting rate of return = Average income/Original investment
The average income of a project is obtained by adding the income for each year of the project and then
dividing this total by the number of years. Average income is computed by summing annual income over
the life of the project and then dividing by the number of years of the project. Annual income is
approximated as annual cash flow less annual depreciation expense. Average income for a project also
can be approximated by subtracting average depreciation from average cash flow.
Unlike the payback period, the accounting rate of return does consider a project’s profitability; like the
payback period, it ignores the time value of money.
Cornerstone 19.2 (p. 987) illustrates the how and why of calculating the accounting rate of return.
III. THE NET PRESENT VALUE METHOD
Net present value (NPV) is the difference in the present value of the cash inflows and outflows associated
with a project. NPV is a measure of the profitability of an investment:
NPV = P – I
where
P = The present value of the project’s future cash inflows
I = The present value of the project’s cost (usually the initial outlay)
To use the NPV method, a required rate of return must be defined. The required rate of return is the
minimum acceptable rate of return. It is also referred to as the discount rate or the hurdle rate and should
correspond to the cost of capital. The cost of capital is a weighted average of the costs from various
sources, where the weight is defined by the relative amount from each source.
If the NPV > 0, this indicates:
1. The initial investment has been recovered.
2. The required rate of return has been recovered.
3. A return in excess of 1 and 2 has been received.
Thus, the project should be accepted.
If NPV = 0, this indicates:
1. The initial investment has been recovered.
2. The required rate of return has been recovered.
Thus, a break-even scenario has been achieved, and acceptance or rejection of the investment is equal.
If NPV < 0, this indicates:
1. The initial investment may or may not be recovered.
2. The required rate of return has not been recovered.
Thus, the project should be rejected.
Cornerstone 19.3 (p. 988) illustrates the use of NPV.
IV. INTERNAL RATE OF RETURN
The internal rate of return (IRR) is defined as the interest rate that sets the present value of a project’s
cash inflows equal to present value of the project’s cost (the point where NPV = 0).
The decision criteria for IRR are as follows:
• If the IRR > the required rate of return, the project should be accepted.
• If the IRR = the required rate of return, acceptance or rejection is equal.
• If the IRR < the required rate of return, the project should be rejected.
Cornerstone 19.4 (p. 990) shows how the IRR is calculated and used.
Teaching hint: Exercise 19.16 provides a good introductory illustration of IRR.
V. NPV VERSUS IRR: MUTUALLY EXCLUSIVE PROJECTS
Because NPV consistently selects the wealth-maximizing alternative and IRR does not, NPV is generally
preferred to IRR for choosing among mutually exclusive alternatives.
There are two major differences between these two approaches:
1. NPV assumes that each cash inflow received is reinvested at the required rate of return, whereas
the IRR method assumes that each cash inflow is reinvested at the computed IRR.
2. NPV measures profitability in absolute terms, whereas the IRR method measures it in relative
terms.
Selecting the best project from several competing projects involves three steps:
1. Assessing the cash flow pattern for each project
2. Computing the NPV for each project
3. Selecting the project with the greatest NPV
Cornerstone 19.5 (p. 994) illustrates NPV and IRR analysis for mutually exclusive projects.
VI. COMPUTING AFTER-TAX CASH FLOWS
Two steps are needed to compute cash flows:
1. Forecasting revenues, expenses, and capital outlays
2. Adjusting these gross cash flows for inflation and tax effects
Once gross cash flows are estimated, they should be adjusted for significant inflationary effects.
Straightforward applications of tax law can then be used to compute the after-tax cash flows.
A. Conversion of Gross Cash Flows to After-Tax Cash Flows
To analyze tax effects, cash flows are usually broken into three categories:
1. The initial cash outflows needed to acquire the assets of the project
2. The cash flows produced over the life of the project (operating cash flows)
3. The cash flows from the final disposal of the project
Cash outflows and cash inflows adjusted for tax effects are called net cash outflows and inflows. Net cash
flows provide provisions for revenues, operating expenses, depreciation, and relevant tax implications.
Net cash flows are the proper inputs for capital investment decisions.
The net cash outflow in Year 0 (the initial out-of-pocket outlay) is simply the difference between the
initial cost of the project and any cash inflows directly associated with it. The gross cost of the project
includes such things as the cost of land, the cost of equipment, taxes on gains from the sale of assets, and
increases in working capital. Cash inflows occurring at the time of acquisition include tax savings from
the sale of assets, cash from the sale of assets, and other tax benefits such as tax credits.
Under current tax law, all costs relating to the acquisition of assets other than land must be capitalized and
written off over the useful life of the assets. (The write-off is achieved through depreciation.)
Depreciation is deducted from revenues in computing taxable income during each year of the asset’s life;
however, at the point of acquisition, no depreciation expense is computed.
Gains on the sale of assets produce additional taxes and, accordingly, reduce the cash proceeds received
from the sale of old assets. Losses, on the other hand, are noncash expenses that reduce taxable income,
producing tax savings.
In addition to determining the initial out-of-pocket outlay, managers must also estimate the annual after-
tax operating cash flows expected over the life of the project. If the project generates revenue, the
principal source of cash flows is from operations. Operating cash flows can be assessed from the project’s
income statement. The annual after-tax cash flows are the sum of the project’s after-tax profits and its
noncash expenses. In terms of a simple formula, this computation can be represented as follows:
After-tax cash flow = After-tax net income + Noncash expenses
CF = NI + NC
The most prominent examples of noncash expenses are depreciation and losses.
The income approach to determine operating cash flows can be decomposed to assess the after-tax, cash
flow effects of each individual item on the income statement. The decomposition approach calculates the
operating cash flows by computing the after-tax cash flows for each item of the income statement as
follows:
CF = [(1 – Tax rate) × Revenues] – [(1 – Tax rate) × Cash expenses] + (Tax rate × Noncash expenses)
Because cash expenses can be deducted from revenues to arrive at taxable income, the effect is to shield
revenues from taxation. The consequence of this shielding is to save taxes and to reduce the actual cash
outflow associated with a given expenditure. Noncash expenses, such as depreciation, also shield
revenues from taxation and thus create a tax savings. Cornerstone 19.6 (p. 998) illustrates the use of the
income and decomposition approaches for calculating after-tax cash flows.
A taxpayer can use either the straight-line method or the modified accelerated cost recovery system
(MACRS) to compute annual depreciation. MACRS uses double-declining balance with a half-year
convention. This method also switches to the method of straight-line depreciation whenever the straight-
line amount exceeds the double-declining balance amount. Exhibit 19.5 (p. 1000) provides the MACRS
depreciation rates for assets belonging to the three-, five-, and seven-year classes.
At the end of the life of a project, there are two major sources of cash:
1. Release of working capital
2. Preparation, removal, and sale of the equipment
Any working capital committed to a project is released at this point. The release of working capital is a
cash inflow with no tax consequences.
Teaching hint: Begin by asking students how depreciation, a noncash expense, can be part of an after-tax
cash flow computation. Shielding revenues from taxation should be the response. Some students may see
this immediately, but many will not. Ask the students which of the two methods would be preferred:
straight-line depreciation with a half-year convention or MACRS. Most will select MACRS. Ask them to
explain why. Exercise 19.18 provides a good illustration of the tax savings provided by MACRS
compared to the straight-line method of depreciation.
VII. CAPITAL INVESTMENT: ADVANCED TECHNOLOGY AND ENVIRONMENTAL
CONSIDERATIONS
Long-term investments in advanced technology and in pollution prevention (P2) technology can be the
sources of a significant competitive advantage. When making capital investment decisions related to this
type of technology, careful attention must be paid to the inputs used in the discounted cash flow models.
A. How Investment Differs
For automated manufacturing and P2 investments, software, engineering, training, and implementation
make up a significant percentage of the total investment.
B. How Estimates of Operating Cash Flows Differ
Operating cash flows should reflect both tangible and intangible benefits. With advanced technology and
P2 investments, more effort is needed to measure the intangible and indirect benefits in order to assess
more accurately the potential value of investments. Greater quality, more reliability, reduced lead time,
improved customer satisfaction, and an enhanced ability to maintain market share are examples of
important intangible benefits that need to be considered.
C. Salvage Value
Salvage value should be explicitly considered. It may mean the difference between acceptance and
rejection. Sensitivity analysis changes the assumptions on which the capital investment analysis relies and
assesses the effect on the cash flow pattern.
D. Discount Rates
Being overly conservative with discount rates can prove to be damaging. In theory, if future cash flows
are known with certainty, the correct discount rate is a firm’s cost of capital. In practice, future cash flows
are uncertain, and managers often choose a discount rate higher than the cost of capital to deal with that
uncertainty. If the rate chosen is excessively high, it will bias the selection process toward short-term
investments.
VIII. APPENDIX A: PRESENT VALUE CONCEPTS
A. Future Value
Future value is the value that will accumulate by the end of an investment’s life if the investment earns a
specified compound return. The future value of a dollar invested today is the original dollar plus the
return (or interest) accumulated over time. Future value can be expressed by the following equation:
F = P(1 + i)
where
F = The future amount
P = The initial or current outlay
i = The interest rate
B. Present Value
Present value is the current value of a future cash flow. It represents the amount that must be invested now if the
future cash flow is to be received assuming compounding at a given rate of interest. The process of computing the
present value of future cash flows is called discounting. Discounting can be done either by using the equation
directly for computing the present value or by using the tabled discount factors in Appendix B. Exhibit 19B.1 (p.
1010) presents the values for computing the present value of a single payment. Exhibit 19B.2 (p. 1011)
presents the values for computing the present value of an annuity.
Teaching hint: Work the following scenarios during class using the present value tables in Exhibits 19B.1
and 19B.2 in Appendix B, pages 1010 and 1011. Each example becomes progressively more difficult.
1. How much will I need to deposit today in a fund paying 24 percent, compounded annually, in
order to have $10,000 at the end of four years?
2. How much will I need to deposit today in a fund paying 24 percent, compounded semiannually,
in order to have $10,000 at the end of four years?
3. How much will I need to deposit today in a fund paying 24 percent, compounded quarterly, in
order to have $10,000 at the end of four years?
4. How much will I need to deposit today in a fund paying 10 percent, compounded annually, in
order to be able to withdraw $1,000 at the end of year 1, $3,000 at the end of year 2, and $5,000
at the end of year 3?
5. How much will I need to deposit today in a fund paying 10 percent, compounded annually, in
order to be able to withdraw $2,000 annually for the next five years?
First, solve these five problems using Exhibit 19B.1. Then, discuss how to use Exhibit 19B.2 to simplify
the calculations for the last problem.
You may also want to illustrate how a single sum as well as an annuity will grow over a period of time
given compound interest.
IX. INFORMATION ABOUT EXERCISES, PROBLEMS, AND CASES
Exercises and problems are described below and on the following page according to coverage of content,
learning objective(s), and level of difficulty. The time required to solve the problems is roughly
proportional to the level of difficulty.
In general, basic exercises/problems are fairly simple and straightforward. The text material is relatively
brief; only one or two concepts are covered. Basic exercises and problems should take about 15 to 20
minutes each.
Moderate exercises/problems may take longer and involve more concepts. These problems may have a
“twist” and require more thought. Moderate exercises and problems may take 20 to 40 minutes each.
Challenging problems are more comprehensive and may cover more concepts. The text material is
relatively longer and may include some ambiguity. Challenging problems may take 60 to 90 minutes
each.
Cornerstone
Exercise (CS)/
Exercise/
Problem/Case
Topic
Learning
Objective
Degree of
Difficulty
CS 19.1
Payback Period
LO 2
Basic
CS 19.2
Accounting Rate of Return
LO 2
Basic
CS 19.3
Net Present Value
LO 3
Basic
CS 19.4
Internal Rate of Return
LO 4
Basic
CS 19.5
NPV Versus Internal Rate of Return
LO 5
Basic
CS 19.6
After-Tax Cash Flows
LO 6
Basic
19.7
Payback and ARR
LO 2
Basic
19.8
Future Value, Present Value
Appendix
Basic
19.9
NPV and IRR
LO 1, 3, 4
Basic
19.10
Basic Concepts
LO 1, 2, 3, 4
Basic
19.11
NPV
LO 1, 3
Basic
19.12
Payback, Accounting Rate of Return
LO 1, 2
Basic
19.13
NPV: Basic Concepts
LO 3
Basic
19.14
Solving for Unknowns
LO 3, 4
Basic
19.15
Advanced Technology, Payback, NPV, IRR,
Sensitivity Analysis
LO 2, 3, 4, 5, 7
Moderate
19.16
NPV Versus IRR
LO 5
Moderate
19.17
Computation of After-Tax Cash Flows
LO 6
Basic
19.18
MACRS, NPV
LO 3, 6
Moderate
19.19
CPA-Type Exercise
LO 3
Basic
19.20
CPA-Type Exercise
LO 3
Basic
19.21
CPA-Type Exercise
LO 4
Basic
19.22
CPA-Type Exercise
LO 3
Basic
Cornerstone
Exercise (CS)/
Exercise/
Problem/Case
Topic
Learning
Objective
Degree of
Difficulty
19.23
CPA-Type Exercise
LO 2
Basic
19.24
Pollution Prevention, P2 Investment
LO 2, 3, 4, 5,
6, 7
Moderate
19.25
Discount Rates, Quality, Market Share,
Contemporary Manufacturing Environment
LO 3, 5, 7
Moderate
19.26
Competing P2 Investments
LO 3, 5, 6, 7
Moderate
19.27
Payback, NPV, Managerial Incentives, Ethical
Behavior
LO 1, 2, 3
Moderate
19.28
Basic IRR Analysis
LO 1, 4
Moderate
19.29
Replacement Decision, Computing After-Tax Cash
Flows, Basic NPV Analysis
LO 1, 3, 5, 6
Moderate
19.30
Capital Investment, Discount Rates, Intangible and
Indirect Benefits, Time Horizon, Contemporary
Manufacturing Environment
LO 3, 6, 7
Challenging
19.31
NPV, Make or Buy, MACRS, Basic Analysis
LO 3, 6
Moderate
19.32
Structured Problem Solving, Cash Flows, NPV, Choice
of Discount Rate, Advanced Manufacturing
Environment
LO 3, 6, 7
Challenging
19.33
Cyber Research Case
LO 1, 2, 3, 4, 7
Challenging
LIST OF ILLUSTRATIONS
Illustration
Topic
Exhibit 19.1
NPV and IRR: Conflicting Signals
Exhibit 19.2
Modified Comparison of Projects A and B
Exhibit 19.3
Modified Cash Flows with Additional Opportunity
Exhibit 19.4
Tax Effects of the Sale of M1 and M2
Exhibit 19.5
MACRS Depreciation Rates
Exhibit 19.6
Value of Accelerated Methods Illustrated
Exhibit 19.7
Investment Data: Direct, Intangible, and Indirect Benefits
Exhibit 19A.1
Present Value of an Uneven Series of Cash Flows
Exhibit 19A.2
Present Value of a Uniform Series of Cash Flows
Exhibit 19B.1
Present Value of $1
Exhibit 19B.2
Present Value of an Annuity of $1 in Arrears