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Learning Objectives
1. Explain the nature and importance of capital
2.
3.
4.
5.
investment analysis.
Evaluate capital investment proposals using the
average rate of return and cash payback
methods.
Evaluate capital investment proposals using the
net present value and internal rate of return
methods.
List and describe factors that complicate capital
investment analysis.
Diagram the capital rationing process.
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Nature of Capital Investment Analysis
o Capital investment analysis (or capital
budgeting) is the process by which
management plans, evaluates, and controls
investments in fixed assets.
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Nature of Capital Investment Analysis
o Methods that do not use present values
 Average rate of return method
 Cash payback method
o Methods that use present values
 Net present value method
 Internal rate of return method
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NATURE OF CAPITAL
INVESTMENT
ANALYSIS
Nature of Capital Investment Analysis
o The time value of money concept recognizes
that a dollar today is worth more than a dollar
tomorrow because today’s dollar can earn
interest.
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c. 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, or posted to a publicly accessible website, in whole or in part.
Average Rate of Return Method
o The average rate of return, sometimes called
the accounting rate of return, measures the
average income as a percent of the average
investment. The average rate of return is
computed as follows:
Average Rate
of Return =
Estimated Average
Annual Income
Average Investment
(Initial Cost + Residual Value)/2
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Average Rate of Return Method
o Management is evaluating the purchase of a
new machine as follows:
Machine cost
Residual value
Estimated total income from machine
Expected useful life
Average Rate
of Return =
$500,000
0
200,000
4 years
Estimated Average
Annual Income
Average Investment
Average Rate
$200,000/4
=
of Return
($500,000 + $0)/2
= 20%
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Average Rate of Return Method
o The average rate of return of 20% should be
compared to the minimum rate of return
required by management. If the average rate of
return equals or exceeds the minimum rate,
the machine should be purchased or
considered for further analysis.
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Average Rate of Return Method
o The average rate of return has the following
three advantages:
 It is easy to compute.
 It includes the entire amount of income earned over
the life of the proposal.
 It emphasizes accounting income.
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Average Rate of Return Method
o The average rate of return has the following
two disadvantages:
 It does not directly consider the expected cash flows
from the proposal.
 It does not directly consider the timing of the
expected cash flows.
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Cash Payback Method
o The expected period of time that will pass
between the date of an investment and the
complete recovery in cash of the amount
invested is the cash payback period.
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Cash Payback Method
o When annual net cash inflows are equal, the
cash payback period is computed as follows:
Cash
Payback =
Period
Initial Cost
Annual Net
Cash Inflow
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Cash Payback Method
Cost of new machine
Cash revenue from machine per year
Expenses of machine per year
Depreciation per year
$200,000
50,000
30,000
20,000
Net cash inflow per year:
Cash revenue from machine
$50,000
Less cash expenses of machine:
Expenses of machine
$30,000
Less depreciation
20,000 10,000
Net cash inflow per year
$40,000
(continued)
Cash Payback Method
o The time required for the net cash inflow to
equal the cost of the new machine is the
payback period. The estimated cash payback
period for the investment in the machine is five
years, as computed below.
Cash
Payback =
Period
Initial Cost
Annual Net
Cash Inflow
Cash
$200,000
= 5 years
Payback = $40,000
Period
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Cash Payback Method
o Assume that a proposed investment has an
initial cost of $400,000. The annual and
cumulative net cash inflows over the proposal’s
six-year life are as follows:
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Cash Payback Method
o The cash payback method has the following
two advantages:
 It is simple to use and understand.
 It analyzes cash flows.
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Cash Payback Method
o The cash payback method has the following
two disadvantages:
 It ignores cash flows occurring after the payback
period.
 It does not use present value concepts in valuing
cash flows occurring in different periods.
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Present Value Concepts
o Both the net present value and the internal rate
of return methods use the following two
present value concepts:
 Present value of an amount
 Present value of an annuity
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Present Value of an Amount
o If you had $1 to invest for three years at 12%,
how much would you have after one year? By
the end of the second year? By the end of the
third year?
$1 x 1.12 = $1.12
$1.12 x 1.12 = $1.254
$1.254 x 1.12 = $1.404
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Present Value of an Amount
o This process of interest earning interest is
called compounding. The illustration below
demonstrates the concept of compounding.
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Present Value of an Amount
Using the PV of $1 Table
o On January 1, 2014, what is the present value of
$1.404 to be received on December 31, 2016
(assuming an interest rate of 12 percent)? To
determine the answer, we need to go to
Exhibit 1 (next slide) and find the table value
for three years at 12 percent.
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PRESENT VALUE OF
AN AMOUNT
0.712 × $1.404 = $1.00
Present Value of an Amount
o Another way of stating this is that the present
value of $1.404 to be received in three years
using a compound interest rate of 12% is $1, as
shown below.
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Present Value of an Annuity
o An annuity is a series of equal net cash flows at
fixed time intervals.
o The present value of an annuity is the amount
of cash needed today to yield a series of equal
net cash flows at fixed time intervals in the
future.
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Present Value of an Annuity
o The present value of a $100 annuity for five
periods at 12% could be determined by using
the present value factors in Exhibit 1. This is
shown graphically in the next slide.
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PRESENT VALUE OF
AN ANNUITY
Present Value of an Annuity
Using the PV of an Annuity of $1 Table
o Using a present value of an annuity of $1 table,
such as the one in Exhibit 2 (next slide), is a
simpler approach.
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PRESENT VALUE OF
AN ANNUITY
3.605 × $100 = $360.50
Net Present Value Method
o The net present value method compares the
amount to be invested with the present value of
the net cash inflows. It is sometimes called the
discounted cash flow method.
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Net Present Value Method
o Assume the following data for a proposed
investment in new equipment:
Cost of new equipment
$200,000
Expected useful life
5 years
Minimum desired rate of return
10%
Expected cash flows to be received each year:
Year 1
$70,000
Year 2
60,000
Year 3
50,000
Year 4
40,000
Year 5
40,000
Total expected cash flows
$260,000
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Net Present Value Method
o Using the present value of $1 (Exhibit 1) at
10%, the present value of the net cash flow for
each year is shown below.
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Net Present Value Method
o The preceding computations are also
graphically illustrated below.
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Net Present Value Method
o The net present value of $2,900 indicates that
the purchase of the new equipment is
expected to recover the investment and
provide more than the minimum rate of return
of 10%.
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Net Present Value Method
o Capital investment proposals can be ranked by
using a present value index. The present value
index is computed as follows:
Total Present Value
of Net Cash Flow
Present Value Index =
Amount to Be
Invested
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Net Present Value Method
o The present value index for the investment in
the preceding slides is 1.0145, as computed
below.
Total Present Value
of Net Cash Flow
Present Value Index =
Amount to Be
Invested
$202,900
= 1.0145
Present Value Index =
$200,000
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Net Present Value Method
o A company is considering three proposals. The
net present value and the present value index
for each proposal are as follows:
Most desirable proposal
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Net Present Value Method
o The net present value method has the
following three advantages:
 It considers the cash flows of the investment.
 It considers the time value of money.
 It can rank equal lived projects using the present
value index.
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Net Present Value Method
o The net present value method has the
following two disadvantages:
 It has more complex computations than methods
that don’t use present value.
 It assumes the cash flows can be reinvested at the
minimum desired rate of return, which may not be
valid.
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Internal Rate of Return Method
o The internal rate of return (IRR) method uses
present value concepts to compute the rate of
return from a capital investment proposal
based on its expected net cash flows.
o This method, sometimes called the timeadjusted rate of return method, starts with the
proposal’s net cash flows and works backward
to estimate the proposal’s expected rate of
return.
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Internal Rate of Return Method
o Management is evaluating the following
proposal to purchase new equipment:
Cost of new equipment
Yearly expected cash flows to be received
Expected life
Minimum desired rate of return
$33,530
10,000
5 years
12%
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INTERNAL RATE OF
RETURN METHOD
The present value of the net cash flows,
using the present value of an annuity table
(Exhibit 2), is $2,520, as shown below in
Exhibit 3.
Internal Rate of Return Method
o Through trial and error, the rate of return
equating the $33,530 cost of the investment
with the present value of the net cash flows can
be determined to be 15%, as shown on the
next slide.
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INTERNAL RATE OF
RETURN METHOD
Internal Rate of Return Method
o A trial-and-error procedure is time-consuming.
To illustrate a simpler procedure, assume that
management is considering a proposal to
acquire equipment costing $97,360. The
equipment is expected to provide equal annual
net cash flows of $20,000 for seven years.
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Internal Rate of Return Method
STEP 1: Determine the present value factor for an
annuity of $1 as follows:
Amount to be Invested
Equal Annual Net Cash Flows
$97,360
= 4.868
$20,000
(continued)
Internal Rate of Return Method
STEP 2: Find the seven-year line on Exhibit 2
(the present value of an annuity of $1 at
compound interest). Proceed horizontally across
the table until you find the present value factor
computed in Step 1 (or the closest present value
factor).
(continued)
Internal Rate of Return Method
3.605
Internal Rate of Return Method
STEP 3: Now that you have located 4.868 on the
seven-year line, go vertically to the top of the
table to determine the interest rate.
Internal Rate of Return Method
The minimum acceptable
rate of return is 10%.
Internal Rate of Return Method
o The internal rate of return method has the
following three advantages:
 It considers the cash flows of the investment.
 It considers the time value of money.
 It ranks proposals based upon the cash flows over
their complete useful life, even if the project lives
are not the same.
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Internal Rate of Return Method
o The internal rate of return method has the
following two disadvantages:
 It has complex computations, requiring a computer
if the periodic cash flows are not equal (an annuity).
 It assumes the cash received from a proposal can be
reinvested at the internal rate of return, which may
not be valid.
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Factors That Complicate Capital Investment
Analysis
1.
2.
3.
4.
5.
6.
Income tax
Proposals with unequal lives
Leasing versus purchasing
Uncertainty
Changes in price levels
Qualitative factors
Income Tax
o For federal income tax purposes, depreciation
on fixed assets can be much shorter than the
actual useful lives. Also, depreciation for tax
purposes often differs from depreciation for
financial statement purposes.
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Unequal Proposal Lives
o Assume that a company is considering
purchasing a new truck or a new computer
network. The data for each proposal are shown
below.
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UNEQUAL
PROPOSAL LIVES
(continued)
UNEQUAL
PROPOSAL LIVES
Lease versus Capital Investment
o Some advantages of leasing a fixed asset
include the following:
 The company has use of the fixed asset without
spending large amounts of cash to purchase the
asset.
 The company eliminates the risk of owning an
obsolete asset.
 The company may deduct the annual lease
payments for income tax purposes.
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Lease versus Capital Investment
o One disadvantage of leasing a fixed asset is
the following:
 The leasing arrangement normally is more costly
than the outright purchase of the asset.
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Uncertainty
o All capital investment analyses rely on factors
that are uncertain.
 Estimates of revenue and expenses
 The amount of cash flows
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Changes in Price Levels
o General price levels often increase in a rapidly
growing economy, which is called inflation.
o Price levels may change for foreign
investments. This occurs as currency exchange
rates change. Currency exchange rates are the
rates at which currency in another country can
be exchanged for U.S. dollars.
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Qualitative Considerations
o
Improvements that increase quality and
competitiveness are difficult to quantify. The
following qualitative factors are important
considerations.

Product quality

Manufacturing flexibility

Employee morale
 Manufacturing productivity

Market (strategic) opportunities
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Capital Rationing
o Capital rationing is the process by which
management allocates funds among
competing capital investment proposals.
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CAPITAL
RATIONING
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