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2. This implies that the cash inflows are
sufficient to recover the $3,169 initial
investment and to provide exactly a 10%
return on the investment
IV. The internal rate of return method
Learning Objective 3: Evaluate the acceptability of an
investment project using the internal rate of return
method.
A. Key concepts
i. The internal rate of return is the rate of
return promised by an investment project over
its useful life. It is sometimes referred to as
the yield on a project.
ii. The internal rate of return is the discount rate
that will result in a net present value of zero.
iii. This technique works very well if a project’s
cash flows are identical every year. If the cash
flows are not identical every year a trial-and-
error process can be used to find the internal
rate of return.
iv. If the internal rate of return is equal to or
greater than the minimum required rate of
return, then the project is acceptable. If it is
less than the required rate of return, then the
project is rejected.
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v. When using internal rate of return, the cost of
capital acts as a hurdle rate that a project
must clear for acceptance.
B. Internal rate of return – an example
i. Assume the facts as shown with respect to the
Decker Company.
ii. Since the cash flows are the same every year,
the equation shown can be used to compute
the appropriate present value factor of 5.216.
iii. Using the present value of an annuity of $1
table, the internal rate of return equals 14%.
iv. If Decker’s minimum required rate of return
is equal to or greater than 14%, then the
machine should be purchased.
Quick Check – internal rate of return calculations
C. Comparing the net present value and internal rate
of return methods
i. The net present value method offers two
important advantages over the internal rate
of return method.
1. The net present value method is often
simpler to use.
2. The internal rate of return method makes a
questionable assumption—that cash
inflows can be reinvested at the internal rate
of return.
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a. If the internal rate of return is high,
this assumption may be unrealistic. It
is more realistic to assume that the
cash flows can be reinvested at the
discount rate, which is the underlying
assumption of the net present value
method.
V. Expanding the net present value method
A. We will now expand the net present value method to
include two alternatives. We will analyze the
alternatives using the total cost approach.
B. Net present value analysis: an expanded example
i. Assume that White Co. has two
alternatives—remodel an old car wash or
remove the old car wash and replace it with a
new one.
1. The company uses a discount rate of 10%.
2. The net annual cash inflows are $60,000 for
the new car wash and $45,000 for the old car
wash.
ii. In addition, assume that the information as
shown relates to the installation of a new
washer.
iii. The net present value of installing a new
washer is $83,202.
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iv. If White chooses to remodel the existing
washer, the remodeling costs would be
$175,000 and the cost to replace the brushes
at the end of six years would be $80,000.
v. The net present value of remodeling the old
washer is $56,405.
vi. While both projects yield a positive net
present value, the net present value of the new
washer alternative is $26,797 higher than the
remodeling alternative.
C. Least cost decisions
i. In decisions where revenues are not directly
involved, managers should choose the
alternative that has the least total cost from a
present value perspective.
ii. Home Furniture Company – an example
(we will analyze this decision using the total-
cost approach.
1. Assume the following:
a. Home Furniture Company is trying to
decide whether to overhaul an old
delivery truck or purchase a new one.
b. The company uses a discount rate of
10%.
2. The information pertaining to the old and
new trucks is as shown.
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3. The net present value of buying a new truck
is ($32,883). The net present value of
overhauling the old truck is ($42,255).
a. Notice both numbers are negative
because there is no revenue involved
– this is a least cost decision.
4. The net present value in favor of purchasing
the new truck is $9,372.
VI. Uncertain cash flows
Learning Objective 4: Evaluate an investment project
that has uncertain cash flows.
A. Handling the complication of uncertain future cash
flows – an example
i. Assume that all of the cash flows related to an
investment in a supertanker have been
estimated except for its salvage value in 20
years.
1. Using a discount rate of 12%, management
has determined that the net present value of
all the cash flows except the salvage value is
a negative $1.04 million.
2. This negative net present value will be offset
by the salvage value of the supertanker.
3. How large would the salvage value need
to be to make this investment attractive?
ii. The equation shown can be used to determine
that if the salvage value of the supertanker is
at least $10 million, the net present value of
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the investment would be positive and
therefore acceptable.
1. While the salvage value is not known with
certainty, the $10 million dollar figure offers
a useful reference point for making the
decision.
Quick Check – uncertain cash flows
VII. Preference decisions – the ranking of investment
projects
Learning Objective 5: Rank investment projects in
order of preference.
A. Background
i. Recall that when considering investment
opportunities, managers must make two types
of decisions – screening decisions and
preference decisions.
1. Screening decisions, which come first,
pertain to whether or not some proposed
investment is acceptable.
2. Preference decisions, which come after
screening decisions, attempt to rank
acceptable alternatives from the most to
least appealing.
a. Preference decisions need to be made
because the number of acceptable
investment alternatives usually
exceeds the amount of available funds.
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B. Internal rate of return method
i. When using the internal rate of return method
to rank competing investment projects, the
preference rule is: the higher the internal
rate of return, the more desirable the
project.
C. Net present value method
i. The net present value of one project cannot
be directly compared to the net present
value of another project unless the
investments are equal.
ii. In the case of unequal investments, a project
profitability index can be computed as
shown. Notice:
1. The project profitability indexes for
investments A and B are 0.01 and 0.20,
respectively.
2. The higher the project profitability index,
the more desirable the project. Therefore,
investment B is more desirable than
investment A.
3. Since in this type of situation, the
constrained resource is the limited funds
available for investment, the project
profitability index is similar to the
contribution margin per unit of the
constrained resource discussed in an earlier
chapter.
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VIII. The simple rate of return method
Learning Objective 6: Compute the simple rate of
return for an investment.
i. Key concepts
1. The simple rate of return method (also
known as the accounting rate of return or
the unadjusted rate of return) does not
focus on cash flows, rather it focuses on
accounting net operating income.
2. The equation for computing the simple rate
of return is as shown.
ii. The Daily Grind – an example
1. Assume the management of the Daily Grind
wants to install an espresso bar in its
restaurant.
a. The cost of the espresso bar is
$140,000 and it has a 10-year life.
b. The espresso bar will generate
incremental revenues of $100,000 and
incremental expenses of $65,000
including depreciation.
c. What is the simple rate of return on
this project?
2. The simple rate of return is 25%.
iii. Criticisms of the simple rate of return
1. It does not consider the time value of
money.
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2. The simple rate of return fluctuates from
year to year when used to evaluate projects
that do not have constant annual incremental
revenues and expenses.
a. The same project may appear desirable
in some years and undesirable in
others.
iv. The behavioral implications of the simple
rate of return
1. When investment center managers are
evaluated using return on investment (ROI),
a project’s simple rate of return may
motivate them to bypass investment
opportunities that earn positive net present
values.
IX. Postaudit of investment projects
A. A postaudit is a follow-up after the project has been
completed to see whether or not expected results were
actually realized.
i. The data used in a postaudit analysis should
be actual observed data rather than
estimated data.
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