Chapter 09 – Net Present Value and Other Investment Criteria
Chapter 9
NET PRESENT VALUE AND OTHER INVESTMENT
CRITERIA
CHAPTER ORGANIZATION
9.1 Net Present Value
The Basic Idea
Estimating Net Present Value
9.2 The Payback Rule
Defining the Rule
Analyzing the Rule
Redeeming Qualities of the Rule
Summary of the Rule
9.3 The Discounted Payback
9.4 The Average Accounting Return
9.5 The Internal Rate of Return
Problems with the IRR
Redeeming Qualities of the IRR
The Modified Internal Rate of Return (MIRR)
9.6 The Profitability Index
9.7 The Practice of Capital Budgeting
9.8 Summary and Conclusions
ANNOTATED CHAPTER OUTLINE
Lecture Tip: A logical prerequisite to the analysis of investment
opportunities is the creation of investment opportunities. Unlike
the field of investments, where the analyst more or less takes the
investment opportunity set as a given, the field of capital
budgeting relies on the work of people in the areas of engineering,
research and development, information technology and others for
the creation of investment opportunities. As such, it is important to
remind students of the importance of creativity in this area, as well
as the importance of analytical techniques.
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Chapter 09 – Net Present Value and Other Investment Criteria
1. Net Present Value
A. The Basic Idea
Net present value – the difference between the market value of an
investment and its cost. Estimating cost is usually straightforward;
however, finding the market value of assets can be tricky. The
principle is to find the market price of comparables.
Lecture Tip: You may wish to take the opportunity to use this
example to illustrate the interpretation of NPV and its relationship
to organizational form. Specifically, assume that, in order to raise
the $50,000 needed to buy and rehab the house in the text example,
you had sold 50,000 shares of stock in the venture for $1 apiece.
Your father purchased 15,000 shares, your brother purchased
15,000 shares, and you purchased the remaining 20,000 shares.
How much are the shares worth upon the sale of the house for
$60,000? Your father’s share of the selling price is $18,000
=(15,000/50,000)(60,000), as is your brother’s. Your share is
$24,000 =(20,000/50,000)(60,000). In other words, the value
created accrued to the owners of the investment. This is the
essence of the NPV approach: The NPV measures the increase in
firm value, which is also the increase in the value of what the
shareholders own. Thus, making decisions with the NPV rule
facilitates the achievement of our goal in Chapter 1 – making
decisions that will maximize shareholder wealth.
B. Estimating Net Present Value
Lecture Tip: Although this point may seem obvious, it is often
helpful to stress the word “net” in net present value. It is not
uncommon for some students to carelessly calculate the PV of a
project’s future cash flows and fail to subtract out its cost (after all
this is what the programmers of Excel did when they programmed
the NPV function). The PV of future cash flows is not NPV; rather,
NPV is the amount remaining after offsetting the PV of future cash
flows with the initial cost. Thus, the NPV amount determines the
incremental value created by undertaking the investment.
Discounted cash flow (DCF) valuation – finding the market value
of assets or their benefits by taking the present value of future cash
flows, i.e., by estimating what the future cash flows would trade
for in today’s dollars.
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Chapter 09 – Net Present Value and Other Investment Criteria
Lecture Tip: Here’s another perspective on the meaning of NPV. If
we accept a project with a negative NPV of -$2,422, this is
financially equivalent to investing $2,422 today and receiving
nothing in return. Therefore, the total value of the firm would
decrease by $2,422. This assumes that the various components
(cash flow estimates, discount rate, etc.) used are correct.
Lecture Tip: In practice, financial managers are rarely presented
with zero NPV projects for at least two reasons. First, in an
abstract sense, zero is just another of the infinite number of values
the NPV can take; as such, the likelihood of obtaining any
particular number is small. Second, and more pragmatically, in
most large firms, capital investment proposals are submitted to the
finance group from other areas for analysis. Those submitting
proposals recognize the ambivalence associated with zero NPVs
and are less likely to send them to the finance group in the first
place.
Conceptually, a zero-NPV project earns exactly its required return.
Assuming that risk has been adequately accounted for, investing in
a zero-NPV project is equivalent to purchasing a financial asset in
an efficient market. In this sense, one would be indifferent between
the capital expenditure project and the financial asset investment.
Further, since firm value is completely unaffected by the
investment, there is no reason for shareholders to prefer either
one.
However, several real-world considerations make such
comparisons difficult. For example, adjusting for risk in capital
budgeting projects can be problematic. And, some investment
projects may have benefits that are difficult to quantify, but exist,
nonetheless. Consider an investment with a low or zero NPV that
enhances a firm’s image as a good corporate citizen. Additionally,
the secondary market for most physical assets is less efficient than
the secondary market for financial assets. While, in theory, you
can adjust for differences in liquidity, it is problematic. Finally, all
else equal, some investors prefer larger firms to smaller; if true,
investing in any project with a nonnegative NPV may be desirable.
Ethics Note: Because a project is financially sound, it must be
ethically sound, right? Well … the question of ethical
appropriateness is less frequently discussed in the context of
capital budgeting than that of financial appropriateness.
Consider the following simple example. An ABC poll in the spring
of 2004 found that one-third of students 12 – 17 admitted to
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Chapter 09 – Net Present Value and Other Investment Criteria
cheating and the percentage increased as the students got older
and felt more grade pressure. You might pose the ethical question
of whether it would be proper for a publishing company to offer a
new book “How to Cheat: A User’s Guide.” The company has a
cost of capital of 8% and estimates it could sell 10,000 volumes by
the end of year one and 5,000 volumes in each of the following two
years. The immediate printing costs for the 20,000 volumes would
be $20,000. The book would sell for $7.50 per copy and net the
company a profit of $6 per copy after royalties, marketing costs
and taxes. Year one net would be $60,000.
From a capital budgeting standpoint, is it financially wise to buy
the publication rights? What is the NPV of this investment? The
year 0 cash flow is -20,000, year 1 is 60,000, and years 2 and 3
are 30,000 each. Given a cost of capital of 8%, the NPV is just
over $85,000. It looks good, right? Now ask the class if the
publishing of this book would encourage cheating and if the
publishing company would want to be associated with this text and
its message. Some students may feel that one should accept these
profitable investment opportunities, while others might prefer that
the publication of this profitable text be rejected due to the
behavior it could encourage. Although the example is simplistic,
this type of issue is not uncommon and serves as a starting point
for a discussion of the value of “reputational capital.”
2. The Payback Rule
A. Defining the Rule
Payback period – length of time until the accumulated cash flows
equal or exceed the original investment.
Payback period rule – investment is acceptable if its calculated
payback is less than some prespecified number of years.
B. Analyzing the Rule
-No discounting involved
-Doesn’t consider risk differences
-How do we determine the cutoff point
-Biased toward short-term investments
Real-World Tip: Teaching the payback rule seems to put one in a
delicate situation – as the text indicates, the rule is flawed as an
indicator of project desirability. Yet, past surveys suggest that
practitioners often use it as a secondary decision measure. How
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Chapter 09 – Net Present Value and Other Investment Criteria
can we explain this apparent discrepancy between theory and
practice?
While the payback period is widely used in practice, it is rarely the
primary decision criterion. As William Baumol pointed out in the
early 1960s, the payback rule serves as a crude “risk screening”
device – the longer cash is tied up, the greater the likelihood that it
will not be returned. The payback period may be helpful when
mutually exclusive projects are compared. Given two similar
projects with different paybacks, the project with the shorter
payback is often, but not always, the better project.
C. Redeeming Qualities of the Rule
-Simple to use
-Bias for short-term promotes liquidity
Real-World Tip: Interestingly, the payback period technique is
used quite heavily in determining the viability of certain
investment projects in the health care industry. Why? Consider the
nature of the health care industry: the technology is rapidly
changing, some of the equipment tends to be extremely expensive,
and the industry itself is increasingly competitive. What this means
is that, in many cases, an equipment purchase is complicated by
the fact that, while the machine may be able to perform its function
for, say, 6 years or more, new and improved equipment is likely to
be developed that will supersede the “old” equipment long before
its useful life is over. Demand from patients and physicians for
“cutting-edge technology” can drive a push for new investment. In
the face of such a situation, many hospital administrators then
focus on how long it will take to recoup the initial outlay, in
addition to the NPV and IRR of the equipment.
D. Summary of the Rule
Advantages:
Easy to understand
Adjusts for uncertainty of later cash flows
Biased towards liquidity
Disadvantages:
Ignores the time value of money
Requires an arbitrary cutoff point
Ignores cash flows beyond the cutoff date
Biased against long-term projects
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Chapter 09 – Net Present Value and Other Investment Criteria
Lecture Tip: The payback period can be interpreted as a naïve
form of discounting if we consider the class of investments with
level cash flows over arbitrarily long lives. Since the present value
of a perpetuity is the payment divided by the discount rate, a
payback period cutoff can be seen to imply a certain discount rate.
cost/annual cash flow = payback period cutoff
cost = annual cash flow times payback period cutoff
The PV of a perpetuity is: PV = annual cash flow / R. This
illustrates the inverse relationship between the payback period
cutoff and the discount rate.
International Note: Firms that have operations in countries with
volatile governments may also be concerned with quick paybacks.
When there is always a possibility that the government may seize
your assets, you want to make sure that you can recover your
investment as quickly as possible.
3. The Discounted Payback
Discounted payback rule – An investment is acceptable if its
discounted payback is less than some prespecified number of
years.
Lecture Tip: The discounted payback period is the length of time
until accumulated discounted cash flows equal or exceed the
initial investment. Use of this technique entails all the work of
NPV, but its decision rule is arbitrary. Redeeming features of this
approach are that (1) the time value of money is accounted for and
(2) if the project pays back on a discounted basis, it has a positive
NPV (assuming no large negative cash flows after the cut-off
period).
Advantages
-All those of the simple payback rule, plus, the time value of
money is taken into account
-If a project pays back on a discounted basis, and has all positive
cash flows after the initial investment, then it must have a positive
NPV
Disadvantages
-The arbitrary cut-off period may eliminate projects that would
increase firm value
-If there are negative cash flows after the cut-off period, the rule
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Chapter 09 – Net Present Value and Other Investment Criteria
may indicate acceptance of a project that has a negative NPV
4. The Average Accounting Return
The average accounting return = measure of accounting profit /
measure of average accounting value. In other words, it is a
benefit/cost ratio that produces a pseudo rate of return. However,
due to the accounting conventions involved, the lack of risk
adjustment and the use of profits rather than cash flows, it isn’t
clear what is being measured.
The text gives the following specific definition:
AAR = average net income / average book value
Average accounting return rule – project is acceptable if its AAR
return exceeds a target return.
-Since it involves accounting figures rather than cash flows, it is
not comparable to returns in capital markets
-It treats money in all periods as having the same value
-There is no objective way to find the cutoff rate
Real-World Tip: Surveys indicate that few large firms employ the
payback period and/or the AAR methods exclusively; rather, these
techniques are used in conjunction with one or more of the DCF
techniques. On the other hand, anecdotal evidence suggests that
many smaller firms rely more heavily on non-DCF approaches.
Reasons for this include: (1) small firms don’t have direct access
to the capital markets and therefore find it more difficult to
estimate discount rates based on funds cost; (2) the AAR is the
project-level equivalent to the ROA measure used for
analyzing firm profitability; and (3) some small firm decision-
makers may be less aware of DCF approaches than their large
firm counterparts.
Lecture Tip: An alternative view of the AAR is that it is the micro-
level analogue to the ROA discussed in a previous chapter. As you
remember, firm ROA is normally computed as Firm Net Income /
Firm Total Assets. And, it is not uncommon to employ values
averaged over several quarters or years in order to smooth out
this measure. Some analysts ask, “If the ROA is appropriate for
the firm, why is it less appropriate for a project?” Perhaps the best
answer is that whether you compute the measure for the firm or for
a project, you need to recognize the limitations – it doesn’t account
for risk or the time value of money and it is based on accounting,
rather than market, data.
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Chapter 09 – Net Present Value and Other Investment Criteria
5. The Internal Rate of Return
Internal rate of return (IRR) – the rate that makes the present value
of the future cash flows equal to the initial cost or investment. In
other words, the discount rate that gives a project a $0 NPV.
IRR decision rule – the investment is acceptable if its IRR exceeds
the required return.
Ethics Note: Assume that to comply with the Air Quality Control
Act of 1989, a company must install three smoke stack scrubber
units to its ventilation stacks at an installed cost of $355,000 per
unit. An estimated $100,000 per unit in fines could be saved per
stack each year over the five-year life of the ventilation stacks. The
cost of capital is 14% for the firm. The analysis of the investment
results in a NPV of -$35,076.
Despite the financial assessment dictating rejection of the
investment, public policy might suggest acceptance of the project.
Should the firm exceed the minimum legal limits and be
responsible for the environment, even if this responsibility leads to
a wealth reduction for the firm? Is environmental damage merely a
cost of doing business? Could investment in a healthier working
environment result in lower long-term costs in the form of lower
future health costs? If so, might this decision result in an increase
in shareholder wealth? Notice that if the answer to this second
question is yes, it suggests that our original analysis omitted some
side benefits to the project.
Net present value profile – plot of an investment’s NPV at various
discount rates.
NPV and IRR comparison: If a project’s cash flows are
conventional (costs are paid early and benefits are received over
the life), and if the project is independent, then NPV and IRR will
give the same accept or reject decision.
A. Problems with the IRR
Non-conventional cash flows – the sign of the cash flows changes
more than once or the cash inflow comes first and outflows come
later.
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Chapter 09 – Net Present Value and Other Investment Criteria
If the cash flows are of loan type, meaning money is received at
the beginning and paid out over the life of the project, then the IRR
is really a borrowing rate and lower is better.
If cash flows change sign more than once, then you will have
multiple internal rates of return. This is problematic for the IRR
rule; however, the NPV rule still works fine.
Mutually exclusive investment decisions – taking one project
means another cannot be taken
Lecture Tip: A good introduction to mutually exclusive projects
and non-conventional cash flows is to provide examples that
students can relate to. An excellent example of mutually exclusive
projects is the choice of which college or university to attend.
Many students apply and are accepted to more than one college,
yet they cannot attend more than one at a time. Consequently, they
have to decide between mutually exclusive projects.
Nonconventional cash flows and multiple IRRs occur when there is
a net cost to shutting down a project. The most common examples
deal with collecting natural resources. After the resource has been
harvested, there is generally a cost associated with restoring the
environment.
Another type of nonconventional cash flow involves a “financing”
project, where there is a positive cash flow followed by a series of
negative cash flows. This is the opposite of an “investing” project.
In this case, our decision rule reverses, and we accept a project if
the IRR is less than the cost of capital, since we are borrowing at a
lower rate.
B. Redeeming Qualities of the IRR
-People seem to prefer talking about rates of return to dollars of
value
-NPV requires a market discount rate; IRR relies only on the
project cash flows, although you do need an estimate of a required
return to make the final decision
C. The Modified Internal Rate of Return (MIRR)
One method for eliminating multiple IRRs and removing the
assumption of reinvestment of cash flow at the IRR is to use the
Modified Internal Rate of Return (MIRR). Discount all cash
outflows to the present, and compound all cash inflows to the last
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Chapter 09 – Net Present Value and Other Investment Criteria
period of the project. Then, find the rate that equates the values.
The discounting and compounding can be done at borrowing and
investment rates, respectively.
6. The Profitability Index
Profitability index – present value of future cash flows divided by
the initial investment.
Technically, this is true only if the initial investment is the only
outflow. If there are additional outflows after year 0, then the
profitability index = present value of inflows / present value of
outflows.
If a project has a positive NPV, then the PI will be greater than 1.
7. The Practice of Capital Budgeting
It is common among large firms to employ a discounted cash flow
technique such as IRR or NPV along with payback period or
average accounting return. It is suggested that this is one way to
resolve the considerable uncertainty over future events that
surrounds the estimation of NPV.
Lecture Tip: While uncertainty about inputs and interpretation of
the outputs helps explain why multiple criteria are used to judge
capital investment projects in practice, another reason is
managerial performance assessment. When managers are judged
and rewarded primarily on the basis of periodic accounting
figures, there is an incentive to evaluate projects with methods
such as payback or average accounting return. On the other hand,
when compensation is tied to firm value, it makes more sense to
use NPV as the primary decision tool.
Ethics Note: The use of various financial incentives to induce
firms to locate in a given municipality raises some interesting
issues in the capital budgeting area. From the viewpoint of the
firm’s analysts, how do you estimate the impact of such incentives?
A reduction in the initial outlay? Increases in future cash inflows?
And what discount rate should be assigned to these tax reductions?
Are these promises riskless?
And what about the municipal officials who offer such incentives?
Stated reasons are typically related to “employment growth” or
“increased economic activity.” But, from a capital budgeting
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Chapter 09 – Net Present Value and Other Investment Criteria
standpoint, have you ever seen a fully developed cash flow
analysis of the stated benefits relative to the costs?
Consider this example from a Federal Reserve publication:
“Alabama offered Mercedes-Benz a package valued
at more than the cost of the plant itself. To lure the
$300 million plant, with about 1,500 jobs, the state
promised to buy the site for $30 million, and lease it
to Mercedes for $100. Surrounding communities
will contribute an additional $5 million each, and
the University of Alabama will offer German
language and culture classes to the children of
plant employees. On top of this, the state will
provide a package of tax breaks valued at more
than $300 million, which will, among other things,
allow the plant to be paid for with money that
would have been paid to the state.”
Several incentives described above directly affect the costs and
benefits of the proposed project and would be accounted for in the
capital budgeting analysis performed by Mercedes. However, the
state officials should perform their own capital budgeting analysis
– they, too, are incurring economic costs in the hope of future
benefits. But at least one aspect is different: when a corporation
makes a poor investment, shareholders suffer. When states make
poor decisions, all of the residents of the state suffer. Thus, the
ethics of the capital budgeting decision come into play more
clearly in the latter case.
Video Note: “Capital Budgeting” looks at how Navistar International does its capital
budgeting analysis.
8. Summary and Conclusions
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