Harvard Chapter 7 & 8 Net Present Value and Other Investment Rules Paper Review the attached Chapters 7 & 8.
In this posting, you should also answer the following question:
Include Finance Concepts discussed in Chapter 7 & 8
What is the role of the NPV process in selecting a specific project for investment? page 195
Net Present Value
and Other
Investment Rules
7
OPENING
CASE
In February 2016, Ford announced that it would spend about $1
billion to build a new plant in Sal Luis Potosí, Mexico, to compete
with Toyota’s Prius. This followed Ford’s announcement the
previous year that it would invest $2.5 billion in two new plants in
Mexico to manufacture engines and transmissions. Ford was not
alone in new building in the auto industry. Rival GM was
expected to announce that it would spend $5 billion in new plants
in Mexico as well.
Ford’s new plants are examples of capital budgeting
decisions. Decisions such as this one, with a price tag of $3.5
billion, are obviously major undertakings, and the risks and
rewards must be carefully weighed. In this chapter, we discuss
the basic tools used in making such decisions.
In Chapter 1, we saw that increasing the value of the stock in
a company is the goal of financial management. Thus, what we
need to know is how to tell whether a particular investment will
achieve that or not. This chapter considers a variety of
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techniques that are used in practice for this purpose. More
importantly, it shows how many of these techniques can be
misleading, and it explains why the net present value approach is
the right one.
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7.1 WHY USE NET PRESENT VALUE?
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This chapter, as well as the next two, focuses on capital budgeting, the
decision-making process for accepting or rejecting projects. This chapter
develops the basic capital budgeting methods, leaving much of the
practical application to Chapters 8 and 9. But we don’t have to develop
these methods from scratch. In Chapter 4, we pointed out that a dollar
received in the future is worth less than a dollar received today. The
reason, of course, is that today’s dollar can be reinvested, yielding a
greater amount in the future. And we showed in Chapter 4 that the exact
worth of a dollar to be received in the future is its present value.
Furthermore, Section 4.1 suggested calculating the net present value of
any project. That is, the section suggested calculating the difference
between the sum of the present values of the project’s future cash flows
and the initial cost of the project.
The net present value (NPV) method is the first one to be considered in
this chapter. We begin by reviewing the approach with a simple example.
Next, we ask why the method leads to good decisions.
Find out more about capital budgeting for small businesses at
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page 196
EXAMPLE
7.1
Net Present Value
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The Alpha Corporation is considering investing in a riskless project
costing $100. The project receives $107 in one year and has no other
cash flows. The discount rate is 6 percent.
The NPV of the project can easily be calculated as:
From Chapter 4, we know that the project should be accepted since its
NPV is positive. Had the NPV of the project been negative, as would
have been the case with an interest rate greater than 7 percent, the
project should be rejected.
The basic investment rule can be generalized to:
Accept a project if the NPV is greater than zero.
Reject a project if the NPV is less than zero.
We refer to this as the NPV rule.
Now why does the NPV rule lead to good decisions? Consider the
following two strategies available to the managers of Alpha Corporation:
1. Use $100 of corporate cash to invest in the project. The $107 will be
paid as a dividend in one year.
2. Forgo the project and pay the $100 of corporate cash as a dividend
today.
If Strategy 2 is employed, the stockholder might deposit the dividend in
his bank for one year. With an interest rate of 6 percent, Strategy 2 would
produce cash of $106 (= $100 × 1.06) at the end of the year. The
stockholder would prefer Strategy 1, since Strategy 2 produces less than
$107 at the end of the year.
Thus, our basic point is:
Accepting positive NPV projects benefits the stockholders.
You can get a freeware NPV calculator at www.wheatworks.com.
How do we interpret the exact NPV of $.94? This is the increase in the
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value of the firm from the project. For example, imagine that the firm
today has productive assets worth $V and has $100 of cash. If the firm
forgoes the project, the value of the firm today would simply be:
If the firm accepts the project, the firm will receive $107 in one year but
will have no cash today. Thus, the firm’s value today would be:
The difference between the above equations is just $.94, the present value
of Example 7.1. Thus:
The value of the firm rises by the NPV of the project.
Note that the value of the firm is merely the sum of the values of the
different projects, divisions, or other entities within the firm. This
property, called value additivity, is quite important. It implies that the
contribution of any project to a firm’s value is simply the NPV of the
project. As we will see later, alternative methods discussed in this chapter
do not generally have this nice property.
One detail remains. We assumed that the project was riskless, a rather
implausible assumption. Future cash flows of real-world projects are
invariably risky. In other words, cash flows can only be
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estimated, rather than known. Imagine that the managers of
Alpha expect the cash flow of the project to be $107 next year. That is, the
cash flow could be higher, say $117, or lower, say $97. With this slight
change, the project is risky. Suppose the project is about as risky as the
stock market as a whole, where the expected return this year is, say, 10
percent. Then 10 percent becomes the discount rate, implying that the
NPV of the project would be:
Since the NPV is negative, the project should be rejected. This makes
sense because a stockholder of Alpha receiving a $100 dividend today
could invest it in the stock market, expecting a 10 percent return. Why
accept a project with the same risk as the market but with an expected
return of only 7 percent?
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Conceptually, the discount rate on a risky project is the return that one
can expect to earn on a financial asset of comparable risk. This discount
rate is often referred to as an opportunity cost, since corporate investment
in the project takes away the stockholder’s opportunity to invest the same
cash in a financial asset. The calculation is by no means impossible. While
we forgo the calculation in this chapter, we present it in Chapter 12 of the
text.
Having shown that NPV is a sensible approach, how can we tell
whether alternative methods are as good as NPV? The key to NPV is its
three attributes:
1. NPV Uses Cash Flows. Cash flows from a project can be used for
other corporate purposes (e.g., dividend payments, other capital
budgeting projects, or payments of corporate interest). By contrast,
earnings are an artificial construct. While earnings are useful to
accountants, they should not be used in capital budgeting because
they do not represent cash.
2. NPV Uses All the Cash Flows of the Project. Other approaches ignore
cash flows beyond a particular date; beware of these approaches.
3. NPV Discounts the Cash Flows Properly. Other approaches may
ignore the time value of money when handling cash flows. Beware of
these approaches as well.
Calculating NPVs by hand can be tedious. A nearby Spreadsheet
Techniques box shows how to do it the easy way and also illustrates an
important caveat.
7.2 THE PAYBACK PERIOD METHOD
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Defining the Rule
One of the most popular alternatives to NPV is payback. Here is how
payback works: Consider a project with an initial investment of −$50,000.
Cash flows are $30,000, $20,000, and $10,000 in the first three years,
respectively. These flows are illustrated in Figure 7.1. A useful way of
writing down investments like the preceding is with the notation:
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FIGURE 7.1
Cash Flows of an Investment Project
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SPREADSHEET
TECHNIQUES
Calculating NPVs with a
Spreadsheet
Spreadsheets are commonly used to calculate NPVs. Examining the use
of spreadsheets in this context also allows us to issue an important
warning. Consider the following:
In our spreadsheet example, notice that we have provided two
answers. The first answer is wrong even though we used the
spreadsheet’s NPV formula. What happened is that the “NPV” function in
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our spreadsheet is actually a PV function; unfortunately, one of the original
spreadsheet programs many years ago got the definition wrong, and
subsequent spreadsheets have copied it! Our second answer shows how
to use the formula properly.
The example here illustrates the danger of blindly using calculators or
computers without understanding what is going on; we shudder to think of
how many capital budgeting decisions in the real world are based on
incorrect use of this particular function.
The minus sign in front of the $50,000 reminds us that this is a cash
outflow for the investor, and the commas between the different numbers
indicate that they are received—or if they are cash outflows, that they are
paid out—at different times. In this example we are assuming that the cash
flows occur one year apart, with the first one occurring the moment we
decide to take on the investment.
The firm receives cash flows of $30,000 and $20,000 in the first two
years, which add up to the $50,000 original investment. This means that
the firm has recovered its investment within two years. In this case two
years is the payback period of the investment.
The payback period rule for making investment decisions is simple and
potentially informative. The payback tells us when the cash outflow of an
investment is “paid back” by cash inflows. If a particular cutoff date, say
two years, is selected, all investment projects that have payback periods of
two years or less are accepted and all of those that pay off in more than
two years—if at all—are rejected.
Problems with the Payback Method
There are at least three problems with payback. To illustrate the first two
problems, we consider the three projects in Table 7.1. All three projects
have the same three-year payback period, so they should all be equally
attractive—right?
TABLE 7.1
Expected Cash Flows for Projects A through C ($)
YEAR
A
B
C
0
−$100
−$100
−$100
1
20
50
50
2
30
30
30
3
50
20
20
400
4
60
60
100
Payback period (years)
3
3
3
Actually, they are not equally attractive, as can be seen by a
comparison of different pairs of projects. To illustrate the payback period
problems, consider Table 7.1. Suppose the expected return on comparable
risky projects is 10 percent. Then we would use a discount rate of 10
percent for these projects. If so, the NPV would be $21.5, $26.3, and $53.6
for A, B and C, respectively. When using the payback
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period, these projects are equal to one another (i.e., they
each have a payback period of three years). However, when considering all
cash flows, B has a higher NPV than A because of the timing of cash flows
within the payback period. And C has the highest NPV because of the
$100 cash flow after the payback period.
PROBLEM 1: TIMING OF CASH FLOWS WITHIN THE PAYBACK
PERIOD Let us compare Project A with Project B. In Years 1 through 3,
the cash flows of Project A rise from $20 to $50, while the cash flows of
Project B fall from $50 to $20. Because the large cash flow of $50 comes
earlier with Project B, its net present value must be higher. Nevertheless,
we saw above that the payback periods of the two projects are identical.
Thus, a problem with the payback method is that it does not consider the
timing of the cash flows within the payback period. This example shows
that the payback method is inferior to NPV because, as we pointed out
earlier, the NPV method discounts the cash flows properly.
PROBLEM 2: PAYMENTS AFTER THE PAYBACK PERIOD
Now consider Projects B and C, which have identical cash flows within the
payback period. However, Project C is clearly preferred because it has a
cash flow of $60,000 in the fourth year. Thus, another problem with the
payback method is that it ignores all cash flows occurring after the
payback period. Because of the short-term orientation of the payback
method, some valuable long-term projects are likely to be rejected. The
NPV method does not have this flaw since, as we pointed out earlier, this
method uses all the cash flows of the project.
PROBLEM 3: ARBITRARY STANDARD FOR PAYBACK
PERIOD We do not need to refer to Table 7.1 when considering a third
problem with the payback method. Capital markets help us estimate the
discount rate used in the NPV method. The riskless rate, perhaps proxied
401
by the yield on a Treasury instrument, would be the appropriate rate for a
riskless investment. Later chapters of this textbook show how to use
historical returns in the capital markets in order to estimate the discount
rate for a risky project. However, there is no comparable guide for
choosing the payback cutoff date, so the choice is somewhat arbitrary.
Managerial Perspective
The payback method is often used by large, sophisticated companies when
making relatively small decisions. The decision to build a small
warehouse, for example, or to pay for a tune-up for a truck is the sort of
decision that is often made by lower-level management. Typically, a
manager might reason that a tune-up would cost, say, $200, and if it saved
$120 each year in reduced fuel costs, it would pay for itself in less than
two years. On such a basis the decision would be made.
Although the treasurer of the company might not have made the
decision in the same way, the company endorses such decision making.
Why would upper management condone or even encourage such
retrograde activity in its employees? One answer would be that it is easy to
make decisions using payback. Multiply the tune-up decision into 50 such
decisions a month, and the appeal of this simple method becomes clearer.
The payback method also has some desirable features for managerial
control. Just as important as the investment decision itself is the
company’s ability to evaluate the manager’s decision-making ability.
Under the NPV method, a long time may pass before one
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decides whether or not a decision was correct. With the
payback method we may know in just a few years whether the manager’s
assessment of the cash flows was correct.
It has also been suggested that firms with good investment
opportunities but no available cash may justifiably use payback. For
example, the payback method could be used by small, privately held firms
with good growth prospects but limited access to the capital markets.
Quick cash recovery enhances the reinvestment possibilities for such
firms.
Finally, practitioners often argue that standard academic criticisms of
payback overstate any real-world problems with the method. For example,
textbooks typically make fun of payback by positing a project with low
cash inflows in the early years but a huge cash inflow right after the
payback cutoff date. This project is likely to be rejected under the payback
method, though its acceptance would, in truth, benefit the firm. Project C
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in our Table 7.1 is an example of such a project. Practitioners point out
that the pattern of cash flows in these textbook examples is much too
stylized to mirror the real world. In fact, a number of executives have told
us that, for the overwhelming majority of real-world projects, both
payback and NPV lead to the same decision. In addition, these executives
indicate that, if an investment like Project C were encountered in the real
world, decision makers would almost certainly make ad hoc adjustments
to the payback rule so that the project would be accepted.
Notwithstanding all of the preceding rationale, it is not surprising to
discover that as the decisions grow in importance, which is to say when
firms look at bigger projects, NPV becomes the order of the day. When
questions of controlling and evaluating the manager become less important
than making the right investment decision, payback is used less frequently.
For big-ticket decisions, such as whether or not to buy a machine, build a
factory, or acquire a company, the payback method is seldom used.
Summary of Payback
The payback method differs from NPV and is therefore conceptually
wrong. With its arbitrary cutoff date and its blindness to cash flows after
that date, it can lead to some flagrantly foolish decisions if it is used too
literally. Nevertheless, because of its simplicity, as well as its other
advantages mentioned above, companies often use it as a screen for
making the myriad minor investment decisions they continually face.
Although this means that you should be wary of trying to change
approaches such as the payback method when you encounter them in
companies, you should probably be careful not to accept the sloppy
financial thinking they represent. After this course, you would do your
company a disservice if you used payback instead of NPV when you had a
choice.
7.3 THE DISCOUNTED PAYBACK
PERIOD METHOD
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Aware of the pitfalls of payback, some decision makers use a variant
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called the discounted payback period method. Under this approach, we
first discount the cash flows. Then we ask how long it takes for the
discounted cash flows to equal the initial investment.
For example, suppose that the discount rate is 10 percent and the cash
flows for a project are given by:
This investment has a payback period of two years, because the investment
is paid back in that time.
To compute the project’s discounted payback period, we first discount
each of the cash flows at the 10 percent rate. These discounted cash flows
are:
The discounted payback period of the original investment is simply the
payback period for these discounted cash flows. The payback period for
the discounted cash flows is slightly less than three years since the
discounted cash flows over the three years are $101.80 (= page 201
$45.45 + 41.32 + 15.03). As long as the cash flows are
positive, the discounted payback period will never be smaller than the
payback period, because discounting reduces the value of the cash flows.
At first glance, discounted payback may seem like an attractive
alternative, but on closer inspection we see that it has some of the same
major flaws as payback. Like payback, discounted payback first requires
us to make a somewhat magical choice of an arbitrary cutoff period, and
then it ignores all of the cash flows after that date.
If we have already gone to the trouble of discounting the cash flows,
any small appeal to simplicity or to managerial control that payback may
have has been lost. We might just as well add up all the discounted cash
flows and use NPV to make the decision. Although discounted payback
looks a bit like NPV, it is just a poor compromise between the payback
method and NPV.
7.4 THE AVERAGE ACCOUNTING
RETURN METHOD
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Defining the Rule
Another attractive, but fatally flawed, approach to capital budgeting is the
average accounting return. The average accounting return is the average
project earnings after taxes and depreciation, divided by the average book
value of the investment during its life. In spite of its flaws, the average
accounting return method is worth examining because it is used frequently
in the real world.
EXAMPLE
7.2
Average Accounting Return
Consider a company that is evaluating whether to buy a store in a new
mall. The purchase price is $500,000. We will assume that the store
has an estimated life of five years and will need to be completely
scrapped or rebuilt at the end of that time. The projected yearly sales
and expense figures are shown in Table 7.2.
TABLE 7.2
Proj…
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