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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the world of corporate finance.

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

395

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

page 198

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

402

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

403

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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