Brealey−Meyers: Principles of Corporate Finance, 7th Edition - Chapter 2 pps

Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
CHAPTER TWO
12
P R E S E N T V A L U E
A N D T H E
OPPORTUNITY
COST OF CAPITAL
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
COMPANIES INVEST IN a variety of real assets. These include tangible assets such as plant and ma-
chinery and intangible assets such as management contracts and patents. The object of the invest-
ment, or capital budgeting, decision is to find real assets that are worth more than they cost. In this
chapter we will take the first, most basic steps toward understanding how assets are valued.
There are a few cases in which it is not that difficult to estimate asset values. In real estate, for ex-
ample, you can hire a professional appraiser to do it for you. Suppose you own a warehouse. The odds
are that your appraiser’s estimate of its value will be within a few percent of what the building would
actually sell for.
1
After all, there is continuous activity in the real estate market, and the appraiser’s
stock-in-trade is knowledge of the prices at which similar properties have recently changed hands.

Thus the problem of valuing real estate is simplified by the existence of an active market in which all
kinds of properties are bought and sold. For many purposes no formal theory of value is needed. We
can take the market’s word for it.
But we need to go deeper than that. First, it is important to know how asset values are reached in
an active market. Even if you can take the appraiser’s word for it, it is important to understand why
that warehouse is worth, say, $250,000 and not a higher or lower figure. Second, the market for most
corporate assets is pretty thin. Look in the classified advertisements in The Wall Street Journal: It is
not often that you see a blast furnace for sale.
Companies are always searching for assets that are worth more to them than to others. That ware-
house is worth more to you if you can manage it better than others. But in that case, looking at the
price of similar buildings will not tell you what the warehouse is worth under your management. You
need to know how asset values are determined. In other words, you need a theory of value.
This chapter takes the first, most basic steps to develop that theory. We lead off with a simple nu-
merical example: Should you invest to build a new office building in the hope of selling it at a profit
next year? Finance theory endorses investment if net present value is positive, that is, if the new
building’s value today exceeds the required investment. It turns out that net present value is positive
in this example, because the rate of return on investment exceeds the opportunity cost of capital.
So this chapter’s first task is to define and explain net present value, rate of return, and oppor-
tunity cost of capital. The second task is to explain why financial managers search so assiduously
for investments with positive net present values. Is increased value today the only possible finan-
cial objective? And what does “value” mean for a corporation?
Here we will come to the fundamental objective of corporate finance: maximizing the current mar-
ket value of the firm’s outstanding shares. We will explain why all shareholders should endorse this
objective, and why the objective overrides other plausible goals, such as “maximizing profits.”
Finally, we turn to the managers’ objectives and discuss some of the mechanisms that help to align
the managers’ and stockholders’ interests. We ask whether attempts to increase shareholder value
need be at the expense of workers, customers, or the community at large.
In this chapter, we will stick to the simplest problems to make basic ideas clear. Readers with a
taste for more complication will find plenty to satisfy them in later chapters.
13

1
Needless to say, there are some properties that appraisers find nearly impossible to value—for example, nobody knows the po-
tential selling price of the Taj Mahal or the Parthenon or Windsor Castle.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
Your warehouse has burned down, fortunately without injury to you or your em-
ployees, leaving you with a vacant lot worth $50,000 and a check for $200,000 from
the fire insurance company. You consider rebuilding, but your real estate adviser
suggests putting up an office building instead. The construction cost would be
$300,000, and there would also be the cost of the land, which might otherwise be
sold for $50,000. On the other hand, your adviser foresees a shortage of office space
and predicts that a year from now the new building would fetch $400,000 if you
sold it. Thus you would be investing $350,000 now in the expectation of realizing
$400,000 a year hence. You should go ahead if the present value (PV) of the ex-
pected $400,000 payoff is greater than the investment of $350,000. Therefore, you
need to ask, What is the value today of $400,000 to be received one year from now,
and is that present value greater than $350,000?
Calculating Present Value
The present value of $400,000 one year from now must be less than $400,000. After
all, a dollar today is worth more than a dollar tomorrow, because the dollar today can
be invested to start earning interest immediately. This is the first basic principle of
finance. Thus, the present value of a delayed payoff may be found by multiplying
the payoff by a discount factor which is less than 1. (If the discount factor were
more than 1, a dollar today would be worth less than a dollar tomorrow.) If C
1

de-
notes the expected payoff at period 1 (one year hence), then
Present value (PV) ϭ discount factor ϫ C
1
This discount factor is the value today of $1 received in the future. It is usually ex-
pressed as the reciprocal of 1 plus a rate of return:
The rate of return r is the reward that investors demand for accepting delayed
payment.
Now we can value the real estate investment, assuming for the moment that the
$400,000 payoff is a sure thing. The office building is not the only way to obtain
$400,000 a year from now. You could invest in United States government securities
maturing in a year. Suppose these securities offer 7 percent interest. How much
would you have to invest in them in order to receive $400,000 at the end of the
year? That’s easy: You would have to invest $400,000/1.07, which is $373,832.
2
Therefore, at an interest rate of 7 percent, the present value of $400,000 one year
from now is $373,832.
Let’s assume that, as soon as you’ve committed the land and begun construc-
tion on the building, you decide to sell your project. How much could you sell it
for? That’s another easy question. Since the property will be worth $400,000 in a
year, investors would be willing to pay $373,832 for it today. That’s what it would
Discount factor ϭ
1
1 ϩ r
14 PART I
Value
2.1 INTRODUCTION TO PRESENT VALUE
2
Let’s check this. If you invest $373,832 at 7 percent, at the end of the year you get back your initial in-
vestment plus interest of .07 ϫ 373,832 ϭ $26,168. The total sum you receive is 373,832 ϩ 26,168 ϭ

$400,000. Note that 373,832 ϫ 1.07 ϭ $400,000.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
cost them to get a $400,000 payoff from investing in government securities. Of
course, you could always sell your property for less, but why sell for less than the
market will bear? The $373,832 present value is the only feasible price that satis-
fies both buyer and seller. Therefore, the present value of the property is also its
market price.
To calculate present value, we discount expected payoffs by the rate of return
offered by equivalent investment alternatives in the capital market. This rate of
return is often referred to as the discount rate, hurdle rate, or opportunity cost
of capital. It is called the opportunity cost because it is the return foregone by in-
vesting in the project rather than investing in securities. In our example the op-
portunity cost was 7 percent. Present value was obtained by dividing $400,000
by 1.07:
Net Present Value
The building is worth $373,832, but this does not mean that you are $373,832 bet-
ter off. You committed $350,000, and therefore your net present value (NPV) is
$23,832. Net present value is found by subtracting the required investment:
NPV ϭ PV Ϫ required investment ϭ 373,832 Ϫ 350,000 ϭ $23,832
In other words, your office development is worth more than it costs—it makes a
net contribution to value. The formula for calculating NPV can be written as
remembering that C
0
, the cash flow at time 0 (that is, today), will usually be a neg-

ative number. In other words, C
0
is an investment and therefore a cash outflow. In
our example, C
0
ϭϪ$350,000.
A Comment on Risk and Present Value
We made one unrealistic assumption in our discussion of the office development:
Your real estate adviser cannot be certain about future values of office buildings.
The $400,000 represents the best forecast, but it is not a sure thing.
If the future value of the building is risky, our calculation of NPV is wrong.
Investors could achieve $400,000 with certainty by buying $373,832 worth of
United States government securities, so they would not buy your building
for that amount. You would have to cut your asking price to attract investors’
interest.
Here we can invoke a second basic financial principle: A safe dollar is worth more
than a risky one. Most investors avoid risk when they can do so without sacrificing
return. However, the concepts of present value and the opportunity cost of capital
still make sense for risky investments. It is still proper to discount the payoff by the
rate of return offered by an equivalent investment. But we have to think of expected
payoffs and the expected rates of return on other investments.
3
NPV ϭ C
0
ϩ
C
1
1 ϩ r
PV ϭ discount factor ϫ C
1

ϭ
1
1 ϩ r
ϫ C
1
ϭ
400,000
1.07
ϭ $373,832
CHAPTER 2
Present Value and the Opportunity Cost of Capital 15
3
We define “expected” more carefully in Chapter 9. For now think of expected payoff as a realistic fore-
cast, neither optimistic nor pessimistic. Forecasts of expected payoffs are correct on average.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
Not all investments are equally risky. The office development is more risky
than a government security but less risky than a start-up biotech venture. Suppose
you believe the project is as risky as investment in the stock market and that stock
market investments are forecasted to return 12 percent. Then 12 percent becomes
the appropriate opportunity cost of capital. That is what you are giving up by not
investing in equally risky securities. Now recompute NPV:
NPV ϭ PV Ϫ 350,000 ϭ $7,143
If other investors agree with your forecast of a $400,000 payoff and your assess-
ment of its risk, then your property ought to be worth $357,143 once construction

is underway. If you tried to sell it for more, there would be no takers, because the
property would then offer an expected rate of return lower than the 12 percent
available in the stock market. The office building still makes a net contribution to
value, but it is much smaller than our earlier calculations indicated.
The value of the office building depends on the timing of the cash flows and
their uncertainty. The $400,000 payoff would be worth exactly that if it could be
realized instantaneously. If the office building is as risk-free as government se-
curities, the one-year delay reduces value to $373,832. If the building is as risky
as investment in the stock market, then uncertainty further reduces value by
$16,689 to $357,143.
Unfortunately, adjusting asset values for time and uncertainty is often more
complicated than our example suggests. Therefore, we will take the two effects
separately. For the most part, we will dodge the problem of risk in Chapters 2
through 6, either by treating all cash flows as if they were known with certainty or
by talking about expected cash flows and expected rates of return without worry-
ing how risk is defined or measured. Then in Chapter 7 we will turn to the prob-
lem of understanding how financial markets cope with risk.
Present Values and Rates of Return
We have decided that construction of the office building is a smart thing to do,
since it is worth more than it costs—it has a positive net present value. To calcu-
late how much it is worth, we worked out how much one would need to pay to
achieve the same payoff by investing directly in securities. The project’s present
value is equal to its future income discounted at the rate of return offered by
these securities.
We can say this in another way: Our property venture is worth undertaking
because its rate of return exceeds the cost of capital. The rate of return on the in-
vestment in the office building is simply the profit as a proportion of the initial
outlay:
The cost of capital is once again the return foregone by not investing in securities.
If the office building is as risky as investing in the stock market, the return foregone

is 12 percent. Since the 14 percent return on the office building exceeds the 12 per-
cent opportunity cost, you should go ahead with the project.
Return ϭ
profit
investment
ϭ
400,000 Ϫ 350,000
350,000
ϭ .143, about 14%
PV ϭ
400,000
1.12
ϭ $357,143
16 PART I Value
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
Here then we have two equivalent decision rules for capital investment:
4
• Net present value rule. Accept investments that have positive net present values.
• Rate-of-return rule. Accept investments that offer rates of return in excess of
their opportunity costs of capital.
5
The Opportunity Cost of Capital
The opportunity cost of capital is such an important concept that we will give one
more example. You are offered the following opportunity: Invest $100,000 today,

and, depending on the state of the economy at the end of the year, you will receive
one of the following payoffs:
CHAPTER 2
Present Value and the Opportunity Cost of Capital 17
4
You might check for yourself that these are equivalent rules. In other words, if the return
50,000/350,000 is greater than r, then the net present value Ϫ 350,000 ϩ [400,000/(1 ϩ r)] must be greater
than 0.
5
The two rules can conflict when there are cash flows in more than two periods. We address this prob-
lem in Chapter 5.
6
We are assuming that the probabilities of slump and boom are equal, so that the expected (average)
outcome is $110,000. For example, suppose the slump, normal, and boom probabilities are all 1/3. Then
the expected payoff C
1
ϭ (80,000 ϩ 110,000 ϩ 140,000)/3 ϭ $110.000.
Slump Normal Boom
$80,000 $110,000 $140,000
You reject the optimistic (boom) and the pessimistic (slump) forecasts. That gives
an expected payoff of C
1
ϭ 110,000,
6
a 10 percent return on the $100,000 investment.
But what’s the right discount rate?
You search for a common stock with the same risk as the investment. Stock X
turns out to be a perfect match. X’s price next year, given a normal economy, is fore-
casted at $110. The stock price will be higher in a boom and lower in a slump, but
to the same degrees as your investment ($140 in a boom and $80 in a slump). You

conclude that the risks of stock X and your investment are identical.
Stock X’s current price is $95.65. It offers an expected rate of return of 15 percent:
This is the expected return that you are giving up by investing in the project rather
than the stock market. In other words, it is the project’s opportunity cost of capital.
To value the project, discount the expected cash flow by the opportunity cost of
capital:
This is the amount it would cost investors in the stock market to buy an expected cash
flow of $110,000. (They could do so by buying 1,000 shares of stock X.) It is, therefore,
also the sum that investors would be prepared to pay you for your project.
To calculate net present value, deduct the initial investment:
NPV ϭ 95,650 Ϫ 100,000 ϭϪ$4,350
PV ϭ
110,000
1.15
ϭ $95,650
Expected return ϭ
expected profit
investment
ϭ
110 Ϫ 95.65
95.65
ϭ .15, or 15%
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
The project is worth $4,350 less than it costs. It is not worth undertaking.

Notice that you come to the same conclusion if you compare the expected proj-
ect return with the cost of capital:
The 10 percent expected return on the project is less than the 15 percent return in-
vestors could expect to earn by investing in the stock market, so the project is not
worthwhile.
Of course in real life it’s impossible to restrict the future states of the economy
to just “slump,” “normal,” and “boom.” We have also simplified by assuming a
perfect match between the payoffs of 1,000 shares of stock X and the payoffs to the
investment project. The main point of the example does carry through to real life,
however. Remember this: The opportunity cost of capital for an investment project
is the expected rate of return demanded by investors in common stocks or other se-
curities subject to the same risks as the project. When you discount the project’s ex-
pected cash flow at its opportunity cost of capital, the resulting present value is the
amount investors (including your own company’s shareholders) would be willing
to pay for the project. Any time you find and launch a positive-NPV project (a proj-
ect with present value exceeding its required cash outlay) you have made your
company’s stockholders better off.
A Source of Confusion
Here is a possible source of confusion. Suppose a banker approaches. “Your company
is a fine and safe business with few debts,” she says. “My bank will lend you the
$100,000 that you need for the project at 8 percent.” Does that mean that the cost of
capital for the project is 8 percent? If so, the project would be above water, with PV at
8 percent ϭ 110,000/1.08 ϭ $101,852 and NPV ϭ 101,852 Ϫ 100,000 ϭϩ$1,852.
That can’t be right. First, the interest rate on the loan has nothing to do with the risk
of the project: It reflects the good health of your existing business. Second, whether you
take the loan or not, you still face the choice between the project, which offers an ex-
pected return of only 10 percent, or the equally risky stock, which gives an expected
return of 15 percent. A financial manager who borrows at 8 percent and invests at
10 percent is not smart, but stupid, if the company or its shareholders can borrow at
8 percent and buy an equally risky investment offering 15 percent. That is why the

15 percent expected return on the stock is the opportunity cost of capital for the project.
ϭ
110,000 Ϫ 100,000
100,000
ϭ .10, or 10%
Expected return on project ϭ
expected profit
investment
18 PART I Value
2.2 FOUNDATIONS OF THE NET PRESENT VALUE
RULE
So far our discussion of net present value has been rather casual. Increasing value
sounds like a sensible objective for a company, but it is more than just a rule of
thumb. You need to understand why the NPV rule makes sense and why managers
look to the bond and stock markets to find the opportunity cost of capital.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
In the previous example there was just one person (you) making 100 percent of
the investment and receiving 100 percent of the payoffs from the new office build-
ing. In corporations, investments are made on behalf of thousands of shareholders
with varying risk tolerances and preferences for present versus future income.
Could a positive-NPV project for Ms. Smith be a negative-NPV proposition for Mr.
Jones? Could they find it impossible to agree on the objective of maximizing the
market value of the firm?
The answer to both questions is no; Smith and Jones will always agree if both have

access to capital markets. We will demonstrate this result with a simple example.
How Capital Markets Reconcile Preferences for Current
vs. Future Consumption
Suppose that you can look forward to a stream of income from your job. Unless you
have some way of storing or anticipating this income, you will be compelled to con-
sume it as it arrives. This could be inconvenient or worse. If the bulk of your income
comes late in life, the result could be hunger now and gluttony later. This is where the
capital market comes in. The capital market allows trade between dollars today and
dollars in the future. You can therefore eat moderately both now and in the future.
We will now illustrate how the existence of a well-functioning capital market
allows investors with different time patterns of income and desired consump-
tion to agree on whether investment projects should be undertaken. Suppose
that there are two investors with different preferences. A is an ant, who wishes
to save for the future; G is a grasshopper, who would prefer to spend all his
wealth on some ephemeral frolic, taking no heed of tomorrow. Now suppose
that each is confronted with an identical opportunity—to buy a share in a
$350,000 office building that will produce a sure-fire $400,000 at the end of the
year, a return of about 14 percent. The interest rate is 7 percent. A and G can bor-
row or lend in the capital market at this rate.
A would clearly be happy to invest in the office building. Every hundred dollars
that she invests in the office building allows her to spend $114 at the end of the year,
while a hundred dollars invested in the capital market would enable her to spend
only $107.
But what about G, who wants money now, not in one year’s time? Would he pre-
fer to forego the investment opportunity and spend today the cash that he has in
hand? Not as long as the capital market allows individuals to borrow as well as to
lend. Every hundred dollars that G invests in the office building brings in $114 at
the end of the year. Any bank, knowing that G could look forward to this sure-fire
income, would be prepared to lend him $114/1.07 ϭ $106.54 today. Thus, instead
of spending $100 today, G can spend $106.54 if he invests in the office building and

then borrows against his future income.
This is illustrated in Figure 2.1. The horizontal axis shows the number of dol-
lars that can be spent today; the vertical axis shows spending next year. Suppose
that the ant and the grasshopper both start with an initial sum of $100. If they
invest the entire $100 in the capital market, they will be able to spend 100 ϫ 1.07
ϭ $107 at the end of the year. The straight line joining these two points (the in-
nermost line in the figure) shows the combinations of current and future con-
sumption that can be achieved by investing none, part, or all of the cash at the
7 percent rate offered in the capital market. (The interest rate determines the
slope of this line.) Any other point along the line could be achieved by spending
CHAPTER 2
Present Value and the Opportunity Cost of Capital 19
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
part of the $100 today and investing the balance.
7
For example, one could choose
to spend $50 today and $53.50 next year. However, A and G would each reject
such a balanced consumption schedule.
The burgundy arrow in Figure 2.1 shows the payoff to investing $100 in a share
of your office project. The rate of return is 14 percent, so $100 today transmutes to
$114 next year.
The sloping line on the right in Figure 2.1 (the outermost line in the figure)
shows how A’s and G’s spending plans are enhanced if they can choose to invest
their $100 in the office building. A, who is content to spend nothing today, can in-

vest $100 in the building and spend $114 at the end of the year. G, the spendthrift,
also invests $100 in the office building but borrows 114/1.07 ϭ $106.54 against the
future income. Of course, neither is limited to these spending plans. In fact, the
right-hand sloping line shows all the combinations of current and future expendi-
ture that an investor could achieve from investing $100 in the office building and
borrowing against some fraction of the future income.
You can see from Figure 2.1 that the present value of A’s and G’s share in the
office building is $106.54. The net present value is $6.54. This is the distance be-
20 PART I
Value
7
The exact balance between present and future consumption that each individual will choose depends
on personal preferences. Readers who are familiar with economic theory will recognize that the choice
can be represented by superimposing an indifference map for each individual. The preferred combina-
tion is the point of tangency between the interest-rate line and the individual’s indifference curve. In
other words, each individual will borrow or lend until 1 plus the interest rate equals the marginal rate
of time preference (i.e., the slope of the indifference curve). A more formal graphical analysis of invest-
ment and the choice between present and future consumption is on the Brealey–Myers website at
www://mhhe.com/bm/7e.
Dollars now
A
invests $100 in office
building and consumes $114
next year.
106.54
114
107
Dollars next year
G
invests $100 in office

building, borrows $106.54, and
consumes that amount now.
100
FIGURE 2.1
The grasshopper (G) wants consumption
now. The ant (A) wants to wait. But each
is happy to invest. A prefers to invest at
14 percent, moving up the burgundy arrow,
rather than at the 7 percent interest rate.
G invests and then borrows at 7 percent,
thereby transforming $100 into $106.54 of
immediate consumption. Because of the
investment, G has $114 next year to pay
off the loan. The investment’s NPV is
106.54 Ϫ 100 ϭϩ6.54.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
tween the $106.54 present value and the $100 initial investment. Despite their dif-
ferent tastes, both A and G are better off by investing in the office block and then
using the capital markets to achieve the desired balance between consumption
today and consumption at the end of the year. In fact, in coming to their invest-
ment decision, both would be happy to follow the two equivalent rules that we
proposed so casually at the end of Section 2.1. The two rules can be restated as
follows:
• Net present value rule. Invest in any project with a positive net present value.

This is the difference between the discounted, or present, value of the future
cash flow and the amount of the initial investment.
• Rate-of-return rule. Invest as long as the return on the investment exceeds the
rate of return on equivalent investments in the capital market.
What happens if the interest rate is not 7 percent but 14.3 percent? In this case
the office building would have zero NPV:
NPV ϭ 400,000/1.143 Ϫ 350,000 ϭ $0
Also, the return on the project would be 400,000/350,000 Ϫ 1 ϭ .143, or 14.3 per-
cent, exactly equal to the rate of interest in the capital market. In this case our two
rules would say that the project is on a knife edge. Investors should not care
whether the firm undertakes it or not.
It is easy to see that with a 14.3 percent interest rate neither A nor G would gain
anything by investing in the office building. A could spend exactly the same
amount at the end of the year, regardless of whether she invests her money in the
office building or in the capital market. Equally, there is no advantage in G in-
vesting in an office block to earn 14.3 percent and at the same time borrowing at
14.3 percent. He might just as well spend whatever cash he has on hand.
In our example the ant and the grasshopper placed an identical value on the of-
fice building and were happy to share in its construction. They agreed because they
faced identical borrowing and lending opportunities. Whenever firms discount
cash flows at capital market rates, they are implicitly assuming that their share-
holders have free and equal access to competitive capital markets.
It is easy to see how our net present value rule would be damaged if we did
not have such a well-functioning capital market. For example, suppose that G
could not borrow against future income or that it was prohibitively costly for
him to do so. In that case he might well prefer to spend his cash today rather
than invest it in an office building and have to wait until the end of the year be-
fore he could start spending. If A and G were shareholders in the same enter-
prise, there would be no simple way for the manager to reconcile their different
objectives.

No one believes unreservedly that capital markets are perfectly competitive.
Later in this book we will discuss several cases in which differences in taxation,
transaction costs, and other imperfections must be taken into account in financial
decision making. However, we will also discuss research which indicates that, in
general, capital markets function fairly well. That is one good reason for relying on
net present value as a corporate objective. Another good reason is that net present
value makes common sense; we will see that it gives obviously silly answers less
frequently than its major competitors. But for now, having glimpsed the problems
of imperfect markets, we shall, like an economist in a shipwreck, simply assume our
life jacket and swim safely to shore.
CHAPTER 2
Present Value and the Opportunity Cost of Capital 21
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
Our justification of the present value rule was restricted to two periods and to a
certain cash flow. However, the rule also makes sense for uncertain cash flows that
extend far into the future. The argument goes like this:
1. A financial manager should act in the interests of the firm’s owners, its
stockholders. Each stockholder wants three things:
a. To be as rich as possible, that is, to maximize current wealth.
b. To transform that wealth into whatever time pattern of consumption he
or she desires.
c. To choose the risk characteristics of that consumption plan.
2. But stockholders do not need the financial manager’s help to achieve the
best time pattern of consumption. They can do that on their own, providing

they have free access to competitive capital markets. They can also choose
the risk characteristics of their consumption plan by investing in more or
less risky securities.
3. How then can the financial manager help the firm’s stockholders? There is
only one way: by increasing the market value of each stockholder’s stake in
the firm. The way to do that is to seize all investment opportunities that
have a positive net present value.
Despite the fact that shareholders have different preferences, they are unani-
mous in the amount that they want to invest in real assets. This means that they
can cooperate in the same enterprise and can safely delegate operation of that en-
terprise to professional managers. These managers do not need to know anything
about the tastes of their shareholders and should not consult their own tastes. Their
task is to maximize net present value. If they succeed, they can rest assured that
they have acted in the best interest of their shareholders.
This gives us the fundamental condition for successful operation of a modern
capitalist economy. Separation of ownership and control is essential for most cor-
porations, so authority to manage has to be delegated. It is good to know that man-
agers can all be given one simple instruction: Maximize net present value.
Other Corporate Goals
Sometimes you hear managers speak as if the corporation has other goals. For ex-
ample, they may say that their job is to maximize profits. That sounds reasonable.
After all, don’t shareholders prefer to own a profitable company rather than an un-
profitable one? But taken literally, profit maximization doesn’t make sense as a cor-
porate objective. Here are three reasons:
1. “Maximizing profits” leaves open the question, Which year’s profits?
Shareholders might not want a manager to increase next year’s profits at
the expense of profits in later years.
2. A company may be able to increase future profits by cutting its dividend
and investing the cash. That is not in the shareholders’ interest if the
company earns only a low return on the investment.

3. Different accountants may calculate profits in different ways. So you may
find that a decision which improves profits in one accountant’s eyes will
reduce them in the eyes of another.
22 PART I
Value
2.3 A FUNDAMENTAL RESULT
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
We have explained that managers can best serve the interests of shareholders by
investing in projects with a positive net present value. But this takes us back to the
principal–agent problem highlighted in the first chapter. How can shareholders
(the principals) ensure that management (their agents) don’t simply look after their
own interests? Shareholders can’t spend their lives watching managers to check
that they are not shirking or maximizing the value of their own wealth. However,
there are several institutional arrangements that help to ensure that the sharehold-
ers’ pockets are close to the managers’ heart.
A company’s board of directors is elected by the shareholders and is supposed
to represent them. Boards of directors are sometimes portrayed as passive
stooges who always champion the incumbent management. But when company
performance starts to slide and managers do not offer a credible recovery plan,
boards do act. In recent years the chief executives of Eastman Kodak, General
Motors, Xerox, Lucent, Ford Motor, Sunbeam, and Lands End were all forced to
step aside when each company’s profitability deteriorated and the need for new
strategies became clear.
If shareholders believe that the corporation is underperforming and that the

board of directors is not sufficiently aggressive in holding the managers to task,
they can try to replace the board in the next election. If they succeed, the new board
will appoint a new management team. But these attempts to vote in a new board
are expensive and rarely successful. Thus dissidents do not usually stand and fight
but sell their shares instead.
Selling, however, can send a powerful message. If enough shareholders bail out,
the stock price tumbles. This damages top management’s reputation and compen-
sation. Part of the top managers’ paychecks comes from bonuses tied to the com-
pany’s earnings or from stock options, which pay off if the stock price rises but are
worthless if the price falls below a stated threshold. This should motivate man-
agers to increase earnings and the stock price.
If managers and directors do not maximize value, there is always the threat
of a hostile takeover. The further a company’s stock price falls, due to lax man-
agement or wrong-headed policies, the easier it is for another company or
group of investors to buy up a majority of the shares. The old management team
is then likely to find themselves out on the street and their place is taken by a
fresh team prepared to make the changes needed to realize the company’s
value.
These arrangements ensure that few managers at the top of major United States
corporations are lazy or inattentive to stockholders’ interests. On the contrary, the
pressure to perform can be intense.
CHAPTER 2
Present Value and the Opportunity Cost of Capital 23
2.4 DO MANAGERS REALLY LOOK AFTER
THE INTERESTS OF SHAREHOLDERS?
2.5 SHOULD MANAGERS LOOK AFTER THE INTERESTS
OF SHAREHOLDERS?
We have described managers as the agents of the shareholders. But perhaps this
begs the question, Is it desirable for managers to act in the selfish interests of their
shareholders? Does a focus on enriching the shareholders mean that managers

must act as greedy mercenaries riding roughshod over the weak and helpless? Do
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
they not have wider obligations to their employees, customers, suppliers, and the
communities in which the firm is located?
8
Most of this book is devoted to financial policies that increase a firm’s value.
None of these policies requires gallops over the weak and helpless. In most in-
stances there is little conflict between doing well (maximizing value) and doing
good. Profitable firms are those with satisfied customers and loyal employees;
firms with dissatisfied customers and a disgruntled workforce are more likely to
have declining profits and a low share price.
Of course, ethical issues do arise in business as in other walks of life, and there-
fore when we say that the objective of the firm is to maximize shareholder wealth,
we do not mean that anything goes. In part, the law deters managers from making
blatantly dishonest decisions, but most managers are not simply concerned with
observing the letter of the law or with keeping to written contracts. In business and
finance, as in other day-to-day affairs, there are unwritten, implicit rules of behav-
ior. To work efficiently together, we need to trust each other. Thus huge financial
deals are regularly completed on a handshake, and each side knows that the other
will not renege later if things turn sour.
9
Whenever anything happens to weaken
this trust, we are all a little worse off.
10

In many financial transactions, one party has more information than the other.
It can be difficult to be sure of the quality of the asset or service that you are buy-
ing. This opens up plenty of opportunities for financial sharp practice and outright
fraud, and, because the activities of scoundrels are more entertaining than those of
honest people, airport bookstores are packed with accounts of financial fraudsters.
The response of honest firms is to distinguish themselves by building long-term
relationships with their customers and establishing a name for fair dealing and fi-
nancial integrity. Major banks and securities firms know that their most valuable
asset is their reputation. They emphasize their long history and responsible be-
havior. When something happens to undermine that reputation, the costs can be
enormous.
Consider the Salomon Brothers bidding scandal in 1991.
11
A Salomon trader
tried to evade rules limiting the firm’s participation in auctions of U.S. Treasury
bonds by submitting bids in the names of the company’s customers without the
customers’ knowledge. When this was discovered, Salomon settled the case by
paying almost $200 million in fines and establishing a $100 million fund for pay-
ments of claims from civil lawsuits. Yet the value of Salomon Brothers stock fell by
24 PART I
Value
8
Some managers, anxious not to offend any group of stakeholders, have denied that they are maximiz-
ing profits or value. We are reminded of a survey of businesspeople that inquired whether they at-
tempted to maximize profits. They indignantly rejected the notion, objecting that their responsibilities
went far beyond the narrow, selfish profit motive. But when the question was reformulated and they
were asked whether they could increase profits by raising or lowering their selling price, they replied
that neither change would do so. The survey is cited in G. J. Stigler, The Theory of Price, 3rd ed. (New
York: Macmillan Company, 1966).
9

In U.S. law, a contract can be valid even if it is not written down. Of course documentation is prudent,
but contracts are enforced if it can be shown that the parties reached a clear understanding and agree-
ment. For example, in 1984, the top management of Getty Oil gave verbal agreement to a merger offer
with Pennzoil. Then Texaco arrived with a higher bid and won the prize. Pennzoil sued—and won—
arguing that Texaco had broken up a valid contract.
10
For a discussion of this issue, see A. Schleifer and L. H. Summers, “Breach of Trust in Corporate
Takeovers,” Corporate Takeovers: Causes and Consequences (Chicago: University of Chicago Press, 1988).
11
This discussion is based on Clifford W. Smith, Jr., “Economics and Ethics: The Case of Salomon Broth-
ers,” Journal of Applied Corporate Finance 5 (Summer 1992), pp. 23–28.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
CHAPTER 2 Present Value and the Opportunity Cost of Capital 25
far more than $300 million. In fact the price dropped by about a third, representing
a $1.5 billion decline in the company’s market value.
Why did the value of Salomon Brothers drop so dramatically? Largely because
investors were worried that Salomon would lose business from customers that
now distrusted the company. The damage to Salomon’s reputation was far greater
than the explicit costs of the scandal and was hundreds or thousands of times more
costly than the potential gains Salomon could have reaped from the illegal trades.
SUMMARY
In this chapter we have introduced the concept of present value as a way of valu-
ing assets. Calculating present value is easy. Just discount future cash flow by an
appropriate rate r, usually called the opportunity cost of capital, or hurdle rate:

Net present value is present value plus any immediate cash flow:
Remember that C
0
is negative if the immediate cash flow is an investment, that is,
if it is a cash outflow.
The discount rate is determined by rates of return prevailing in capital markets.
If the future cash flow is absolutely safe, then the discount rate is the interest rate
on safe securities such as United States government debt. If the size of the future
cash flow is uncertain, then the expected cash flow should be discounted at the ex-
pected rate of return offered by equivalent-risk securities. We will talk more about
risk and the cost of capital in Chapters 7 through 9.
Cash flows are discounted for two simple reasons: first, because a dollar today
is worth more than a dollar tomorrow, and second, because a safe dollar is worth
more than a risky one. Formulas for PV and NPV are numerical expressions of
these ideas. The capital market is the market where safe and risky future cash flows
are traded. That is why we look to rates of return prevailing in the capital markets
to determine how much to discount for time and risk. By calculating the present
value of an asset, we are in effect estimating how much people will pay for it if they
have the alternative of investing in the capital markets.
The concept of net present value allows efficient separation of ownership and
management of the corporation. A manager who invests only in assets with pos-
itive net present values serves the best interests of each one of the firm’s owners,
regardless of differences in their wealth and tastes. This is made possible by the
existence of the capital market which allows each shareholder to construct a per-
sonal investment plan that is custom tailored to his or her own requirements. For
example, there is no need for the firm to arrange its investment policy to obtain
a sequence of cash flows that matches its shareholders’ preferred time patterns
of consumption. The shareholders can shift funds forward or back over time per-
fectly well on their own, provided they have free access to competitive capital
markets. In fact, their plan for consumption over time is limited by only two

things: their personal wealth (or lack of it) and the interest rate at which they can
borrow or lend. The financial manager cannot affect the interest rate but can
Net present value 1NPV2ϭ C
0
ϩ
C
1
1 ϩ r
Present value 1PV2ϭ
C
1
1 ϩ r
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I. Value 2. Present Value and the
Opportunity Cost of Capital
© The McGraw−Hill
Companies, 2003
26 PART I Value
increase stockholders’ wealth. The way to do so is to invest in assets having pos-
itive net present values.
There are several institutional arrangements which help to ensure that man-
agers pay close attention to the value of the firm:
• Managers’ actions are subject to the scrutiny of the board of directors.
• Shirkers are likely to find that they are ousted by more energetic managers. This
competition may arise within the firm, but poorly performing companies are
also more likely to be taken over. That sort of takeover typically brings in a fresh
management team.

• Managers are spurred on by incentive schemes, such as stock options, which
pay off big if shareholders gain but are valueless if they do not.
Managers who focus on shareholder value need not neglect their wider obliga-
tions to the community. Managers play fair by employees, customers, and suppli-
ers partly because they know that it is for the common good, but partly because
they know that their firm’s most valuable asset is its reputation. Of course, ethical
issues do arise in financial management and, whenever unscrupulous managers
abuse their position, we all trust each other a little less.
FURTHER
READING
QUIZ
The pioneering works on the net present value rule are:
I. Fisher: The Theory of Interest, Augustus M. Kelley, Publishers. New York, 1965. Reprinted
from the 1930 edition.
J. Hirshleifer: “On the Theory of Optimal Investment Decision,” Journal of Political Economy,
66:329–352 (August 1958).
For a more rigorous textbook treatment of the subject, we suggest:
E. F. Fama and M. H. Miller: The Theory of Finance, Holt, Rinehart and Winston. New
York, 1972.
If you would like to dig deeper into the question of how managers can be motivated to maximize share-
holder wealth, we suggest:
M. C. Jensen and W. H. Meckling: “Theory of the Firm: Managerial Behavior, Agency Costs,
and Ownership Structure,” Journal of Financial Economics, 3:305–360 (October 1976).
E. F. Fama: “Agency Problems and the Theory of the Firm,” Journal of Political Economy,
88:288–307 (April 1980).
1. C
0
is the initial cash flow on an investment, and C
1
is the cash flow at the end of one

year. The symbol r is the discount rate.
a. Is C
0
usually positive or negative?
b. What is the formula for the present value of the investment?
c. What is the formula for the net present value?
d. The symbol r is often termed the opportunity cost of capital. Why?
e. If the investment is risk-free, what is the appropriate measure of r?
2. If the present value of $150 paid at the end of one year is $130, what is the one-year dis-
count factor? What is the discount rate?
3. Calculate the one-year discount factor DF
1
for discount rates of (a) 10 percent, (b) 20 per-
cent, and (c) 30 percent.
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Opportunity Cost of Capital
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CHAPTER 2 Present Value and the Opportunity Cost of Capital 27
4. A merchant pays $100,000 for a load of grain and is certain that it can be resold at the
end of one year for $132,000.
a. What is the return on this investment?
b. If this return is lower than the rate of interest, does the investment have a positive
or a negative NPV?
c. If the rate of interest is 10 percent, what is the PV of the investment?
d. What is the NPV?

5. What is the net present value rule? What is the rate of return rule? Do the two rules give
the same answer?
6. Define the opportunity cost of capital. How in principle would you find the opportu-
nity cost of capital for a risk-free asset? For a risky asset?
7. Look back to the numerical example graphed in Figure 2.1. Suppose the interest rate is
20 percent. What would the ant (A) and grasshopper (G) do? Would they invest in the
office building? Would they borrow or lend? Suppose each starts with $100. How much
and when would each consume?
8. We can imagine the financial manager doing several things on behalf of the firm’s stock-
holders. For example, the manager might:
a. Make shareholders as wealthy as possible by investing in real assets with
positive NPVs.
b. Modify the firm’s investment plan to help shareholders achieve a particular time
pattern of consumption.
c. Choose high- or low-risk assets to match shareholders’ risk preferences.
d. Help balance shareholders’ checkbooks.
But in well-functioning capital markets, shareholders will vote for only one of these
goals. Which one? Why?
9. Why would one expect managers to act in shareholders’ interests? Give some reasons.
10. After the Salomon Brothers bidding scandal, the aggregate value of the company’s
stock dropped by far more than it paid in fines and settlements of lawsuits. Why?
PRACTICE
QUESTIONS
1. Write down the formulas for an investment’s NPV and rate of return. Prove that NPV
is positive only if the rate of return exceeds the opportunity cost of capital.
2. What is the net present value of a firm’s investment in a U.S. Treasury security yielding
5 percent and maturing in one year? Hint: What is the opportunity cost of capital? Ig-
nore taxes.
3. A parcel of land costs $500,000. For an additional $800,000 you can build a motel on the
property. The land and motel should be worth $1,500,000 next year. Suppose that com-

mon stocks with the same risk as this investment offer a 10 percent expected return.
Would you construct the motel? Why or why not?
4. Calculate the NPV and rate of return for each of the following investments. The oppor-
tunity cost of capital is 20 percent for all four investments.
Initial Cash Cash Flow
Investment Flow, C
0
in Year 1, C
1
1 Ϫ10,000 ϩ18,000
2 Ϫ5,000 ϩ9,000
3 Ϫ5,000 ϩ5,700
4 Ϫ2,000 ϩ4,000
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28 PART I Value
a. Which investment is most valuable?
b. Suppose each investment would require use of the same parcel of land. Therefore
you can take only one. Which one? Hint: What is the firm’s objective: to earn a high
rate of return or to increase firm value?
5. In Section 2.1, we analyzed the possible construction of an office building on a plot of
land appraised at $50,000. We concluded that this investment had a positive NPV of

$7,143 at a discount rate of 12 percent.
Suppose E. Coli Associates, a firm of genetic engineers, offers to purchase the land
for $60,000, $30,000 paid immediately and $30,000 after one year. United States gov-
ernment securities maturing in one year yield 7 percent.
a. Assume E. Coli is sure to pay the second $30,000 installment. Should you take its
offer or start on the office building? Explain.
b. Suppose you are not sure E. Coli will pay. You observe that other investors demand
a 10 percent return on their loans to E. Coli. Assume that the other investors have
correctly assessed the risks that E. Coli will not be able to pay. Should you accept
E. Coli’s offer?
6. Explain why the discount rate equals the opportunity cost of capital.
7. Norman Gerrymander has just received a $2 million bequest. How should he invest it?
There are four immediate alternatives.
a. Investment in one-year U.S. government securities yielding 5 percent.
b. A loan to Norman’s nephew Gerald, who has for years aspired to open a big
Cajun restaurant in Duluth. Gerald had arranged a one-year bank loan for
$900,000, at 10 percent, but asks for a loan from Norman at 7 percent.
c. Investment in the stock market. The expected rate of return is 12 percent.
d. Investment in local real estate, which Norman judges is about as risky as the stock
market. The opportunity at hand would cost $1 million and is forecasted to be
worth $1.1 million after one year.
Which of these investments have positive NPVs? Which would you advise Norman
to take?
8. Show that your answers to Practice Question 7 are consistent with the rate of return rule
for investment decisions.
9. Take another look at investment opportunity (d) in Practice Question 7. Suppose a bank
offers Norman a $600,000 personal loan at 8 percent. (Norman is a long-time customer
of the bank and has an excellent credit history.) Suppose Norman borrows the money,
invests $1 million in real estate opportunity (d) and puts the rest of his money in op-
portunity (c), the stock market. Is this a smart move? Explain.

10. Respond to the following comments.
a. “My company’s cost of capital is the rate we pay to the bank when we borrow
money.”
b. “Net present value is just theory. It has no practical relevance. We maximize
profits. That’s what shareholders really want.”
c. “It’s no good just telling me to maximize my stock price. I can easily take a short
view and maximize today’s price. What I would prefer is to keep it on a gently
rising trend.”
11. Ms. Smith is retired and depends on her investments for retirement income. Mr. Jones
is a young executive who wants to save for the future. They are both stockholders in
Airbus, which is investing over $12 billion to develop the A380, a new super-jumbo
airliner. This investment’s payoff is many years in the future. Assume the investment
is positive-NPV for Mr. Jones. Explain why it should also be positive-NPV for Ms.
Smith.
12. Answer this question by drawing graphs like Figure 2.1. Casper Milktoast has
$200,000 available to support consumption in periods 0 (now) and 1 (next year). He
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CHAPTER 2 Present Value and the Opportunity Cost of Capital 29
wants to consume exactly the same amount in each period. The interest rate is 8 per-
cent. There is no risk.
a. How much should he invest, and how much can he consume in each period?
b. Suppose Casper is given an opportunity to invest up to $200,000 at 10 percent risk-
free. The interest rate stays at 8 percent. What should he do, and how much can he

consume in each period?
c. What is the NPV of the opportunity in (b)?
13. We said that maximizing value makes sense only if we assume well-functioning capi-
tal markets. What does “well-functioning” mean? Can you think of circumstances in
which maximizing value would not be in all shareholders’ interests?
14. Why is a reputation for honesty and fair business practice important to the financial
value of the corporation?
Dollars, year 0, millions
Owner's preferred
consumption pattern
1
3
3.75
4
5
1.6
Dollars, year 1, millions
42.6
FIGURE 2.2
See Challenge Question 2.
CHALLENGE
QUESTIONS
1. It is sometimes argued that the NPV criterion is appropriate for corporations but not for
governments. First, governments must consider the time preferences of the community
as a whole rather than those of a few wealthy investors. Second, governments must
have a longer horizon than individuals, for governments are the guardians of future
generations. What do you think?
2. In Figure 2.2, the sloping line represents the opportunities for investment in the capital
market and the solid curved line represents the opportunities for investment in plant
and machinery. The company’s only asset at present is $2.6 million in cash.

a. What is the interest rate?
b. How much should the company invest in plant and machinery?
c. How much will this investment be worth next year?
d. What is the average rate of return on the investment?
e. What is the marginal rate of return?
f. What is the PV of this investment?
g. What is the NPV of this investment?
h. What is the total PV of the company?
i. How much will the individual consume today?
j. How much will he or she consume tomorrow?
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30 PART I Value
3. Draw a figure like Figure 2.1 to represent the following situation.
a. A firm starts out with $10 million in cash.
b. The rate of interest r is 10 percent.
c. To maximize NPV the firm invests today $6 million in real assets. This leaves
$4 million which can be paid out to the shareholders.
d. The NPV of the investment is $2 million.
When you have finished, answer the following questions:
e. How much cash is the firm going to receive in year 1 from its investment?
f. What is the marginal return from the firm’s investment?
g. What is the PV of the shareholders’ investment after the firm has announced its

investment plan?
h. Suppose shareholders want to spend $6 million today. How can they do this?
i. How much will they then have to spend next year? Show this on your drawing.
4. For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered in
Rotterdam one year hence. Unfortunately the net cash flow from selling the tanker load
will be very sensitive to the growth rate of the world economy:
Slump Normal Boom
$8 million $12 million $16 million
a. What is the expected cash flow? Assume the three outcomes for the economy are
equally likely.
b. What is the expected rate of return on the investment in the project?
c. One share of stock Z is selling for $10. The stock has the following payoffs after
one year:
Slump Normal Boom
$8 $12 $16
Calculate the expected rate of return offered by stock Z. Explain why this is the
opportunity cost of capital for your bucolic acid project.
d. Calculate the project’s NPV. Is the project a good investment? Explain why.
5. In real life the future health of the economy cannot be reduced to three equally proba-
ble states like slump, normal, and boom. But we’ll keep that simplification for one more
example.
Your company has identified two more projects, B and C. Each will require a $5 mil-
lion outlay immediately. The possible payoffs at year 1 are, in millions:
Slump Normal Boom
B4 6 8
C 5 5.5 6
You have identified the possible payoffs to investors in three stocks, X, Y, and Z:
Current Price
Payoff at Year 1
per Share Slump Normal Boom

X 95.65 80 110 140
Y40 40 4448
Z 10 8 12 16
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CHAPTER 2 Present Value and the Opportunity Cost of Capital 31
a. What are the expected cash inflows of projects B and C?
b. What are the expected rates of return offered by stocks X, Y, and Z?
c. What are the opportunity costs of capital for projects B and C? Hint: Calculate the
percentage differences, slump versus normal and boom versus normal, for stocks
X, Y, and Z. Match up to the percentage differences in B’s and C’s payoffs.
d. What are the NPVs of projects B and C?
e. Suppose B and C are launched and $5 million is invested in each. How much will
they add to the total market value of your company’s shares?