320 SECTION THREE
calculated. Suppose that you are offered the chance to play the following game. You
start by investing $100. Then two coins are flipped. For each head that comes up your
starting balance will be increased by 20 percent, and for each tail that comes up your
starting balance will be reduced by 10 percent. Clearly there are four equally likely
outcomes:
FIGURE 3.15
Historical returns on major asset classes, 1926–1998.
Rate of return, percent
Number of years
0Ϫ10 10
Average
return,
percent
Standard
deviation,
percent
3.8 3.2
Treasury bills
Rate of return, percent
Number of years
0Ϫ10Ϫ20Ϫ30Ϫ40 10 20 30 40 50
13.2 20.3
Common stocks
Rate of return, percent
Number of years
0Ϫ10 10 20
3.2 4.5
Inflation
Rate of return, percent
Number of years

10
35
40
50
45
0
5
10
15
20
25
Source: Stocks, Bonds, Bills and Inflation® 1999 Yearbook, © 1999 Ibbotson Associates, Inc. Based on copyrighted works by Ibbotson and
Sinquefield. All Rights Reserved. Used with permission.
Introduction to Risk, Return, and the Opportunity Cost of Capital 321
• Head + head: You make 20 + 20 = 40%
• Head + tail: You make 20 – 10 = 10%
• Tail + head: You make –10 + 20 = 10%
• Tail + tail: You make –10 – 10 = –20%
There is a chance of 1 in 4, or .25, that you will make 40 percent; a chance of 2 in 4, or
.5, that you will make 10 percent; and a chance of 1 in 4, or .25, that you will lose 20
percent. The game’s expected return is therefore a weighted average of the possible out-
comes:
Expected return = probability-weighted average of possible outcomes
= (.25 × 40) + (.5 × 10) + (.25 × –20) = +10%
If you play the game a very large number of times, your average return should be 10
percent.
Table 3.10 shows how to calculate the variance and standard deviation of the returns
on your game. Column 1 shows the four equally likely outcomes. In column 2 we cal-
culate the difference between each possible outcome and the expected outcome. You can
see that at best the return could be 30 percent higher than expected; at worst it could be

+10 0 0
–20 –30 900
Variance = average of squared deviations = 1,800/4 = 450
Standard deviation = square root of variance =
√
450 = 21.2, about 21%
322 SECTION THREE
outcome. The actual standard deviation is positive because we don’t know what will
happen.
Now think of a second game. It is the same as the first except that each head means
a 35 percent gain and each tail means a 25 percent loss. Again there are four equally
likely outcomes:
• Head + head: You gain 70%
• Head + tail: You gain 10%
• Tail + head: You gain 10%
• Tail + tail: You lose 50%
For this game, the expected return is 10 percent, the same as that of the first game, but
it is more risky. For example, in the first game, the worst possible outcome is a loss of
20 percent, which is 30 percent worse than the expected outcome. In the second game
the downside is a loss of 50 percent, or 60 percent below the expected return. This in-
creased spread of outcomes shows up in the standard deviation, which is double that of
the first game, 42 percent versus 21 percent. By this measure the second game is twice
as risky as the first.
A NOTE ON CALCULATING VARIANCE
When we calculated variance in Table 3.10 we recorded separately each of the four pos-
sible outcomes. An alternative would have been to recognize that in two of the cases the
outcomes were the same. Thus there was a 50 percent chance of a 10 percent return
from the game, a 25 percent chance of a 40 percent return, and a 25 percent chance of
a –20 percent return. We can calculate variance by weighting each squared deviation by
the probability and then summing the results. Table 9.3 confirms that this method gives

erage return. For example, in 1994 the return of 1.31 percent on common stocks was
below the 5-year average by 23.44 percent (1.31 – 24.75 = –23.44 percent). In column
3 we square these deviations from the average. The variance is then the average of these
squared deviations:
Variance = average of squared deviations
=
801.84
= 160.37
5
Since standard deviation is the square root of the variance,
Standard deviation = square root of variance
=
√
160.37 = 12.66%
It is difficult to measure the risk of securities on the basis of just five past outcomes.
Therefore, Table 3.13 lists the annual standard deviations for our three portfolios of
securities over the period 1926–1998. As expected, Treasury bills were the least variable
security, and common stocks were the most variable. Treasury bonds hold the middle
ground.
TABLE 3.12
The average return and
standard deviation of stock
market returns, 1994–1998
Deviation from
Year Rate of Return Average Return Squared Deviation
1994 1.31 –23.44 549.43
1995 37.43 12.68 160.78
1996 23.07 –1.68 2.82
1997 33.36 8.61 74.13
1998 28.58 3.83 14.67

for a recent 5-year period.
7
Do these standard deviations look high to you? They should.
Remember that the market portfolio’s standard deviation was about 20 percent over the
entire 1926–1998 period. Of our individual stocks only Exxon had a standard deviation
of less than 20 percent. Most stocks are substantially more variable than the market
portfolio; only a handful are less variable.
This raises an important question: The market portfolio is made up of individual
stocks, so why isn’t its variability equal to the average variability of its components?
The answer is that diversification reduces variability.
6
We converted the monthly variance to an annual variance by multiplying by 12. In other words, the variance
of annual returns is 12 times that of monthly returns. The longer you hold a security, the more risk you have
to bear.
7
We pointed out earlier that five annual observations are insufficient to give a reliable estimate of variability.
Therefore, these estimates are derived from 60 monthly rates of return and then the monthly variance is mul-
tiplied by 12.
FIGURE 3.16
Stock market volatility,
1926–1998.
Annualized standard deviation
of monthly returns, percent
’26 ’30 ’34
0.00
10.00
20.00
30.00
40.00
50.00

It appears that gold is the more volatile investment. The difference in return across
the boom and bust scenarios is 40 percent (–20 percent in a boom versus +20 percent
in a recession), compared to a spread of only 26 percent for the auto stock. In fact, we
can confirm the higher volatility by measuring the variance or standard deviation of re-
turns of the two assets. The calculations are set out in Table 3.16.
Since all three scenarios are equally likely, the expected return on each stock is
Portfolio diversification works because prices of different stocks do not move
exactly together. Statisticians make the same point when they say that stock
price changes are less than perfectly correlated. Diversification works best
when the returns are negatively correlated, as is the case for our umbrella
and ice cream businesses. When one business does well, the other does badly.
Unfortunately, in practice, stocks that are negatively correlated are as rare as
pecan pie in Budapest.
TABLE 3.14
Standard deviations for
selected common stocks, July
1994–June 1999
Stock Standard Deviation, %
Biogen 46.6
Compaq 46.7
Delta Airlines 26.9
Exxon 16.0
Ford Motor Co. 24.9
MCI WorldCom 34.4
Merck 24.5
Microsoft 34.0
PepsiCo 26.5
Xerox 27.3
326 SECTION THREE
simply the average of the three possible outcomes.

Variance
a
1
(169 + 0 + 169) = 112.7
1
(361 + 4 + 441) = 268.7
33
Standard deviation
√
112.7 = 10.6%
√
268.7 = 16.4%
(=
√
variance)
a
Variance = average of squared deviations from the expected value.
TABLE 3.15
Rate of return assumptions
for two stocks
Rate of Return, %
Scenario Probability Auto Stock Gold Stock
Recession 1/3 –8 +20
Normal 1/3 +5 +3
Boom 1/3 +18 –20
8
If the probabilities were not equal, we would need to weight each outcome by its probability in calculating
the expected outcome and the variance.
Introduction to Risk, Return, and the Opportunity Cost of Capital 327
deviation is 10.6 percent. We’ll compare that portfolio to a partially diversified one, in-

stock to the more volatile gold mining stock, your portfolio variability actually de-
creases. In fact, the volatility of the auto-plus-gold stock portfolio is considerably less
than the volatility of either stock separately. This is the payoff to diversification.
We can understand this more clearly by focusing on asset returns in the two extreme
scenarios, boom and recession. In the boom, when auto stocks do best, the poor return
on gold reduces the performance of the overall portfolio. However, when auto stocks
are stalling in a recession, gold shines, providing a substantial positive return that boosts
TABLE 3.17
Rates of return for two stocks
and a portfolio
Rate of Return, %
Portfolio
Scenario Probability Auto Stock Gold Stock Return, %
a
Recession 1/3 –8 +20 –1.0%
Normal 1/3 +5 +3 +4.5
Boom 1/3 +18 –20 +8.5
Expected return 5% 1% 4%
Variance 112.7 268.7 15.2
Standard deviation 10.6% 16.4% 3.9%
a
Portfolio return = (.75 × auto stock return) + (.25 × gold stock return).
9
Let’s confirm this. Suppose you invest $7,500 in autos and $2,500 in gold. If the recession hits, the rate of
return on autos will be –8 percent, and the value of the auto investment will fall by 8 percent to $6,900. The
rate of return on gold will be 20 percent, and the value of the gold investment will rise 20 percent to $3,000.
The value of the total portfolio falls from its original value of $10,000 to $6,900 + $3,000 = $9,900, which is
a rate of return of –1 percent. This matches the rate of return given by the formula for the weighted average.
328 SECTION THREE
portfolio performance. The gold stock offsets the swings in the performance of the auto

There were many occasions when a
1. Investors care about the expected return and risk of their portfolio of
assets. The risk of the overall portfolio can be measured by the volatility
of returns, that is, the variance or standard deviation.
2. The standard deviation of the returns of an individual security measures
how risky that security would be if held in isolation. But an investor who
holds a portfolio of securities is interested only in how each security
affects the risk of the entire portfolio. The contribution of a security to
the risk of the portfolio depends on how the security’s returns vary with
the investor’s other holdings. Thus a security that is risky if held in
isolation may nevertheless serve to reduce the variability of the portfolio,
as long as its returns vary inversely with those of the rest of the portfolio.
10
For any normal distribution, approximately one-third of the observations lie more than one standard devi-
ation above or below the average. Over short intervals stock returns are roughly normally distributed.
11
Statisticians calculate a correlation coefficient as a measure of how closely two series move together. If
Ford’s and Merck’s stock moved in perfect lockstep, the correlation coefficient between the returns would be
1.0. If their returns were completely unrelated, the correlation would be zero. The actual correlation between
the returns on Ford and Merck was .03. In other words, the returns were almost completely unrelated.
Introduction to Risk, Return, and the Opportunity Cost of Capital 329
decline in the value of one stock was canceled by a rise in the price of the other. Be-
cause the two stocks did not move in exact lockstep, there was an opportunity to reduce
variability by spreading one’s investment between them. For example, Figure 3.17c
FIGURE 3.17
The variability of a portfolio with equal holdings in Merck and Ford Motor would
have been only 70 percent of the variability of the individual stocks.
Ϫ20
Ϫ15
Ϫ10

0
5
10
15
20
25
30
Ϫ25
Ϫ30
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
Ford Motor return, percentPortfolio return, percent
(a)
(b)
(c)
330 SECTION THREE
shows the returns on a portfolio that was equally divided between the stocks. The
monthly standard deviation of this portfolio would have been only 5.1 percent—that is,
about 70 percent of the variability of the individual stocks.
᭤
Self-Test 5 An investor is currently fully invested in gold mining stocks. Which action would do
more to reduce portfolio risk: diversification into silver mining stocks or into automo-
tive stocks? Why?
MARKET RISK VERSUS UNIQUE RISK
Our examples illustrate that even a little diversification can provide a substantial re-
duction in variability. Suppose you calculate and compare the standard deviations of
randomly chosen one-stock portfolios, two-stock portfolios, five-stock portfolios, and
so on. You can see from Figure 3.18 that diversification can cut the variability of returns
by about half. But you can get most of this benefit with relatively few stocks: the im-
provement is slight when the number of stocks is increased beyond, say, 15.
Figure 3.18 also illustrates that no matter how many securities you hold, you cannot

Introduction to Risk, Return, and the Opportunity Cost of Capital 331
Thinking about Risk
How can you tell which risks are unique and diversifiable? Where do market risks come
from? Here are three messages to help you think clearly about risk.
MESSAGE 1: SOME RISKS LOOK BIG AND
DANGEROUS BUT REALLY ARE DIVERSIFIABLE
Managers confront risks “up close and personal.” They must make decisions about
particular investments. The failure of such an investment could cost a promotion, bonus,
or otherwise steady job. Yet that same investment may not seem risky to an investor who
can stand back and combine it in a diversified portfolio with many other assets or
securities.
᭤
EXAMPLE 2 Wildcat Oil Wells
You have just been promoted to director of exploration, Western Hemisphere, of MPS
Oil. The manager of your exploration team in far-off Costaguana has appealed for $20
million extra to drill in an even steamier part of the Costaguanan jungle. The manager
thinks there may be an “elephant” field worth $500 million or more hidden there. But
the chance of finding it is at best one in ten, and yesterday MPS’s CEO sourly com-
mented on the $100 million already “wasted” on Costaguanan exploration.
Is this a risky investment? For you it probably is; you may be a hero if oil is found
and a goat otherwise. But MPS drills hundreds of wells worldwide; for the company as
For a reasonably well-diversified portfolio, only market risk matters.
FIGURE 3.19
Diversification eliminates
unique risk. But there is some
risk that diversification
cannot eliminate. This is
called
market risk.
Number of securities

with average losses, which can be predicted with excellent accuracy.
᭤
Self-Test 6 Imagine a laboratory at IBM, late at night. One scientist speaks to another.
“You’re right, Watson, I admit this experiment will consume all the rest of this year’s
budget. I don’t know what we’ll do if it fails. But if this yttrium–magnoosium alloy su-
perconducts, the patents will be worth millions.”
Would this be a good or bad investment for IBM? Can’t say. But from the ultimate
investors’ viewpoint this is not a risky investment. Explain why.
MESSAGE 2: MARKET RISKS ARE MACRO RISKS
We have seen that diversified portfolios are not exposed to the unique risks of individ-
ual stocks but are exposed to the uncertain events that affect the entire securities mar-
ket and the entire economy. These are macroeconomic, or “macro,” factors such as
changes in interest rates, industrial production, inflation, foreign exchange rates, and
energy costs. These factors affect most firms’ earnings and stock prices. When the rel-
evant macro risks turn generally favorable, stock prices rise and investors do well; when
the same variables go the other way, investors suffer.
You can often assess relative market risks just by thinking through exposures to the
business cycle and other macro variables. The following businesses have substantial
macro and market risks:
Introduction to Risk, Return, and the Opportunity Cost of Capital 333
• Airlines. Because business travel falls during a recession, and individuals postpone
vacations and other discretionary travel, the airline industry is subject to the swings
of the business cycle. On the positive side, airline profits really take off when busi-
ness is booming and personal incomes are rising.
• Machine tool manufacturers. These businesses are especially exposed to the busi-
ness cycle. Manufacturing companies that have excess capacity rarely buy new ma-
chine tools to expand. During recessions, excess capacity can be quite high.
Here, on the other hand, are two industries with less than average macro exposures:
• Food companies. Companies selling staples, such as breakfast cereal, flour, and dog
food, find that demand for their products is relatively stable in good times and bad.

micro risks, but only the former affect the cost of capital.
334 SECTION THREE
Summary
How can one estimate the opportunity cost of capital for an “average-risk”
project?
Over the past 73 years the return on the Standard & Poor’s Composite Index of common
stocks has averaged almost 9.4 percent a year higher than the return on safe Treasury bills.
This is the risk premium that investors have received for taking on the risk of investing in
stocks. Long-term bonds have offered a higher return than Treasury bills but less than stocks.
If the risk premium in the past is a guide to the future, we can estimate the expected
return on the market today by adding that 9.4 percent expected risk premium to today’s
interest rate on Treasury bills. This would be the opportunity cost of capital for an average-
risk project, that is, one with the same risk as a typical share of common stock.
How is the standard deviation of returns for individual common stocks or for a
stock portfolio calculated?
The spread of outcomes on different investments is commonly measured by the variance or
standard deviation of the possible outcomes. The variance is the average of the squared
deviations around the average outcome, and the standard deviation is the square root of the
variance. The standard deviation of the returns on a market portfolio of common stocks has
averaged about 20 percent a year.
Why does diversification reduce risk?
The standard deviation of returns is generally higher on individual stocks than it is on the
market. Because individual stocks do not move in exact lockstep, much of their risk can be
diversified away. By spreading your portfolio across many investments you smooth out the
risk of your overall position. The risk that can be eliminated through diversification is
known as unique risk.
What is the difference between unique risk, which can be diversified away, and
market risk, which cannot?
Even if you hold a well-diversified portfolio, you will not eliminate all risk. You will still be
exposed to macroeconomic changes that affect most stocks and the overall stock market.

3. Real versus Nominal Returns. You purchase 100 shares of stock for $40 a share. The stock
pays a $2 per share dividend at year-end. What is the rate of return on your investment for
these end-of-year stock prices? What is your real (inflation-adjusted) rate of return? Assume
an inflation rate of 5 percent.
a. $38
b. $40
c. $42
4. Real versus Nominal Returns. The Costaguanan stock market provided a rate of return of
95 percent. The inflation rate in Costaguana during the year was 80 percent. In the United
States, in contrast, the stock market return was only 14 percent, but the inflation rate was
only 3 percent. Which country’s stock market provided the higher real rate of return?
5. Real versus Nominal Returns. The inflation rate in the United States between 1950 and
1998 averaged 4.4 percent. What was the average real rate of return on Treasury bills, Trea-
sury bonds, and common stocks in that period? Use the data in Self-Test 2.
6. Real versus Nominal Returns. Do you think it is possible for risk-free Treasury bills to offer
a negative nominal interest rate? Might they offer a negative real expected rate of return?
7. Market Indexes. The accompanying table shows the complete history of stock prices on the
Polish stock exchange for 9 weeks in 1991. At that time only five stocks were traded. Con-
struct two stock market indexes, one using weights as calculated in the Dow Jones Industrial
Average, the other using weights as calculated in the Standard & Poor’s Composite Index.
Prices (in zlotys) for the first 9 weeks’ trading on the Warsaw Stock Exchange,
beginning in April 1991. There was one trading session per week. Only five stocks
were listed in the first 9 weeks.
Stock
Tonsil Prochnik Krosno Exbud Kable
(Electronics) (Garments) (Glass) (Construction) (Electronics)
Week 1,500* 1,500* 2,200* 1,000* 1,000*
1 85 56 59.5 149 80
2 76.5 51 53.5 164 80
3 69 46 49 180 80

in 1977 expect to earn a negative maturity premium? What do these 5 years’ bond returns
tell us about the normal future maturity premium?
12. Risk Premiums. What will happen to the opportunity cost of capital if investors suddenly
become especially conservative and less willing to bear investment risk?
13. Risk Premiums and Discount Rates. You believe that a stock with the same market risk as
the S&P 500 will sell at year-end at a price of $50. The stock will pay a dividend at year-end
of $2. What price will you be willing to pay for the stock today? Hint: Start by checking
today’s 1-year Treasury rates.
14. Scenario Analysis. The common stock of Leaning Tower of Pita, Inc., a restaurant chain,
will generate the following payoffs to investors next year:
Dividend Stock Price
Boom $5.00 $195
Normal economy 2.00 100
Recession 0 0
The company goes out of business if a recession hits. Calculate the expected rate of return
and standard deviation of return to Leaning Tower of Pita shareholders. Assume for sim-
plicity that the three possible states of the economy are equally likely. The stock is selling
today for $90.
15. Portfolio Risk. Who would view the stock of Leaning Tower of Pita (see problem 14) as a
risk-reducing investment—the owner of a gambling casino or a successful bankruptcy
lawyer? Explain.
16. Scenario Analysis. The common stock of Escapist Films sells for $25 a share and offers the
following payoffs next year:
Dividend Stock Price
Boom 0 $18
Normal economy $1.00 26
Recession 3.00 34
Calculate the expected return and standard deviation of Escapist. All three scenarios are
equally likely. Then calculate the expected return and standard deviation of a portfolio half
Practice

22. Risk and Return. A stock will provide a rate of return of either –20 percent or +30
percent.
a. If both possibilities are equally likely, calculate the expected return and standard deviation.
b. If Treasury bills yield 5 percent, and investors believe that the stock offers a satisfactory
expected return, what must the market risk of the stock be?
23. Unique versus Market Risk. Sassafras Oil is staking all its remaining capital on wildcat ex-
ploration off the Côte d’Huile. There is a 10 percent chance of discovering a field with re-
serves of 50 million barrels. If it finds oil, it will immediately sell the reserves to Big Oil,
at a price depending on the state of the economy. Thus the possible payoffs are as follows:
Value of Reserves, Value of Reserves, Value of
per Barrel 50 Million Barrels Dryholes
Boom $4.00 $200,000,000 0
Normal economy $5.00 $250,000,000 0
Recession $6.00 $300,000,000 0
Is Sassafras Oil a risky investment for a diversified investor in the stock market—compared,
say, to the stock of Leaning Tower of Pita, described in problem 14? Explain.
338 SECTION THREE
1 The bond price at the end of the year is $1,050. Therefore, the capital gain on each bond is
$1,050 – 1,020 = $30. Your dollar return is the sum of the income from the bond, $80, plus
the capital gain, $30, or $110. The rate of return is
Income plus capital gain
=
80 + 30
= .108, or 10.8%
Original price 1,020
Real rate of return is
1 + nominal return
– 1 =
1.108
– 1 = .065, or 6.5%

benefit. The power of diversification is lowest when rates of return are highly correlated,
performing well or poorly in tandem. Shifting the portfolio from one such firm to another
has little impact on overall risk.
6 The success of this project depends on the experiment. Success does not depend on the per-
formance of the overall economy. The experiment creates a diversifiable risk. A portfolio of
many stocks will embody “bets” on many such unique risks. Some bets will work out and
some will fail. Because the outcomes of these risks do not depend on common factors, such
as the overall state of the economy, the risks will tend to cancel out in a well-diversified
portfolio.
7 a. The luxury restaurant will be more sensitive to the state of the economy because expense
account meals will be curtailed in a recession. Burger Queen meals should be relatively
recession-proof.
b. The paint company that sells to the auto producers will be more sensitive to the state of
the economy. In a downturn, auto sales fall dramatically as consumers stretch the lives of
their cars. In contrast, in a recession, more people “do it themselves,” which makes paint
sales through small stores more stable and less sensitive to the economy.
Solutions to
Self-Test
Questions
Net Present Value and Other
Investment Criteria
Using Discounted Cash-Flow
Analysis to Make Investment
Decisions
Risk, Return, and Capital Budgeting
The Cost of Capital
Section 4
class="bi x0 y229 wd h2a"
341
NET PRESENT VALUE

© Jim Levitt/Impact Visuals
he investment decision, also known as capital budgeting, is central to the
success of the company. We have already seen that capital investments
sometimes absorb substantial amounts of cash; they also have very long-
term consequences. The assets you buy today may determine the business
you are in many years hence.
For some investment projects “substantial” is an understatement. Consider the fol-
lowing examples:
᭤
Construction of the Channel Tunnel linking England and France cost about $15 bil-
lion from 1986 to 1994.
᭤
The cost of bringing one new prescription drug to market was estimated to be at least
$300 million.
᭤
The development cost of Ford’s “world car,” the Mondeo, was about $6 billion.
᭤
Production and merchandising costs for three new Star Wars movies will amount to
about $3 billion.
᭤
The future development cost of a super-jumbo jet airliner, seating 600 to 800 pas-
sengers, has been estimated at over $10 billion.
᭤
TAPS, The Alaska Pipeline System, which brings crude oil from Prudhoe Bay to
Valdez on the southern coast of Alaska, cost $9 billion.
Notice from these examples of big capital projects that many projects require heavy
investment in intangible assets. The costs of drug development are almost all research
and testing, for example, and much of the development of Ford’s Mondeo went into de-
sign and testing. Any expenditure made in the hope of generating more cash later can
be called a capital investment project, regardless of whether the cash outlay goes to tan-

known as the profitability index.
After studying this material you should be able to
᭤
Calculate the net present value of an investment.
᭤
Calculate the internal rate of return of a project and know what to look out for when
using the internal rate of return rule.
᭤
Explain why the payback rule and book rate of return rule don’t always make share-
holders better off.
᭤
Use the net present value rule to analyze three common problems that involve com-
peting projects: (a) when to postpone an investment expenditure, (b) how to choose
between projects with equal lives, and (c) when to replace equipment.
᭤
Calculate the profitability index and use it to choose between projects when funds
are limited.
Net Present Value
Earlier you learned how to discount future cash payments to find their present value.
We now apply these ideas to evaluate a simple investment proposal.
Suppose that you are in the real estate business. You are considering construction of
an office block. The land would cost $50,000 and construction would cost a further
$300,000. You foresee a shortage of office space and predict that a year from now you
will be able to sell the building for $400,000. Thus you would be investing $350,000
now in the expectation of realizing $400,000 at the end of the year. You should go ahead
if the present value of the $400,000 payoff is greater than the investment of $350,000.
Assume 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 a 1-year
U.S. Treasury bill. Suppose the T-bill offers interest of 7 percent. How much would you
have to invest in it in order to receive $400,000 at the end of the year? That’s easy: you

In our discussion of the office development we assumed we knew the value of the com-
pleted project. Of course, you will never be certain about the future values of office
buildings. The $400,000 represents the best forecast, but it is not a sure thing.
Therefore, our initial conclusion about how much investors would pay for the build-
ing is wrong. Since they could achieve $400,000 risklessly by investing in $373,832
worth of U.S. Treasury bills, 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 basic financial principle:
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 apply to risky invest-
ments. It is still proper to discount the payoff by the rate of return offered by a compa-
rable investment. But we have to think of expected payoffs and the expected rates of re-
A risky dollar is worth less than a safe one.
The net present value rule states that managers increase shareholders’ wealth
by accepting all projects that are worth more than they cost. Therefore, they
should accept all projects with a positive net present value.
OPPORTUNITY COST
OF CAPITAL
Expected
rate of return given up by
investing in a project.
NET PRESENT VALUE
(NPV) Present value of
cash flows minus initial
investment.