Fundamentals of Corporate Finance Phần 8 doc

452 SECTION FOUR
relative risks, at least in industries they are used to, but not about absolute risk or re-
quired rates of return. Therefore, they set a company- or industrywide cost of capital as
a benchmark. This is not the right hurdle rate for everything the company does, but
judgmental adjustments can be made for more risky or less risky ventures.
SOME COMMON MISTAKES
One danger with the weighted-average formula is that it tempts people to make logical
errors. Think back to your estimate of the cost of capital for Big Oil:
WACC =
[
D
×
(1 –
T
c
)
r
debt
]
+
(
E
× r
equity
)
VV
= [.243 × (1 – .35) 9%] + (.757 × 13.5%) = 11.6%
Now you might be tempted to say to yourself, “Aha! Big Oil has a good credit rating. It
could easily push up its debt ratio to 50 percent. If the interest rate is 9 percent and the
required return on equity is 13.5 percent, the weighted-average cost of capital would be
WACC = [.50 × (1 – .35) 9%] + (.50 × 13.5%) = 9.7%

At a discount rate of 9.7 percent, we can justify a lot more investment.”
That reasoning will get you into trouble. First, if Big Oil increased its borrowing, the
lenders would almost certainly demand a higher rate of interest on the debt. Second, as
the borrowing increased, the risk of the common stock would also increase and there-
fore the stockholders would demand a higher return.
When you jumped to the conclusion that Big Oil could lower its weighted-average cost
of capital to 9.7 percent by borrowing more, you were recognizing only the explicit cost
of debt and not the implicit cost.
᭤
Self-Test 7 Jo Ann Cox’s boss has pointed out that Geothermal proposes to finance its expansion
entirely by borrowing at an interest rate of 8 percent. He argues that this is therefore the
appropriate discount rate for the project’s cash flows. Is he right?
HOW CHANGING CAPITAL STRUCTURE
AFFECTS EXPECTED RETURNS
We will illustrate how changes in capital structure affect expected returns by focusing
on the simplest possible case, where the corporate tax rate T
c
is zero.
Think back to our earlier example of Geothermal. Geothermal, you may remember,
has the following market-value balance sheet:
Assets Liabilities and Shareholders’ Equity
Assets = value of Geothermal’s $647 Debt $194 (30%)
existing business
Equity $453 (70%)
Total value $647 Value $647 (100%)
There are actually two costs of debt finance. The explicit cost of debt is the
rate of interest that bondholders demand. But there is also an implicit cost,
because borrowing increases the required return to equity.
The Cost of Capital 453
Geothermal’s debtholders require a return of 8 percent and the shareholders require a

return of 14 percent. Since we assume here that Geothermal pays no corporate tax, its
weighted-average cost of capital is simply the expected return on the firm’s assets:
WACC = r
assets
= (.3 × 8%) + (.7 × 14%) = 12.2%
This is the return you would expect if you held all Geothermal’s securities and therefore
owned all its assets.
Now think what will happen if Geothermal borrows an additional $97 million and
uses the cash to buy back and retire $97 million of its common stock. The revised mar-
ket-value balance sheet is
Assets Liabilities and Shareholders’ Equity
Assets = value of Geothermal’s $647 Debt $291 (45%)
existing business
Equity 356 (55%)
Total value $647 Value $647 (100%)
If there are no corporate taxes, the change in capital structure does not affect the total
cash that Geothermal pays out to its security holders and it does not affect the risk of
those cash flows. Therefore, if investors require a return of 12.2 percent on the total
package of debt and equity before the financing, they must require the same 12.2
percent return on the package afterward. The weighted-average cost of capital is there-
fore unaffected by the change in the capital structure.
Although the required return on the package of the debt and equity is unaffected, the
change in capital structure does affect the required return on the individual securities.
Since the company has more debt than before, the debt is riskier and debtholders are
likely to demand a higher return. Increasing the amount of debt also makes the equity
riskier and increases the return that shareholders require.
WHAT HAPPENS WHEN THE CORPORATE
TAX RATE IS NOT ZERO
We have shown that when there are no corporate taxes the weighted-average cost of cap-
ital is unaffected by a change in capital structure. Unfortunately, taxes can complicate

the picture.
7
For the moment, just remember
• The weighted-average cost of capital is the right discount rate for average-
risk capital investment projects.
• The weighted-average cost of capital is the return the company needs to
earn after tax in order to satisfy all its security holders.
• If the firm increases its debt ratio, both the debt and the equity will
become more risky. The debtholders and equity holders require a higher
return to compensate for the increased risk.
7
There’s nothing wrong with our formulas and examples, provided that the tax deductibility of interest pay-
ments doesn’t change the aggregate risk of the debt and equity investors. However, if the tax savings from
deducting interest are treated as safe cash flows, the formulas get more complicated. If you really want to dive
into the tax-adjusted formulas showing how WACC changes with capital structure, we suggest later
in R. A. Brealey and S. C. Myers, Principles of Corporate Finance, 6th ed. (New York: Irwin/McGraw-Hill,
2000).
454 SECTION FOUR
Flotation Costs and the Cost of Capital
To raise the necessary cash for a new project, the firm may need to issue stocks, bonds,
or other securities. The costs of issuing these securities to the public can easily amount
to 5 percent of funds raised. For example, a firm issuing $100 million in new equity
may net only $95 million after incurring the costs of the issue.
Flotation costs involve real money. A new project is less attractive if the firm must
spend large sums on issuing new securities. To illustrate, consider a project that will
cost $900,000 to install and is expected to generate a level perpetual cash-flow stream
of $90,000 a year. At a required rate of return of 10 percent, the project is just barely
viable, with an NPV of zero: –$900,000 + $90,000/.10 = 0.
Now suppose that the firm needs to raise equity to pay for the project, and that
flotation costs are 10 percent of funds raised. To raise $900,000, the firm actually

must sell $1 million of equity. Since the installed project will be worth only $90,000/.10
= $900,000, NPV including flotation costs is actually –$1 million + $900,000 =
–$100,000.
In our example, we recognized flotation costs as one of the incremental costs of un-
dertaking the project. But instead of recognizing these costs explicitly, some companies
attempt to cope with flotation costs by increasing the cost of capital used to discount
project cash flows. By using a higher discount rate, project present value is reduced.
This procedure is flawed on practical as well as theoretical grounds. First, on a
purely practical level, it is far easier to account for flotation costs as a negative cash
flow than to search for an adjustment to the discount rate that will give the right NPV.
Finding the necessary adjustment is easy only when cash flows are level or will grow
indefinitely at a constant trend rate. This is almost never the case in practice, however.
Of course, there always exists some discount rate that will give the right measure of the
project’s NPV, but this rate could no longer be interpreted as the rate of return available
in the capital market for investments with the same risk as the project.
Summary
Why do firms compute weighted-average costs of capital?
They need a standard discount rate for average-risk projects. An “average-risk” project is
one that has the same risk as the firm’s existing assets and operations.
What about projects that are not average?
The weighted-average cost of capital can still be used as a benchmark. The benchmark is
adjusted up for unusually risky projects and down for unusually safe ones.
How do firms compute weighted-average costs of capital?
Here’s the WACC formula one more time:
The cost of capital depends only on interest rates, taxes, and the risk of the
project. Flotation costs should be treated as incremental (negative) cash flows;
they do not increase the required rate of return.
The Cost of Capital 455
WACC = r
debt

× (1 – T
c
) × D/V + r
equity
× E/V
The WACC is the expected rate of return on the portfolio of debt and equity securities
issued by the firm. The required rate of return on each security is weighted by its proportion
of the firm’s total market value (not book value). Since interest payments reduce the firm’s
income tax bill, the required rate of return on debt is measured after tax, as r
debt
× (1 – T
c
).
This WACC formula is usually written assuming the firm’s capital structure includes just
two classes of securities, debt and equity. If there is another class, say preferred stock, the
formula expands to include it. In other words, we would estimate r
preferred
, the rate of return
demanded by preferred stockholders, determine P/V, the fraction of market value accounted
for by preferred, and add r
preferred
× P/V to the equation. Of course the weights in the WACC
formula always add up to 1.0. In this case D/V + P/V + E/V = 1.0.
How are the costs of debt and equity calculated?
The cost of debt (r
debt
) is the market interest rate demanded by bondholders. In other words,
it is the rate that the company would pay on new debt issued to finance its investment
projects. The cost of preferred (r
preferred

) is just the preferred dividend divided by the market
price of a preferred share.
The tricky part is estimating the cost of equity (r
equity
), the expected rate of return on the
firm’s shares. Financial managers use the capital asset pricing model to estimate expected
return. But for mature, steady-growth companies, it can also make sense to use the constant-
growth dividend discount model. Remember, estimates of expected return are less reliable
for a single firm’s stock than for a sample of comparable-risk firms. Therefore, some
managers also consider WACCs calculated for industries.
What happens when capital structure changes?
The rates of return on debt and equity will change. For example, increasing the debt ratio
will increase the risk borne by both debt and equity investors and cause them to demand
higher returns. However, this does not necessarily mean that the overall WACC will
increase, because more weight is put on the cost of debt, which is less than the cost of
equity. In fact, if we ignore taxes, the overall cost of capital will stay constant as the
fractions of debt and equity change.
Should WACC be adjusted for the costs of issuing securities to finance a project?
No. If acceptance of a project would require the firm to issue securities, the flotation costs
of the issue should be added to the investment required for the project. This reduces project
NPV dollar for dollar. There is no need to adjust WACC.
www.geocities.com/WallStreet/Market/1839/irates.html Incorporating risk premiums into the
cost of capital
www.financeadvisor.com/coc.htm Another approach to calculating cost of capital
capital structure weighted-average cost of capital (WACC)
1. Cost of Debt. Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon
rate of 9 percent, paid annually. Today, the debt is selling at $1,050. If the firm’s tax bracket
is 35 percent, what is its after-tax cost of debt?
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Key Terms
Quiz
456 SECTION FOUR
2. Cost of Preferred Stock. Micro Spinoffs also has preferred stock outstanding. The stock
pays a dividend of $4 per share, and the stock sells for $40. What is the cost of preferred
stock?
3. Calculating WACC. Suppose Micro Spinoffs’s cost of equity is 12.5 percent. What is its
WACC if equity is 50 percent, preferred stock is 20 percent, and debt is 30 percent of total
capital?
4. Cost of Equity. Reliable Electric is a regulated public utility, and it is expected to provide
steady growth of dividends of 5 percent per year for the indefinite future. Its last dividend
was $5 per share; the stock sold for $60 per share just after the dividend was paid. What is
the company’s cost of equity?
5. Calculating WACC. Reactive Industries has the following capital structure. Its corporate tax
rate is 35 percent. What is its WACC?
Security Market Value Required Rate of Return
Debt $20 million 8%
Preferred stock $10 million 10%
Common stock $50 million 15%
6. Company versus Project Discount Rates. Geothermal’s WACC is 11.4 percent. Executive
Fruit’s WACC is 12.3 percent. Now Executive Fruit is considering an investment in geother-
mal power production. Should it discount project cash flows at 12.3 percent? Why or why
not?
7. Flotation Costs. A project costs $10 million and has NPV of $+2.5 million. The NPV is
computed by discounting at a WACC of 15 percent. Unfortunately, the $10 million invest-
ment will have to be raised by a stock issue. The issue would incur flotation costs of $1.2
million. Should the project be undertaken?
8. WACC. The common stock of Buildwell Conservation & Construction, Inc., has a beta of
.80. The Treasury bill rate is 4 percent and the market risk premium is estimated at 8 per-
cent. BCCI’s capital structure is 30 percent debt paying a 5 percent interest rate, and 70 per-

cent equity. What is BCCI’s cost of equity capital? Its WACC? Buildwell pays no taxes.
9. WACC and NPV. BCCI (see the previous problem) is evaluating a project with an internal
rate of return of 12 percent. Should it accept the project? If the project will generate a cash
flow of $100,000 a year for 7 years, what is the most BCCI should be willing to pay to ini-
tiate the project?
10. Calculating WACC. Find the WACC of William Tell Computers. The total book value of the
firm’s equity is $10 million; book value per share is $20. The stock sells for a price of $30
per share, and the cost of equity is 15 percent. The firm’s bonds have a par value of $5 mil-
lion and sell at a price of 110 percent of par. The yield to maturity on the bonds is 9 percent,
and the firm’s tax rate is 40 percent.
11. WACC. Nodebt, Inc., is a firm with all-equity financing. Its equity beta is .80. The Treasury
bill rate is 5 percent and the market risk premium is expected to be 10 percent. What is
Nodebt’s asset beta? What is Nodebt’s weighted-average cost of capital? The firm is exempt
from paying taxes.
12. Cost of Capital. A financial analyst at Dawn Chemical notes that the firm’s total interest
payments this year were $10 million while total debt outstanding was $80 million, and he
concludes that the cost of debt was 12.5 percent. What is wrong with this conclusion?
13. Cost of Equity. Bunkhouse Electronics is a recently incorporated firm that makes electronic
entertainment systems. Its earnings and dividends have been growing at a rate of 30 percent,
Practice
Problems
The Cost of Capital 457
and the current dividend yield is 2 percent. Its beta is 1.2, the market risk premium is 8 per-
cent, and the risk-free rate is 4 percent.
a. Calculate two estimates of the firm’s cost of equity.
b. Which estimate seems more reasonable to you? Why?
14. Cost of Debt. Olympic Sports has two issues of debt outstanding. One is a 9 percent coupon
bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10
percent. The coupons are paid annually. The other bond issue has a maturity of 15 years, with
coupons also paid annually, and a coupon rate of 10 percent. The face value of the issue

is $25 million, and the issue sells for 92.8 percent of par value. The firm’s tax rate is 35
percent.
a. What is the before-tax cost of debt for Olympic?
b. What is Olympic’s after-tax cost of debt?
15. Capital Structure. Examine the following book-value balance sheet for University Prod-
ucts, Inc. What is the capital structure of the firm based on market values? The preferred
stock currently sells for $15 per share and the common stock for $20 per share. There are
one million common shares outstanding.
BOOK VALUE BALANCE SHEET
(all values in millions)
Assets Liabilities and Net Worth
Cash and short-term securities $ 1 Bonds, coupon = 8%, paid $10.0
annually (maturity = 10 years,
current yield to maturity = 9%)
Accounts receivable 3 Preferred stock (par value $20 2.0
per share)
Inventories 7 Common stock (par value $.10) .1
Plant and equipment 21 Additional paid in stockholders’ 9.9
capital
Retained earnings 10.0
Total $32 Total $32.0
16. Calculating WACC. Turn back to University Products’s balance sheet from the previous
problem. If the preferred stock pays a dividend of $2 per share, the beta of the stock is .8,
the market risk premium is 10 percent, the risk-free rate is 6 percent, and the firm’s tax rate
is 40 percent, what is University’s weighted-average cost of capital?
17. Project Discount Rate. University Products is evaluating a new venture into home com-
puter systems (see problems 15 and 16). The internal rate of return on the new venture
is estimated at 13.4 percent. WACCs of firms in the personal computer industry tend to
average around 14 percent. Should the new project be pursued? Will University Products
make the correct decision if it discounts cash flows on the proposed venture at the firm’s

WACC?
18. Cost of Capital. The total market value of Okefenokee Real Estate Company is $6 million,
and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock
currently is 1.5 and that the expected risk premium on the market is 10 percent. The Trea-
sury bill rate is 4 percent.
a. What is the required rate of return on Okefenokee stock?
b. What is the beta of the company’s existing portfolio of assets? The debt is perceived to
be virtually risk-free.
458 SECTION FOUR
c. Estimate the weighted-average cost of capital assuming a tax rate of 40 percent.
d. Estimate the discount rate for an expansion of the company’s present business.
e. Suppose the company wants to diversify into the manufacture of rose-colored glasses.
The beta of optical manufacturers with no debt outstanding is 1.2. What is the required
rate of return on Okefenokee’s new venture?
19. Changes in Capital Structure. Look again at our calculation of Big Oil’s WACC. Suppose
Big Oil is excused from paying taxes. How would its WACC change? Now suppose Big Oil
makes a large stock issue and uses the proceeds to pay off all its debt. How would the cost
of equity change?
20. Changes in Capital Structure. Refer again to problem 19. Suppose Big Oil starts from the
financing mix in Table 4.13, and then borrows an additional $200 million from the bank. It
then pays out a special $200 million dividend, leaving its assets and operations unchanged.
What happens to Big Oil’s WACC, still assuming it pays no taxes? What happens to the cost
of equity?
21. WACC and Taxes. “The after-tax cost of debt is lower when the firm’s tax rate is higher;
therefore, the WACC falls when the tax rate rises. Thus, with a lower discount rate, the firm
must be worth more if its tax rate is higher.” Explain why this argument is wrong.
22. Cost of Capital. An analyst at Dawn Chemical notes that its cost of debt is far below that
of equity. He concludes that it is important for the firm to maintain the ability to increase its
borrowing because if it cannot borrow, it will be forced to use more expensive equity to fi-
nance some projects. This might lead it to reject some projects that would have seemed at-

tractive if evaluated at the lower cost of debt. Comment on this reasoning.
1 Hot Rocks’s 4 million common shares are worth $40 million. Its market value balance sheet
is:
Assets Liabilities and Shareholders’ Equity
Assets $90 Debt $50 (56%)
Equity 40 (44%)
Value $90 Value $90
WACC = (.56 × 9%) + (.44 × 17%) = 12.5%
We use Hot Rocks’s pretax return on debt because the company pays no taxes.
2 Burg’s 6 million shares are now worth only 6 million × $4 = $24 million. The debt is sell-
ing for 80 percent of book, or $20 million. The market value balance sheet is:
Assets Liabilities and Shareholders’ Equity
Assets $44 Debt $20 (45%)
Equity 24 (55%)
Value $44 Value $44
WACC = (.45 × 14%) + (.55 × 20%) = 17.3%
Note that this question ignores taxes.
Challenge
Problems
Solutions to
Self-Test
Questions
The Cost of Capital 459
3 Compare the two income statements, one for Criss-cross Industries and the other for a firm
with identical EBIT but no debt in its capital structure. (All figures in millions.)
Criss-cross Firm with No Debt
EBIT $10.0 $10.0
Interest expense 2.0 0.0
Taxable income 8.0 10.0
Taxes owed 2.8 3.5

Net income 5.2 6.5
Total income accruing to debt & equity holders 7.2 6.5
Notice that Criss-cross pays $.7 million less in taxes than its debt-free counterpart. Ac-
cordingly, the total income available to debt plus equity holders is $.7 million higher.
4 For Hot Rocks,
WACC = [.56 × 9 × (1 – .35)] + (.44 × 17) = 10.76%
For Burg Associates,
WACC = [.45 × 14 × (1 – .35)] + (.55 × 20) = 15.1%
5 WACC measures the expected rate of return demanded by debt and equity investors in the
firm (plus a tax adjustment capturing the tax-deductibility of interest payments). Thus the
calculation must be based on what investors are actually paying for the firm’s debt and eq-
uity securities. In other words, it must be based on market values.
6 From the CAPM:
r
equity
= r
f
+ β
equity
(r
m
– r
f
)
= 6% + 1.20(9%) = 16.8%
WACC = .3(1 – .35) 8% + .7(16.8%) = 13.3%
7 Jo Ann’s boss is wrong. The ability to borrow at 8 percent does not mean that the cost of
capital is 8 percent. This analysis ignores the side effects of the borrowing, for example, that
at the higher indebtedness of the firm the equity will be riskier, and therefore the equity-
holders will demand a higher rate of return on their investment.

MINICASE
Bernice Mountaindog was glad to be back at Sea Shore Salt.
Employees were treated well. When she had asked a year ago for
a leave of absence to complete her degree in finance, top man-
agement promptly agreed. When she returned with an honors de-
gree, she was promoted from administrative assistant (she had
been secretary to Joe-Bob Brinepool, the president) to treasury
analyst.
Bernice thought the company’s prospects were good. Sure,
table salt was a mature business, but Sea Shore Salt had grown
steadily at the expense of its less well-known competitors. The
company’s brand name was an important advantage, despite the
difficulty most customers had in pronouncing it rapidly.
Bernice started work on January 2, 2000. The first two weeks
went smoothly. Then Mr. Brinepool’s cost of capital memo as-
signed her to explain Sea Shore Salt’s weighted-average cost of
capital to other managers. The memo came as a surprise to Ber-
nice, so she stayed late to prepare for the questions that would
surely come the next day.
Bernice first examined Sea Shore Salt’s most recent balance
sheet, summarized in Table 4.14. Then she jotted down the fol-
lowing additional points:
• The company’s bank charged interest at current market rates,
and the long-term debt had just been issued. Book and market
values could not differ by much.
• But the preferred stock had been issued 35 years ago, when
460 SECTION FOUR
interest rates were much lower. The preferred stock was now
trading for only $70 per share.
• The common stock traded for $40 per share. Next year’s earn-

ings per share would be about $4.00 and dividends per share
probably $2.00. Sea Shore Salt had traditionally paid out 50
percent of earnings as dividends and plowed back the rest.
• Earnings and dividends had grown steadily at 6 to 7 percent
per year, in line with the company’s sustainable growth rate:
Sustainable
=
return
×
plowback
growth rate on equity ratio
= 4.00/30 × .5
= .067, or 6.7%
• Sea Shore Salt’s beta had averaged about .5, which made
sense, Bernice thought, for a stable, steady-growth business.
She made a quick cost of equity calculation using the capital
asset pricing model (CAPM). With current interest rates of
about 7 percent, and a market risk premium of 8 percent,
CAPM cost of equity = r
E
= r
f
+ β(r
m
– r
f
)
= 7% + .5(8%) = 11%
This cost of equity was significantly less than the 16 percent
decreed in Mr. Brinepool’s memo. Bernice scanned her notes ap-

prehensively. What if Mr. Brinepool’s cost of equity was wrong?
Was there some other way to estimate the cost of equity as a
check on the CAPM calculation? Could there be other errors in
his calculations?
Bernice resolved to complete her analysis that night. If neces-
sary, she would try to speak with Mr. Brinepool when he arrived
at his office the next morning. Her job was not just finding the
right number. She also had to figure out how to explain it all to
Mr. Brinepool.
TABLE 4.14
Sea Shore Salt’s balance
sheet, taken from the
company’s 1999 balance
sheet (figures in millions)
Assets Liabilities and Net Worth
Working capital $200 Bank loan $120
Plant and equipment 360 Long-term debt 80
Other assets 40 Preferred stock 100
Common stock, including retained earnings 300
Total $600 Total $600
Notes:
1. At year-end 1999, Sea Shore Salt had 10 million common shares outstanding.
2. The company had also issued 1 million preferred shares with book value of $100 per share. Each share
receives an annual dividend of $6.00.
The Cost of Capital 461
Sea Shore Salt Company
Spring Vacation Beach, Florida
CONFIDENTIAL MEMORANDUM
DATE: January 15, 2000
TO: S.S.S. Management

FROM: Joe-Bob Brinepool, President
SUBJECT: Cost of Capital
This memo states and clarifies our company’s long-standing policy regarding hurdle rates
for capital investment decisions. There have been many recent questions, and some evident
confusion, on this matter.
Sea Shore Salt evaluates replacement and expansion investments by discounted cash flow.
The discount or hurdle rate is the company’s after-tax weighted-average cost of capital.
The weighted-average cost of capital is simply a blend of the rates of return expected by
investors in our company. These investors include banks, bond holders, and preferred
stock investors in addition to common stockholders. Of course many of you are, or soon
will be, stockholders of our company.
The following table summarizes the composition of Sea Shore Salt’s financing.
Amount (in millions) Percent of Total Rate of Return
Bank loan $120 20% 8%
Bond issue 80 13.3 7.75
Preferred stock 100 16.7 6
Common stock 300 50 16
$600 100%
The rates of return on the bank loan and bond issue are of course just the interest rates
we pay. However, interest is tax-deductible, so the after-tax interest rates are lower
than shown above. For example, the after-tax cost of our bank financing, given our 35%
tax rate, is 8(1 – .35) = 5.2%.
The rate of return on preferred stock is 6%. Sea Shore Salt pays a $6 dividend on each
$100 preferred share.
Our target rate of return on equity has been 16% for many years. I know that some
newcomers think this target is too high for the safe and mature salt business. But we
must all aspire to superior profitability.
Once this background is absorbed, the calculation of Sea Shore Salt’s weighted-average
cost of capital (WACC) is elementary:
WACC = 8(1 – .35)(.2) + 7.75(1 – .35)(.133) + 6(.167) + 16(.50) = 10.7%

The official corporate hurdle rate is therefore 10.7%.
If you have further questions about these calculations, please direct them to our new
Treasury Analyst, Ms. Bernice Mountaindog. It is a pleasure to have Bernice back at Sea
Shore Salt after a year’s leave of absence to complete her degree in finance.
Project Analysis
An Overview of Corporate Financing
How Corporations Issue Securities
Section 5
465
PROJECT ANALYSIS
How Firms Organize the
Investment Process
Stage 1: The Capital Budget
Stage 2: Project Authorizations
Problems and Some Solutions
Some “What-If” Questions
Sensitivity Analysis
Scenario Analysis
Break-Even Analysis
Accounting Break-Even Analysis
NPV Break-Even Analysis
Operating Leverage
Flexibility in Capital
Budgeting
Decision Trees
The Option to Expand
Abandonment Options
Flexible Production Facilities

Investment Timing Options
Summary
“But Mr. Mitterand, have you thought of sensitivity analysis?”
Prime Minister Margaret Thatcher and President Francois Mitterand meet to sign the treaty
leading to construction of a railway tunnel under the English Channel between England and
France.
AP/Wide World Photos
t helps to use discounted cash-flow techniques to value new projects but
good investment decisions also require good data. Therefore, we start
this material by thinking about how firms organize the capital budgeting
operation to get the kind of information they need. In addition, we look at
how they try to ensure that everyone involved works together toward a common goal.
Project evaluation should never be a mechanical exercise in which the financial man-
ager takes a set of cash-flow forecasts and cranks out a net present value. Cash-flow es-
timates are just that—estimates. Financial managers need to look behind the forecasts
to try to understand what makes the project tick and what could go wrong with it. A
number of techniques have been developed to help managers identify the key assump-
tions in their analysis. These techniques involve asking a number of “what-if ” ques-
tions. What if your market share turns out to be higher or lower than you forecast? What
if interest rates rise during the life of the project? In the second part of this material we
show how managers use the techniques of sensitivity analysis, scenario analysis, and
break-even analysis to help answer these what-if questions.
Books about capital budgeting sometimes create the impression that once the man-
ager has made an investment decision, there is nothing to do but sit back and watch the
cash flows develop. But since cash flows rarely proceed as anticipated, companies con-
stantly need to modify their operations. If cash flows are better than anticipated, the
project may be expanded; if they are worse, it may be scaled back or abandoned alto-
gether. In the third section of this material we describe how good managers take account
of these options when they analyze a project and why they are willing to pay money
today to build in future flexibility.

After studying this material you should be able to
᭤
Appreciate the practical problems of capital budgeting in large corporations.
᭤
Use sensitivity, scenario, and break-even analysis to see how project profitability
would be affected by an error in your forecasts and understand why an overestimate
of sales is more serious for projects with high operating leverage.
᭤
Recognize the importance of managerial flexibility in capital budgeting.
466
I
How Firms Organize
the Investment Process
For most sizable firms, investments are evaluated in two separate stages.
Project Analysis 467
STAGE 1: THE CAPITAL BUDGET
Once a year, the head office generally asks each of its divisions and plants to provide a
list of the investments that they would like to make.
1
These are gathered together into a
proposed capital budget.
This budget is then reviewed and pruned by senior management and staff specializ-
ing in planning and financial analysis. Usually there are negotiations between the firm’s
senior management and its divisional management, and there may also be special analy-
ses of major outlays or ventures into new areas. Once the budget has been approved, it
generally remains the basis for planning over the ensuing year.
Many investment proposals bubble up from the bottom of the organization. But
sometimes the ideas are likely to come from higher up. For example, the managers of
plants A and B cannot be expected to see the potential benefits of closing their plants
and consolidating production at a new plant C. We expect divisional management to

propose plant C. Similarly, divisions 1 and 2 may not be eager to give up their own data
processing operations to a large central computer. That proposal would come from sen-
ior management.
Senior management’s concern is to see that the capital budget matches the firm’s
strategic plans. It needs to ensure that the firm is concentrating its efforts in areas where
it has a real competitive advantage. As part of this effort, management must also iden-
tify declining businesses that should be sold or allowed to run down.
The firm’s capital investment choices should reflect both “bottom-up” and “top-
down” processes—capital budgeting and strategic planning, respectively. The two
processes should complement each other. Plant and division managers, who do most of
the work in bottom-up capital budgeting, may not see the forest for the trees. Strategic
planners may have a mistaken view of the forest because they do not look at the trees.
STAGE 2: PROJECT AUTHORIZATIONS
The annual budget is important because it allows everybody to exchange ideas before
attitudes have hardened and personal commitments have been made. However, the fact
that your pet project has been included in the annual budget doesn’t mean you have per-
mission to go ahead with it. At a later stage you will need to draw up a detailed proposal
describing particulars of the project, engineering analyses, cash-flow forecasts, and
present value calculations. If your project is large, this proposal may have to pass a
number of hurdles before it is finally approved.
The type of backup information that you need to provide depends on the project cat-
egory. For example, some firms use a fourfold breakdown:
1. Outlays required by law or company policy, for example, for pollution control equip-
ment. These outlays do not need to be justified on financial grounds. The main issue
is whether requirements are satisfied at the lowest possible cost. The decision is
therefore likely to hinge on engineering analyses of alternative technologies.
2. Maintenance or cost reduction, such as machine replacement. Engineering analysis
is also important in machine replacement, but new machines have to pay their own
way.
3. Capacity expansion in existing businesses. Projects in this category are less straight-

ACAPITAL BUDGET
List of planned investment
projects.
1
Large firms may be divided into several divisions. For example, International Paper has divisions that spe-
cialize in printing paper, packaging, specialty products, and forest products. Each of these divisions may be
responsible for a number of plants.
468 SECTION FIVE
forward; these decisions may hinge on forecasts of demand, possible shifts in tech-
nology, and the reactions of competitors.
4. Investment for new products. Projects in this category are most likely to depend on
strategic decisions. The first projects in a new area may not have positive NPVs if
considered in isolation, but they may give the firm a valuable option to undertake
follow-up projects. More about this later.
PROBLEMS AND SOME SOLUTIONS
Valuing capital investment opportunities is hard enough when you can do the entire job
yourself. In most firms, however, capital budgeting is a cooperative effort, and this
brings with it some challenges.
Ensuring that Forecasts Are Consistent. Inconsistent assumptions often creep into
investment proposals. For example, suppose that the manager of the furniture division
is bullish (optimistic) on housing starts but the manager of the appliance division is
bearish (pessimistic). This inconsistency makes the projects proposed by the furniture
division look more attractive than those of the appliance division.
To ensure consistency, many firms begin the capital budgeting process by establish-
ing forecasts of economic indicators, such as inflation and the growth in national in-
come, as well as forecasts of particular items that are important to the firm’s business,
such as housing starts or the price of raw materials. These forecasts can then be used as
the basis for all project analyses.
Eliminating Conflicts of Interest. Earlier we pointed out that while managers want
to do a good job, they are also concerned about their own futures. If the interests of

managers conflict with those of stockholders, the result is likely to be poor investment
decisions. For example, new plant managers naturally want to demonstrate good per-
formance right away. To this end, they might propose quick-payback projects even if
NPV is sacrificed. Unfortunately, many firms measure performance and reward man-
agers in ways that encourage such behavior. If the firm always demands quick results,
it is unlikely that plant managers will concentrate only on NPV.
Reducing Forecast Bias. Someone who is keen to get a project proposal accepted is
also likely to look on the bright side when forecasting the project’s cash flows. Such
overoptimism is a common feature in financial forecasts. For example, think of large
public expenditure proposals. How often have you heard of a new missile, dam, or high-
way that actually cost less than was originally forecast? Think back to the Eurotunnel
project. The final cost of the project was about 50 percent higher than initial forecasts.
It is probably impossible to ever eliminate bias completely, but if senior management is
aware of why bias occurs, it is at least partway to solving the problem.
Project sponsors are likely to overstate their case deliberately only if the head office
encourages them to do so. For example, if middle managers believe that success de-
pends on having the largest division rather than the most profitable one, they will pro-
pose large expansion projects that they do not believe have the largest possible net pres-
ent value. Or if divisions must compete for limited resources, they will try to outbid
each other for those resources. The fault in such cases is top management’s—if lower
level managers are not rewarded based on net present value and contribution to firm
value, it should not be surprising that they focus their efforts elsewhere.
Other problems stem from sponsors’ eagerness to obtain approval for their favorite
Project Analysis 469
projects. As the proposal travels up the organization, alliances are formed. Thus once a
division has screened its own plants’ proposals, the plants in that division unite in com-
peting against outsiders. The result is that the head office may receive several thousand
investment proposals each year, all essentially sales documents presented by united
fronts and designed to persuade. The forecasts have been doctored to ensure that NPV
appears positive.

Since it is difficult for senior management to evaluate each specific assumption in
an investment proposal, capital investment decisions are effectively decentralized what-
ever the rules say. Some firms accept this; others rely on head office staff to check cap-
ital investment proposals.
Sorting the Wheat from the Chaff. Senior managers are continually bombarded
with requests for funds for capital expenditures. All these requests are supported with
detailed analyses showing that the projects have positive NPVs. How then can managers
ensure that only worthwhile projects make the grade? One response of senior managers
to this problem of poor information is to impose rigid expenditure limits on individual
plants or divisions. These limits force the subunits to choose among projects. The firm
ends up using capital rationing not because capital is unobtainable but as a way of de-
centralizing decisions.
2
Senior managers might also ask some searching questions about why the project has
a positive NPV. After all, if the project is so attractive, why hasn’t someone already un-
dertaken it? Will others copy your idea if it is so profitable? Positive NPVs are plausi-
ble only if your company has some competitive advantage.
Such an advantage can arise in several ways. You may be smart or lucky enough to
be the first to the market with a new or improved product for which customers will pay
premium prices. Your competitors eventually will enter the market and squeeze out ex-
cess profits, but it may take them several years to do so. Or you may have a proprietary
technology or production cost advantage that competitors cannot easily match. You may
have a contractual advantage such as the distributorship for a particular region. Or your
advantage may be as simple as a good reputation and an established customer list.
Analyzing competitive advantage can also help ferret out projects that incorrectly
appear to have a negative NPV. If you are the lowest cost producer of a profitable prod-
uct in a growing market, then you should invest to expand along with the market. If your
calculations show a negative NPV for such an expansion, then you probably have made
a mistake.
Some “What-If” Questions

SENSITIVITY ANALYSIS
Uncertainty means that more things can happen than will happen. Therefore, whenever
managers are given a cash-flow forecast, they try to determine what else might happen
and the implications of those possible events. This is called sensitivity analysis.
Put yourself in the well-heeled shoes of the financial manager of the Finefodder su-
permarket chain. Finefodder is considering opening a new superstore in Gravenstein
2
We discussed capital rationing earlier.
SENSITIVITY
ANALYSIS Analysis of
the effects on project
profitability of changes in
sales, costs, and so on.
470 SECTION FIVE
and your staff members have prepared the figures shown in Table 5.1. The figures are
fairly typical for a new supermarket, except that to keep the example simple we have
assumed no inflation. We have also assumed that the entire investment can be depreci-
ated straight-line for tax purposes, we have neglected the working capital requirement,
and we have ignored the fact that at the end of the 12 years you could sell off the land
and buildings.
As an experienced financial manager, you recognize immediately that these cash
flows constitute an annuity and therefore you calculate present value by multiplying the
$780,000 cash flow by the 12-year annuity factor. If the cost of capital is 8 percent,
present value is
PV = $780,000 × 12-year annuity factor
= $780,000 × 7.536 = $5.878 million
Subtract the initial investment of $5.4 million and you obtain a net present value of
$478,000:
NPV = PV – investment
= $5.878 million – $5.4 million = $478,000

Before you agree to accept the project, however, you want to delve behind these fore-
casts and identify the key variables that will determine whether the project succeeds or
fails.
Some of the costs of running a supermarket are fixed. For example, regardless of the
level of output, you still have to heat and light the store and pay the store manager.
These fixed costs are forecast to be $2 million per year.
Other costs vary with the level of sales. In particular, the lower the sales, the less
food you need to buy. Also, if sales are lower than forecast, you can operate a lower
number of checkouts and reduce the staff needed to restock the shelves. The new su-
perstore’s variable costs are estimated at 81.25 percent of sales. Thus variable costs =
.8125 × $16 million = $13 million.
The initial investment of $5.4 million will be depreciated on a straight-line basis over
the 12-year period, resulting in annual depreciation of $450,000. Profits are taxed at a
rate of 40 percent.
These seem to be the important things you need to know, but look out for things that
may have been forgotten. Perhaps there will be delays in obtaining planning permission,
TABLE 5.1
Cash-flow forecasts for
Finefodder’s new superstore
Year 0 Years 1–12
Investment –$5,400,000
1. Sales $16,000,000
2. Variable costs 13,000,000
3. Fixed costs 2,000,000
4. Depreciation 450,000
5. Pretax profit (1 – 2 – 3 – 4) 550,000
6. Taxes (at 40%) 220,000
7. Profit after tax 330,000
8. Cash flow from operations (4 + 7) 780,000
Net cash flow –$5,400,000 $ 780,000

FIXED COSTS Costs
that do not depend on the
level of output.
VARIABLE COSTS
Costs that change as the
level of output changes.
Project Analysis 471
or perhaps you will need to undertake costly landscaping. The greatest dangers often lie
in these unknown unknowns, or “unk-unks,” as scientists call them.
Having found no unk-unks (no doubt you’ll find them later), you look at how NPV
may be affected if you have made a wrong forecast of sales, costs, and so on. To do this,
you first obtain optimistic and pessimistic estimates for the underlying variables. These
are set out in the left-hand columns of Table 5.2.
Next you see what happens to NPV under the optimistic or pessimistic forecasts for
each of these variables. You recalculate project NPV under these various forecasts to de-
termine which variables are most critical to NPV.
᭤
EXAMPLE 1 Sensitivity Analysis
The right-hand side of Table 5.2 shows the project’s net present value if the variables are
set one at a time to their optimistic and pessimistic values. For example, if fixed costs
are $1.9 million rather than the forecast $2.0 million, annual cash flows are increased
by (1 – tax rate) × ($2.0 million – $1.9 million) = .6 × $100,000 = $60,000. If the cash
flow increases by $60,000 a year for 12 years, then the project’s present value increases
by $60,000 times the 12-year annuity factor, or $60,000 × 7.536 = $452,000. Therefore,
NPV increases from the expected value of $478,000 to $478,000 + $452,000 =
$930,000, as shown in the bottom right corner of the table. The other entries in the three
columns on the right in Table 5.2 similarly show how the NPV of the project changes
when each input is changed.
Your project is by no means a sure thing. The principal uncertainties appear to be
sales and variable costs. For example, if sales are only $14 million rather than the fore-

cast $16 million (and all other forecasts are unchanged), then the project has an NPV
of –$1.218 million. If variable costs are 83 percent of sales (and all other forecasts are
unchanged), then the project has an NPV of –$788,000.
᭤
Self-Test 1 Recalculate cash flow as in Table 5.1 if variable costs are 83 percent of sales. Confirm
that NPV will be –$788,000.
Value of Information. Now that you know the project could be thrown badly off
course by a poor estimate of sales, you might like to see whether it is possible to resolve
TABLE 5.2
Sensitivity analysis for superstore project
Range NPV
Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic
Investment 6,200,000 5,400,000 5,000,000 –121,000 +478,000 +778,000
Sales 14,000,000 16,000,000 18,000,000 –1,218,000 +478,000 +2,174,000
Variable cost as
percent of sales 83 81.25 80 –788,000 +478,000 +1,382,000
Fixed cost 2,100,000 2,000,000 1,900,000 +26,000 +478,000 +930,000
472 SECTION FIVE
some of this uncertainty. Perhaps your worry is that the store will fail to attract suffi-
cient shoppers from neighboring towns. In that case, additional survey data and more
careful analysis of travel times may be worthwhile.
On the other hand, there is less value to gathering additional information about
fixed costs. Because the project is marginally profitable even under pessimistic assump-
tions about fixed costs, you are unlikely to be in trouble if you have misestimated that
variable.
Limits to Sensitivity Analysis. Your analysis of the forecasts for Finefodder’s new
superstore is known as a sensitivity analysis. Sensitivity analysis expresses cash flows
in terms of unknown variables and then calculates the consequences of misestimating
those variables. It forces the manager to identify the underlying factors, indicates where
additional information would be most useful, and helps to expose confused or inappro-

priate forecasts.
Of course, there is no law stating which variables you should consider in your sen-
sitivity analysis. For example, you may wish to look separately at labor costs and the
costs of the goods sold. Or, if you are concerned about a possible change in the corpo-
rate tax rate, you may wish to look at the effect of such a change on the project’s NPV.
One drawback to sensitivity analysis is that it gives somewhat ambiguous results. For
example, what exactly does optimistic or pessimistic mean? One department may be in-
terpreting the terms in a different way from another. Ten years from now, after hundreds
of projects, hindsight may show that one department’s pessimistic limit was exceeded
twice as often as the other’s; but hindsight won’t help you now while you’re making the
investment decision.
Another problem with sensitivity analysis is that the underlying variables are likely
to be interrelated. For example, if sales exceed expectations, demand will likely be
stronger than you anticipated and your profit margins will be wider. Or, if wages are
higher than your forecast, both variable costs and fixed costs are likely to be at the upper
end of your range.
Because of these connections, you cannot push one-at-a-time sensitivity analysis too
far. It is impossible to obtain expected, optimistic, and pessimistic values for total proj-
ect cash flows from the information in Table 5.2. Still, it does give a sense of which vari-
ables should be most closely monitored.
SCENARIO ANALYSIS
When variables are interrelated, managers often find it helpful to look at how their proj-
ect would fare under different scenarios. Scenario analysis allows them to look at dif-
ferent but consistent combinations of variables. Forecasters generally prefer to give an
estimate of revenues or costs under a particular scenario rather than giving some ab-
solute optimistic or pessimistic value.
᭤
EXAMPLE 2 Scenario Analysis
You are worried that Stop and Scoff may decide to build a new store in nearby Salome.
That would reduce sales in your Gravenstein store by 15 percent and you might be

forced into a price war to keep the remaining business. Prices might be reduced to the
point that variable costs equal 82 percent of revenue. Table 5.3 shows that under this
SCENARIO ANALYSIS
Project analysis given a
particular combination of
assumptions.
Project Analysis 473
scenario of lower sales and smaller margins your new venture would no longer be
worthwhile.
An extension of scenario analysis is called simulation analysis. Here, instead of
specifying a relatively small number of scenarios, a computer generates several hundred
or thousand possible combinations of variables according to probability distributions
specified by the analyst. Each combination of variables corresponds to one scenario.
Project NPV and other outcomes of interest can be calculated for each combination of
variables, and the entire probability distribution of outcomes can be constructed from
the simulation results.
᭤
Self-Test 2 What is the basic difference between sensitivity analysis and scenario analysis?
Break-Even Analysis
When we undertake a sensitivity analysis of a project or when we look at alternative
scenarios, we are asking how serious it would be if we have misestimated sales or costs.
Managers sometimes prefer to rephrase this question and ask how far off the estimates
could be before the project begins to lose money. This exercise is known as break-even
analysis.
For many projects, the make-or-break variable is sales volume. Therefore, managers
most often focus on the break-even level of sales. However, you might also look at other
variables, for example, at how high costs could be before the project goes into the red.
As it turns out, “losing money” can be defined in more than one way. Most often,
the break-even condition is defined in terms of accounting profits. More properly, how-
ever, it should be defined in terms of net present value. We will start with accounting

TABLE 5.3
Scenario analysis, NPV of
Finefodder’s Gravenstein
superstore with scenario of
new competing store in
nearby Salome
Cash Flows Years 1–12
Base Case Competing Store Scenario
a
1. Sales $16,000,000 $13,600,000
2. Variable costs 13,000,000 11,152,000
3. Fixed costs 2,000,000 2,000,000
4. Depreciation 450,000 450,000
5. Pretax profit (1 – 2 – 3 – 4) 550,000 –2,000
6. Taxes (40%) 220,000 –800
7. Profit after tax 330,000 –1,200
8. Cash flow from operations (4 + 7) 780,000 448,800
Present value of cash flows 5,878,000 3,382,000
NPV 478,000 –2,018,000
a
Assumptions: Competing store causes (1) a 15 percent reduction in sales, and (2) variable costs to
increase to 82 percent of sales.
SIMULATION
ANALYSIS Estimation of
the probabilities of different
possible outcomes, e.g.,
from an investment project.
BREAK-EVEN
ANALYSIS
Analysis of

the level of sales at which the
company breaks even.
474 SECTION FIVE
break-even, show that it can lead you astray, and then show how NPV break-even can
be used as an alternative.
ACCOUNTING BREAK-EVEN ANALYSIS
The accounting break-even point is the level of sales at which profits are zero or, equiv-
alently, at which total revenues equal total costs. As we have seen, some costs are fixed
regardless of the level of output. Other costs vary with the level of output.
When you first analyzed the superstore project, you came up with the following es-
timates:
Sales $16 million
Variable cost 13 million
Fixed costs 2 million
Depreciation 0.45 million
Notice that variable costs are 81.25 percent of sales. So, for each additional dollar of
sales, costs increase by only $.8125. We can easily determine how much business
the superstore needs to attract to avoid losses. If the store sells nothing, the income
statement will show fixed costs of $2 million and depreciation of $450,000. Thus
there will be a loss of $2.45 million. Each dollar of sales reduces this loss by $1.00 –
$.8125 = $.1875. Therefore, to cover fixed costs plus depreciation, you need sales of
2.45 million/.1875 = $13.067 million. At this sales level, the firm will break even. More
generally,
fixed costs
Break-even level of revenues =
including depreciation
additional profit
from each additional dollar of sales
Table 5.4 shows how the income statement looks with only $13.067 million of sales.
Figure 5.1 shows how the break-even point is determined. The 45-degree line shows

accounting revenues. The cost line shows how costs vary with sales. If the store
doesn’t sell a cent, it still incurs fixed costs and depreciation amounting to $2.45 mil-
lion. Each extra dollar of sales adds $.8125 to these costs. When sales are $13.067 mil-
lion, the two lines cross, indicating that costs equal revenues. For lower sales, revenues
are less than costs and the project is in the red; for higher sales, revenues exceed costs
and the project moves into the black.
Is a project that breaks even in accounting terms an acceptable investment? If you
TABLE 5.4
Income statement, break-even
sales volume
Item $ Thousands
Revenues 13,067
Variable costs 10,617 (81.25 percent of sales)
Fixed costs 2,000
Depreciation 450
Pretax profit 0
Taxes 0
Profit after tax 0
Project Analysis 475
are not sure about the answer, here’s a possibly easier question. Would you be happy
about an investment in a stock that after 5 years gave you a total rate of return of zero?
We hope not. You might break even on such a stock but a zero return does not com-
pensate you for the time value of money or the risk that you have taken.
Let’s check this with the superstore project. Suppose that in each year the store has
sales of $13.067 million—just enough to break even on an accounting basis. What
would be the cash flow from operations?
Cash flow from operations = profit after tax + depreciation
= 0 + $450,000 = $450,000
The initial investment is $5.4 million. In each of the next 12 years, the firm receives a
cash flow of $450,000. So the firm gets its money back:

Total cash flow from operations = initial investment
12 × $450,000 = $5.4 million
But revenues are not sufficient to repay the opportunity cost of that $5.4 million in-
vestment. NPV is negative.
NPV BREAK-EVEN ANALYSIS
Instead of asking how bad sales can get before the project makes an accounting loss, it
is more useful to focus on the point at which NPV switches from positive to negative.
The cash flows of the project in each year will depend on sales as follows:
A project that simply breaks even on an accounting basis gives you your
money back but does not cover the opportunity cost of the capital tied up in
the project. A project that breaks even in accounting terms will surely have a
negative NPV.
FIGURE 5.1
Accounting break-even
analysis
Costs exceed revenue
Sales revenue, $ million
Revenue exceeds costs
13.067
Fixed costs
Variable costs
Revenue
Total costs
Costs and revenue, $ million
13.067
2.45
476 SECTION FIVE
1. Variable costs 81.25 percent of sales
2. Fixed costs $2 million
3. Depreciation $450,000

4. Pretax profit (.1875 × sales) – $2.45 million
5. Tax (at 40%) .40 × (.1875 × sales – $2.45 million)
6. Profit after tax .60 × (.1875 × sales – $2.45 million)
7. Cash flow (3 + 6) $450,000 + .60 × (.1875 × sales – $2.45 million)
= .1125 × sales – $1.02 million
This cash flow will last for 12 years. So to find its present value we multiply by the
12-year annuity factor. With a discount rate of 8 percent, the present value of $1 a year
for each of 12 years is $7.536. Thus the present value of the cash flows is
PV (cash flows) = 7.536 × (.1125 × sales – $1.02 million)
The project breaks even in present value terms (that is, has a zero NPV) if the pres-
ent value of these cash flows is equal to the initial $5.4 million investment. Therefore,
break-even occurs when
PV (cash flows) = investment
7.536 × (.1125 × sales – $1.02 million) = $5.4 million
–$7.69 million + .8478 × sales = $5.4 million
sales =
5.4 + 7.69
= $15.4 million
.8478
This implies that the store needs sales of $15.4 million a year for the investment to have
a zero NPV. This is more than 18 percent higher than the point at which the project has
zero profit.
Figure 5.2 is a plot of the present value of the inflows and outflows from the super-
store as a function of annual sales. The two lines cross when sales are $15.4 million.
This is the point at which the project has zero NPV. As long as sales are greater than
this, the present value of the inflows exceeds the present value of the outflows and the
project has a positive NPV.
FIGURE 5.2
NPV break-even analysis
NPV is negative

NPV is positive
15.4
PV of
project
cash flows
Investment
Sales
revenue,
millions
of
dollars
Project values, millions of dollars
5.4
0
؊7.69