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the variable cost of mining copper. Why is this a valuable operating option? How does
it increase the NPV of the mine to the operator?

Companies try to avoid becoming dependent on a single source of raw materials, build-
ing flexibility into their production facilities whenever possible. For example, at current
prices gas-fired industrial boilers are cheaper to operate than oil-fired ones. Yet most
companies prefer to buy boilers that can use either oil or natural gas, even though these
dual-fired boilers cost more than a gas-fired boiler.6 The reason is obvious. If gas prices
rise relative to oil prices, the dual-fired boiler gives the company a valuable option to
switch to low-cost oil. In effect the company has the option to exchange one asset (an
oil-fired boiler) for another (a gas-fired boiler).
If the firm is uncertain about the future demand for its products, it may also build in
the option to vary the output mix. For example, in recent years automobile manufac-
turers have made major investments in flexible production facilities that allow them to
change their output rapidly in response to consumer demand.

Suppose that you have a project that might be a big winner or a big loser. The project™s
upside potential outweighs its downside potential, and it has a positive NPV if under-
taken today. However, the project is not “now-or-never.” Should you invest right away
or wait? It™s hard to say. If the project truly is a winner, waiting means loss or deferral
of its early cash flows. But if it turns out to be a loser, it may pay to wait and get a bet-
ter fix on the likely demand.
You can think of any project proposal as giving you the option to invest today. You
don™t have to exercise that option immediately. Instead you need to weigh the value of
the cash flows lost by delaying against the possibility that you will pick up some valu-
able information.
Think again of those tar sands in Athabasca. Suppose that the price of oil rises to 10
cents a barrel above your cost of production. You can extract the oil profitably at this
price, and the required investment has a small positive NPV if the price stays where it
is. But it still might be worth delaying production. After all, if the price plummets, you
will by waiting avoid a costly mistake. If it rises further, however, you can invest and
make a killing.
We repeat, it is because the future is so uncertain that managers value flexibility. Ide-
ally, a project will give the firm an option to expand if things go well and to bail out or
switch production if they don™t. In addition, it may pay the firm to postpone the project.
Some managers treat capital investment decisions as black boxes; they are handed
cash-flow forecasts and they churn out present values without looking inside the black
box. But successful firms ask not only what could be wrong with the forecasts but
whether there are opportunities to respond to surprises. In other words, they recognize
the value of flexibility.

Investments in new products or production capacity often include an option to expand.
Self-Test 7
What are the other major types of options encountered in capital investment decisions?
6See N. Kulatilaka, “The Value of Flexibility: The Case of a Dual-Fuel Industrial Steam Boiler,” Financial
Management 22 (Autumn 1993), pp. 271“280.
Project Analysis 485

What are some of the practical problems of capital budgeting in large corporations?
For most large corporations there are two stages in the investment process: the preparation
of the capital budget, which is a list of planned investments, and the authorization process
for individual projects. This process is usually a cooperative effort.
Investment projects should never be selected through a purely mechanical process.
Managers need to ask why a project should have a positive NPV A positive NPV is
plausible only if the company has some competitive advantage that prevents its rivals from
stealing most of the gains.

How are sensitivity, scenario, and break-even analysis used to see the effect of an
error in forecasts on project profitability? Why is an overestimate of sales more se-
rious for projects with high operating leverage?
Good managers realize that the forecasts behind NPV calculations are imperfect. Therefore,
they explore the consequences of a poor forecast and check whether it is worth doing some
more homework. They use the following principal tools to answer these what-if questions:

• Sensitivity analysis, where one variable at a time is changed.
• Scenario analysis, where the manager looks at the project under alternative scenarios.
• Simulation analysis, an extension of scenario analysis in which a computer generates
hundreds or thousands of possible combinations of variables.
• Break-even analysis, where the focus is on how far sales could fall before the project
begins to lose money. Often the phrase “lose money” is defined in terms of accounting
losses, but it makes more sense to define it as “failing to cover the opportunity cost of
capital””in other words, as a negative NPV.
• Operating leverage, the degree to which costs are fixed. A project™s break-even point
will be affected by the extent to which costs can be reduced as sales decline. If the
project has mostly fixed costs, it is said to have high operating leverage. High operating
leverage implies that profits are more sensitive to changes in sales.

Why is managerial flexibility important in capital budgeting?
Some projects may take on added value because they give the firm the option to bail out if
things go wrong or to capitalize on success by expanding. We showed how decision trees
may be used to analyze such flexibility.

www.windpower.dk/tour/econ/econ.htm Evaluation of a sample energy-saving project
Related Web www.palisade.com Software for Monte Carlo analysis
capital budget scenario analysis degree of operating
Key Terms sensitivity analysis simulation analysis leverage (DOL)
fixed costs break-even analysis decision tree
variable costs operating leverage

1. Fixed and Variable Costs. In a slow year, Wimpy™s Burgers will produce 1 million ham-
burgers at a total cost of $1.75 million. In a good year, it can produce 2 million hamburgers
at a total cost of $2.25 million. What are the fixed and variable costs of hamburger produc-

2. Average Cost. Reconsider Wimpy™s Burgers from problem 1.
a. What is the average cost per burger when the firm produces 1 million hamburgers?
b. What is average cost when the firm produces 2 million hamburgers?
c. Why is average cost lower when more burgers are produced?

3. Sensitivity Analysis. A project currently generates sales of $10 million, variable costs equal
to 50 percent of sales, and fixed costs of $2 million. The firm™s tax rate is 35 percent. What
are the effects of the following changes on after-tax profits and cash flow?

a. Sales increase from $10 million to $11 million.
b. Variable costs increase to 60 percent of sales.

4. Sensitivity Analysis. The project in the preceding problem will last for 10 years. The dis-
Practice count rate is 12 percent.
Problems a. What is the effect on project NPV of each of the changes considered in the problem?
b. If project NPV under the base-case scenario is $2 million, how much can fixed costs in-
crease before NPV turns negative?
c. How much can fixed costs increase before accounting profits turn negative?

5. Sensitivity Analysis. Emperor™s Clothes Fashions can invest $5 million in a new plant for
producing invisible makeup. The plant has an expected life of 5 years, and expected sales are
6 million jars of makeup a year. Fixed costs are $2 million a year, and variable costs are $1
per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-line
over 5 years to a salvage value of zero. The opportunity cost of capital is 12 percent, and the
tax rate is 40 percent.
a. What is project NPV under these base-case assumptions?
b. What is NPV if variable costs turn out to be $1.20 per jar?
c. What is NPV if fixed costs turn out to be $1.5 million per year?
d. At what price per jar would project NPV equal zero?

6. Scenario Analysis. The most likely outcomes for a particular project are estimated as

Unit price: $50
Variable cost: $30
Fixed cost: $300,000
Expected sales: 30,000 units per year

However, you recognize that some of these estimates are subject to error. Suppose that each
variable may turn out to be either 10 percent higher or 10 percent lower than the initial esti-
mate. The project will last for 10 years and requires an initial investment of $1 million,
which will be depreciated straight-line over the project life to a final value of zero. The
firm™s tax rate is 35 percent and the required rate of return is 14 percent. What is project
NPV in the “best-case scenario,” that is, assuming all variables take on the best possible
value? What about the worst-case scenario?
7. Scenario Analysis. Reconsider the best- and worst-case scenarios in the previous problem.
Do the best- and worst-case outcomes when each variable is treated independently seem to
be reasonable scenarios in terms of the combinations of variables? For example, if price is
higher than predicted, is it more or less likely that cost is higher than predicted? What other
relationships may exist among the variables?
Project Analysis 487

8. Break-Even. The following estimates have been prepared for a project under consideration:
Fixed costs: $20,000
Depreciation: $10,000
Price: $2
Accounting break-even: 60,000 units
What must be the variable cost per unit?
9. Break-Even. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each
diamond can be sold for $100. The materials cost for a standard diamond is $30. The fixed
costs incurred each year for factory upkeep and administrative expenses are $200,000. The
machinery costs $1 million and is depreciated straight-line over 10 years to a salvage value
of zero.
a. What is the accounting break-even level of sales in terms of number of diamonds sold?
b. What is the NPV break-even level of sales assuming a tax rate of 35 percent, a 10-year
project life, and a discount rate of 12 percent?
10. Break-Even. Turn back to problem 9.
a. Would the accounting break-even point in the first year of operation increase or decrease
if the machinery were depreciated over a 5-year period?
b. Would the NPV break-even point increase or decrease if the machinery were depreciated
over a 5-year period?
11. Break-Even. You are evaluating a project that will require an investment of $10 million that
will be depreciated over a period of 7 years. You are concerned that the corporate tax rate
will increase during the life of the project. Would such an increase affect the accounting
break-even point? Would it affect the NPV break-even point?
12. Break-Even. Define the cash-flow break-even point as the sales volume (in dollars) at which
cash flow equals zero. Is the cash-flow break-even level of sales higher or lower than the
zero-profit break-even point?
13. Break-Even and NPV. If a project operates at cash-flow break-even (see problem 12) for its
entire life, what must be true of the project™s NPV?
14. Break-Even. Modern Artifacts can produce keepsakes that will be sold for $80 each. Non-
depreciation fixed costs are $1,000 per year and variable costs are $60 per unit.

a. If the project requires an initial investment of $3,000 and is expected to last for 5 years
and the firm pays no taxes, what are the accounting and NPV break-even levels of sales?
The initial investment will be depreciated straight-line over 5 years to a final value of
zero, and the discount rate is 10 percent.
b. How do your answers change if the firm™s tax rate is 40 percent?

15. Break-Even. A financial analyst has computed both accounting and NPV break-even sales
levels for a project under consideration using straight-line depreciation over a 6-year period.
The project manager wants to know what will happen to these estimates if the firm uses
MACRS depreciation instead. The capital investment will be in a 5-year recovery period
class under MACRS rules (see Table 7.4). The firm is in a 35 percent tax bracket.

a. What (qualitatively) will happen to the accounting break-even level of sales in the first
years of the project?
b. What (qualitatively) will happen to NPV break-even level of sales?
c. If you were advising the analyst, would the answer to (a) or (b) be important to you?
Specifically, would you say that the switch to MACRS makes the project more or less at-

16. Break-Even. Reconsider Finefodder™s new superstore. Suppose that by investing an addi-
tional $600,000 initially in more efficient checkout equipment, Finefodder could reduce
variable costs to 80 percent of sales.
a. Using the base-case assumptions (Table 5.1), find the NPV of this alternative scheme.
Hint: Remember to focus on the incremental cash flows from the project.
b. At what level of sales will accounting profits be unchanged if the firm invests in the new
equipment? Assume the equipment receives the same 12-year straight-line depreciation
treatment as in the original example. Hint: Focus on the project™s incremental effects on
fixed and variable costs.
c. What is the NPV break-even point?
17. Break-Even and NPV. If the superstore project (see the previous problem) operates at ac-
counting break-even, will net present value be positive or negative?
18. Operating Leverage. You estimate that your cattle farm will generate $1 million of profits
on sales of $4 million under normal economic conditions, and that the degree of operating
leverage is 7.5. What will profits be if sales turn out to be $3.5 million? What if they are
$4.5 million?
19. Operating Leverage.
a. What is the degree of operating leverage of Modern Artifacts (in problem 14) when sales
are $8,000?
b. What is the degree of operating leverage when sales are $10,000?
c. Why is operating leverage different at these two levels of sales?

20. Operating Leverage. What is the lowest possible value for the degree of operating leverage
for a profitable firm? Show with a numerical example that if Modern Artifacts (see problem
14a) has zero fixed costs, then DOL = 1 and in fact sales and profits are directly propor-
tional so that a 1 percent change in sales results in a 1 percent change in profits.
21. Operating Leverage. A project has fixed costs of $1,000 per year, depreciation charges of
$500 a year, revenue of $6,000 a year, and variable costs equal to two-thirds of revenues.

a. If sales increase by 5 percent, what will be the increase in pretax profits?
b. What is the degree of operating leverage of this project?
c. Confirm that the percentage change in profits equals DOL times the percentage change
in sales.

22. Project Options. Your midrange guess as to the amount of oil in a prospective field is 10
million barrels, but in fact there is a 50 percent chance that the amount of oil is 15 million
barrels, and a 50 percent chance of 5 million barrels. If the actual amount of oil is 15 mil-
lion barrels, the present value of the cash flows from drilling will be $8 million. If the
amount is only 5 million barrels, the present value will be only $2 million. It costs $3
million to drill the well. Suppose that a seismic test that costs $100,000 can verify the
amount of oil under the ground. Is it worth paying for the test? Use a decision tree to justify
your answer.
23. Project Options. A silver mine can yield 10,000 ounces of copper at a variable cost of $8
per ounce. The fixed costs of operating the mine are $10,000 per year. In half the years, sil-
ver can be sold for $12 per ounce; in the other years, silver can be sold for only $6 per ounce.
Ignore taxes.
a. What is the average cash flow you will receive from the mine if it is always kept in op-
eration and the silver always is sold in the year it is mined?
b. Now suppose you can shut down the mine in years of low silver prices. What happens to
the average cash flow from the mine?
Project Analysis 489

24. Project Options. An auto plant that costs $100 million to build can produce a new line of
cars that will produce cash flows with a present value of $140 million if the line is success-


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