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would fall from $2 million to $1.56 million but variable costs would rise from 81.25 to
84 percent of sales. Table 5.6 shows that with the normal level of sales, the two policies
fare equally. In a slump a store that relies on temporary labor does better since its costs
fall along with revenue. In a boom the reverse is true and the store with the higher pro-
portion of fixed costs has the advantage.
If Finefodder follows its normal policy of hiring long-term employees, each extra
dollar of sales results in a change of $1.00 “ $.8125 = $.1875 in pretax profits. If it uses
temporary labor, an extra dollar of sales leads to a change of only $1.00 “ $.84 = $.16
in profits. As a result, a store with high fixed costs is said to have high operating lever-
age. High operating leverage magnifies the effect on profits of a fluctuation in sales.
Degree to which costs are
We can measure a business™s operating leverage by asking how much profits change
for each 1 percent change in sales. The degree of operating leverage, often abbreviated
as DOL, is this measure.
percentage change in profits
(DOL) Percentage DOL =
percentage change in sales
change in profits given a 1
For example, Table 5.6 shows that as the store moves from normal conditions to boom,
percent change in sales.
sales increase from $16 million to $19 million, a rise of 18.75 percent. For the policy
with high fixed costs, profits increase from $550,000 to $1,112,000, a rise of 102.2 per-
cent. Therefore,
DOL = = 5.45
The percentage change in sales is magnified more than fivefold in terms of the per-
centage impact on profits.
High Fixed Costs High Variable Costs
A store with high operating
leverage performs relatively Slump Normal Boom Slump Normal Boom
badly in a slump but
Sales 13,000 16,000 19,000 13,000 16,000 19,000
flourishes in a boom (figures
“ Variable costs 10,563 13,000 15,438 10,920 13,440 15,960
in thousands of dollars)
“ Fixed costs 2,000 2,000 2,000 1,560 1,560 1,560
“ Depreciation 450 450 450 450 450 450
= Pretax profit “13 550 1,112 70 550 1,030

Now look at the operating leverage of the store if it uses the policy with low fixed
costs but high variable costs. As the store moves from normal times to boom, profits in-
crease from $550,000 to $1,030,000, a rise of 87.3 percent. Therefore,
DOL = = 4.65
Because some costs remain fixed, a change in sales continues to have a magnified ef-
fect on profits but the degree of operating leverage is lower.
In fact, one can show that degree of operating leverage depends on fixed charges (in-
cluding depreciation) in the following manner:4
fixed costs
DOL = 1 +
This relationship makes it clear that operating leverage increases with fixed costs.

Operating Leverage
Suppose the firm adopts the high-fixed-cost policy. Then fixed costs including depre-
ciation will be 2.00 + .45 = $2.45 million. Since the store produces profits of $.55 mil-
lion at a normal level of sales, DOL should be
fixed costs 2.00 + .45
DOL = 1 + =1+ = 5.45
profits .55
This value matches the one we obtained by comparing the actual percentage changes in
sales and profits.

You can see from this example that the risk of a project is affected by the
degree of operating leverage. If a large proportion of costs is fixed, a shortfall
in sales has a magnified effect on profits.

We will have more to say about risk later.

Suppose that sales increase by 10 percent from the values in the normal scenario. Com-
Self-Test 5
pute the percentage change in pretax profits from the normal level for both policies in
Table 5.6. Compare your answers to the values predicted by the DOL formula.

4This formula for DOL can be derived as follows. If sales increase by 1 percent, then variable costs also
should increase by 1 percent, and profits will increase by .01 — (sales “ variable costs) = .01 — (profits + fixed
costs). Now recall the definition of DOL:
percentage change in profits change in profits/level of profits
percentage change in sales = .01
.01 — (profits + fixed costs)
change in profits
= 100 — = 100 —
level of profits level of profits
fixed costs
= 1+
Project Analysis 481

Flexibility in Capital Budgeting
Sensitivity analysis and break-even analysis help managers understand why a venture
might fail. Once you know this you can decide whether it is worth investing more time
and effort in trying to resolve the uncertainty.
Of course it is impossible to clear up all doubts about the future. Therefore, man-
agers also try to build flexibility into the project and they value more highly a project
that allows them to mitigate the effect of unpleasant surprises and to capitalize on
pleasant ones.

The scientists of MacCaugh have developed a diet whiskey and the firm is ready to go
ahead with pilot production and test marketing. The preliminary phase will take a year
and cost $200,000. Management feels that there is only a 50-50 chance that the pilot
production and market tests will be successful. If they are, then MacCaugh will build a
$2 million plant which will generate an expected annual cash flow in perpetuity of
$480,000 a year after taxes. Given an opportunity cost of capital of 12 percent, project
NPV in this case will be “$2 million + $480,000/.12 = $2 million. If the tests are not
successful, MacCaugh will discontinue the project and the cost of the pilot production
will be wasted. How can MacCaugh decide whether to spend the money on the pilot
Notice that the only decision MacCaugh needs to make now is whether to go ahead
with the preliminary phase. Depending on how that works out, it may choose to go
ahead with full-scale production.
When faced with projects like this that involve sequential decisions, it is often help-
ful to draw a decision tree, as in Figure 5.3. You can think of the problem as a game be-
tween MacCaugh and fate. The square represents a decision point for MacCaugh and
Diagram of sequential
the circle represents a decision point for fate. MacCaugh starts the play at the left-hand
decisions and possible
box. If MacCaugh decides to test, then fate will cast the enchanted dice and decide the
result of the tests. Given the test results, the firm faces a second decision: Should it in-
vest $2 million and start full-scale production?

Decision tree
Pursue project
NPV $2 million
Test (invest


Stop project
Don™t test

The second-stage decision is obvious: Invest if the tests indicate that NPV is posi-
tive, and stop if they indicate that NPV would be negative. Now the firm can easily de-
cide between paying for the test program or stopping immediately. The net present value
of stopping is zero, so the first-stage decision boils down to a simple problem: Should
MacCaugh invest $200,000 now to obtain a 50 percent chance of a project with an NPV
of $2 million a year later? If payoffs of zero and $2 million are equally likely, the ex-
pected payoff is (.5 — 0) + (.5 — 2 million) = $1 million. Thus the pilot project offers an
expected payoff of $1 million on an investment of $200,000. At any reasonable cost of
capital this is a good deal.

Notice that MacCaugh™s expenditure on the pilot program buys a valuable managerial
option. The firm has the option to produce the new product depending on the outcome
of the tests. If the pilot program turns up disappointing results, the firm can walk away
from the project without incurring additional costs.

The option to walk away once the results are revealed introduces a valuable
asymmetry. Good outcomes can be exploited, while bad outcomes can be
limited by canceling the project.

MacCaugh was not obliged to have a pilot program. Instead, it could have gone di-
rectly into full-scale whiskey production. After all, if diet whiskey is a success, the
sooner MacCaugh can clean up the market the better. But it is possible that the product
will not take off; in that case the expenditure on the pilot operation may help the firm
avoid a costly mistake. When it proposed a pilot project, MacCaugh™s management was
simply following the fundamental rule of swimmers: If you know the water temperature
(and depth), dive in; if you don™t, try putting a toe in first.
Here is another example of an apparently unprofitable investment that has value be-
cause of the flexibility it gives to make further follow-on investments. Some of the
world™s largest oil reserves are found in the tar sands of Athabasca, Canada. Unfortu-
nately, the cost of extracting oil from the sands is substantially higher than the current
market price and almost certainly higher than most people™s estimate of the likely price
in the future. Yet oil companies have been prepared to pay considerable sums for these
tracts of barren land. Why?
The answer is that ownership of these tracts gives the companies an option. They are
not obliged to extract the oil. If oil prices remain below the cost of extraction, the
Athabasca sands will remain undeveloped. But if prices do rise above the cost of ex-
traction, those land purchases could prove very profitable.
Notice that the option to develop the tar sands is valuable because the future price of
oil is uncertain. If we knew that oil prices would remain at their current level, nobody
would pay a cent for the tar sands. It is the possibility that oil prices may fluctuate
sharply above or below their present level that gives the option value.5

As a general rule, flexibility is most valuable when the future is most
uncertain. The ability to change course as events develop and new
information becomes available is most valuable when it is hard to predict
with confidence what the best action ultimately will turn out to be.

5Oil prices sometimes move very sharply. They roughly halved between the beginning of 1997 and the end
of 1998. By early 2000, they had almost trebled.
Project Analysis 483

You can probably think of many other investments that take on added value because
of the further opportunities that they may open up. For example, when designing a fac-
tory, it may make sense to provide for the possibility in the future of an additional pro-
duction line; when building a four-lane highway, it may pay to build six-lane bridges so
that the road can be converted later to six lanes if traffic volume turns out to be higher
than expected.

If the option to expand has value, what about the option to bail out? Projects don™t just
go on until the equipment disintegrates. The decision to terminate a project is usually
taken by management, not by nature. Once the project is no longer profitable, the com-
pany will cut its losses and exercise its option to abandon the project.
Some assets are easier to bail out of than others. Tangible assets are usually easier to
sell than intangible ones. It helps to have active secondhand markets, which really exist
only for standardized, widely used items. Real estate, airplanes, trucks, and certain ma-
chine tools are likely to be relatively easy to sell. On the other hand, the knowledge ac-
cumulated by a drug company™s research and development program is a specialized in-
tangible asset and probably would not have significant abandonment value. Some
assets, such as old mattresses, even have negative abandonment value; you have to pay
to get rid of them. It is very costly to decommission nuclear power plants or to reclaim
land that has been strip-mined. Managers recognize the option to abandon when they
make the initial investment.

Abandonment Option
Suppose that the Wigeon Company must choose between two technologies for the man-
ufacture of a new product, a Wankel engine outboard motor:
1. Technology A uses custom-designed machinery to produce the complex shapes re-
quired for Wankel engines at low cost. But if the Wankel engine doesn™t sell, this
equipment will be worthless.
2. Technology B uses standard machine tools. Labor costs are much higher, but the
tools can easily be sold if the motor doesn™t sell.
Technology A looks better in an NPV analysis of the new product, because it was de-
signed to have the lowest possible cost at the planned production volume. Yet you can
sense the advantage of technology B™s flexibility if you are unsure whether the new out-
board will sink or swim in the marketplace.

When you are unsure about the success of a venture, you may wish to choose
a flexible technology with a good resale market to preserve the option to
abandon the project at low cost.

Consider a firm operating a copper mine that incurs both variable and fixed costs of
Self-Test 6
production. Suppose the mine can be shut down temporarily if copper prices fall below


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