Engineering Economic Analysis

Sensitivityand Breakeven Analysis 287

FIGURE 9-5- Breakeven chart for

Example 9-9.

$250,000

...$200,000

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'Ci $150,000

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i:: $100,000Q)

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£

$50,000

o 10 15 20 25 30

Year

Age When Second Stage C0E-structed

5

Figure 9-5 portrays the PW of cost for the two alternatives. Thex-axis variable is thetime
when the second stage is constructed. We see that the PW of cost for two-stage construction
naturally decreases as the time for the second stage is deferred. The one-stage construction
(full capacity now) is unaffected by thex-axis variable and, hence, is a horizontal line on the
graph.
The breakeven point on the graph is the point at which both alternatives have equivalent costs.
We see that if, in two-stage construction, the second stage is deferred for 15 years, then the PWof
cost of two-stage construction is equal to one-stage construction; Year 15 is the breakeven point.
The graph also shows that if the second stage were to be needed prior to Year 15, then one-stage
construction, with its smaller PW of cost, would be preferred. On the other hand, if the second
stage would not be required until after 15 years, two-stage construction is preferred.
The decision on how to construct the project is sensitive to the age at which the second stage
is neededonlyif the range, of estimates includes 15 years. For example, if one estimated that the
second stage capacity would be needed between 5 and 10 years hence, the decision is insensitive t9
that estimate. For any value within that range, the decision does not change. The more eQollomical
thing to do is to build the full capacity now. But, if the second-stage capacity were to be needed
sometime between, say, 12 and 18 years, the deciSion would be sensitive to the estimate of when
the full capacity would be needed.

One question posed by Example 9-9 ishowsensitive the decision is to the need for

the second stage at 16 years or beyond. The graph shows that the decision is insensitive. In

all cases for construction on or after 16 years, two-stage construction has a lower PW of

cost.

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