Engineering Economic Analysis

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312 UNCERTAINTY IN FUTURE EVENTS

The project described in Example 10-5 has a first cost of $25,000. The finn uses an interest rate

of 10%. Assume that the probability distributions for annual benefit and life are unrelated or

statistically independent. Calculate the probability distribution for the PW.

5.QLUTION

Since there are three outcomes for the annual benefit and two outcomes for the life, there are

six combinations. The first four columns of the following table show the six combinations of

life and annual benefit. The probabilities in columns 2 and 4 are multiplied to calculate the joint

probabilities in column 5. For example, the probability of a low annual benefit and a short life is

0.3 x 2/3, which equals 0.2 or 20%.

The PW values include the $25,000 first cost and the results of each pair of annual benefit

and life. For example, the PW for the combination of high benefit and long life is:

PW$IO,OOO,9= -25,000 + 1O,000(P/A,10%,9) = -25,000 + 10,000(5.759) = $32,590

Figure 10-2 shows the probabilities for the PW. This is called the histogram, relative frequency

distribution, or probability distribution function.

40

o

-$3,224 $3,795 $9,842 $18,553 $21,072

Present Worth

$32,590

I
La

FIGURE 10-2 Probability distribution function for PW.::

Annual Joint

Benefit Probability Life Probability Probability PW

$ 5,000 30%^6 66.7% 20.0% -$ 3,224

8,000^606 66.7 40.0 9,842

10,000^106 66.7 6.7 18,553

5,000^309 33.3 10.0 3,795

8,000^609 33.3 20.0 2.1,072

10,000^109 33.3 3.3 32,590

100.0%

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