Engineering Economic Analysis

156 PRESENT WORTH ANALYSIS

A city plans a pipeline to transport water from a distant watershed area to the city. The pipeline

will cost $8 million and will have an expected life of 70 years. The city anticipates it will need to

keep the water line in service indefinitely.Compute the capitalized cost, assuming 7% interest.

-SOLUTION

The capitalized cost equation

A

p=-

i

is simple to apply when there are end-of-period disbursementsA. Here we have renewals of

the pipeline every 70 years. To compute the capitalized cost, it is necessary to first compute an

end-of-period disbursementAthat is equivalent to $8 million every 70 years.

$8 million

t

o

1

$8 million

t

70 years

$8 million

t

140 years

$8 million

t

n=oo

Capitalized Cost

p

The $8 million disbursement at the end of 70 years may be resolved into an equivalentA.

$8 million

n;:: 70

A

A=F(Aj F, i, n)= $8rnillion(A/ F,7%, 70)

= $8 million(0.0Q()62)

.= $4960

I '

Each 70-year period is identical to this one and the infinite series is shown in Figure 5-2.

..
d $ mil. A $

"

8

.

lli

4960

CapItalIze costP= 8 lIon+ -:-l = ID1 on+_0 0. 7

........ =$8,071,000

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'"

I