Engineering Economic Analysis

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Applying Present Wortb Techniques 157

$8 million

A = 4960

n=oo

Capitalized Cost

p --.

FIGURE 5-2 Using the sinking fund factor to compute an infinite series.

AlTE~NATESOLUTION~1J

Instead of solving for an equivalent end-of-period paymentAbased onafuture$8 million dis-

bursement, we could findA,given apresent$8 million disbursement.

A=P(Aj P, i, n)= $8million(Aj P,7%, 70)

=$8 milIion(0.0706)=$565,000

On this basis, the infinite series is shown in Figure 5-3. Carefully note the difference between this

andFigure5-2. Now:.

.. A 565,000

CapItalizedcostP= - =i 0.07 - $8,071,000

FIGURE5-3 Using the capital recovery

factor to compute an infinite series.

A=565,000

n=oo

p

Another way of solving the problem is to assume the interest is 70 years. Compute an equiv-

alent interest rate for the 70-year period. Then the capitalized cost may be computed by using\.

Equation 4-33 form= 70

=

i70yr =(1 + i1yr)70- 1=(1 + 0.07)70- J=112.989

= ~ ~ ;.

$

.

Ii

$8 million

Capitalized cost= 8 mIl on +. = 8,071,000$

112.989.

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