Engineering Economic Analysis

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154 PRESENTWORTH ANALYSIS

As.illustrated in Figure 5-1, we may assumethat Alternative 1 will bereplacedby an identical

machineafter its 7-year useful life. Alternative 2 hasa 13-yearuseful life. The dieselmanufacturer

has provided an estimated market value of the equipment at the time of the analysis period. As

such we can now comparethe two choices over 10 yearsas follows:

PW (Alt. 1) = -50,000 + (10,000--50,000)(P/F,8%,7)+20,000(P/F,8%,10)

= -50,000 - 40,000(0.5835)+ 20,000(0.4632)

= -$64,076

PW (Alt. 2,)= -75,000 +15,000(P/F,8%, 10)

- -75,000 +. 15,000(0.4632)

= -$69,442

I.

To minimize PW of coststhe diesel manufacturer should selectAlt 1.

3. Infinite Analysis Period: Capitalized Cost
   Another difficulty in presentworth analysis arises when we encounter an infinite analysis
   period(n=00). In governmentalanalyses, a service or condition sometimes must be main-
   tained for an infinite period. The need for roads, dams, pipelines, and other components
   of national, state, or local infrastructure is sometimes considered to be permanent. In these
   situations a present worth of cost analysis would have an infinite analysis period. We call
   this particular analysis capitalized cost.
   Capitalized cost is the present sum of money that would need to be set asidenow,at some
   interest rate, to yield the funds required to provide the service (or whatever) indefinitely.To
   accomplish this, the money set aside for future expenditures must not decline. The interest
   received on the money set aside can be spent, but not the principal. When one stops to
   think about an infinite analysis period (as opposed to something relatively short, like a
   hundred years), we see that an undiminished principal sum is essential; otherwise one will
   of necessity run out of money prior to infinity.
   In Chapter 4 we saw that

principal sum + interest for the period=amount at end of J?~!i0d,or

P + iP = P+iP

If we spendi P,then in the next interest period the principal sumPwill again increase to

P+i P.Thus, we can again spendi P. -

This concept may be illustrated by a numerical example. Suppose you deposited $200

in a bank that paid4%interestannually.Howmuchmoneycouldbe withdrawneachyear

without reducing the balance in the account below the initial $200? At the end of the first

year, the $200 would have earned 4%($200) =$8 interest. If this interest were withdrawn,

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