Engineering Economic Analysis

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Applying Present Worth Techniques 151

In Example 5-4, we compared two alternatives and selected the one in which present worth

of benefitsminuspresent worth of cost was a maximum. The criterion is called the net

present worth criterion and written simply as NPW:

Net present worth=Present worth of benefits - Present worth of cost

NPW=PW of benefits - PW of cost

2. Useful Lives Different from the Analysis Period
   In present worth analysis, there always must be an identified analysis period. It follows,
   then, that each alternative must be considered for the entire period. In Examples 5-1 to 5-4,
   the useful life of each alternative was equal to the analysis period. Often we can arrange
   it this way, but in many situations the alternatives will have useful lives different from the
   analysis period. This section describes one way to evaluate alternatives with lives different
   from the study period..
   In Example 5-3, suppose that the Allied equipment was expected to have a 1O-year
   useful life, or twice that of the Speedy equipment. Assuming the Allied salvage value would
   still be $325 in 10 years, which equipment should now be purchased? We can recompute
   the present worth of cost of the Allied equipment, starting as follows:

PW of cost=1600 - 325(P/F,.7%, 10)

= 1600- 325(0.5083)

= 1600- 165= $1435

The present worthof cost has increased.This is due, of course,to the more distantrecoveryof

the salvage value. More importantly, we now find ourselves attempting to compare Speedy

equipment, with its 5-year life, against the Alliedequipment with a 1O-yearlife. Because

of the variation in the useful life of the equipment, we no longer have a situation offixed

output.Speedy equipment in the mailroom for 5 years is certainly not the same as 10 years

of service with Allied equipment..

For present worth calculations, it is important that we select an analysis period and

judge the consequences of each of the alternatives during the selected analysis period. As

such, it is not a fair comparison to compare the NPW of the Allied equipment over its

1O-yearlife against the NPW of the Speedy equipment over its 5-year life.

Not only is the firm and its economic environment important in selecting an analysis

period, but also the specific situation being analyzed is important. If the Allied equipment

(Example 5-3) has a useful life of 10 years, and the Speedy equipment will last 5 years, one

method is to select an analysis period that is the least common multiple of their useful lives.

Thus we would compare the 1O-yearlife of Allied equipment against an initial purchase of

Speedy equipmentplusits replacement with new Speedy equipment in 5 years. The result

is to judge the alternatives on the basis of a 1O-yearrequirement in the mailroom. On this

basis the economic analysis is as follows.

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