Engineering Economic Analysis

288 OTHER ANALYSISTECHNIQUES

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Example 8-3 posed the following situation. Three mutually exclusivealternatives are given, each

with a 20-year life and no salvage value. The minimum attractive rate of return is 6%.

Initial cost

Uniform annual benefit

A

$2000

410

B

$4000

639

C

$5000

700

In Example 8-3 we found that Alt.Bwas the preferred alternative. Here we would like to know

how sensitive the decision is to our estimate of the initial cost ofB.IfBis preferred at an initial

cost of $4000, it will continue to be preferred at any smaller initial cost. Buthow muchhigher

than $4000 can the initial cost be and still haveBthe preferred alternative? The computations

may be done several different ways. With neither input nor output fixed, maximizing net present

worth is a suitable criterion.

Alternative A

NPW=PW of benefit- PW of cost

=41O(P j A,6%, 20)- 2000

=410(11.470) - 2000=$2703

Alternative B

Letx= initial cost ofB.

NPW=639(P j A,6%, 20) - x

= 639(11.470)- x

= 7329- x

Alternative C

NPW= 700(PjA,6%,20)- 5000

=700(11.470) - 5000=$3029

For the three alternatives,we see thatBwill only maximize NPW as long as its NPW is greater

than 3029.

3029 =7329 - x

x =7329 - 3029=$4300

:: Therefore,Bis tbe preferred alternative if its initial cost does not exceed $4300.

Figure 9-6 is a breakeven chart for the three alternatives. Here the criterion is to maximize

NPW; as a result, the graph shows thatBis preferred if its initial cost is less than $4300. At an

f