Engineering Economic Analysis

A Range of Estimates 307

Cost

Net annual benefit

Usefullife, in years

Salvage value

Optimistic

$950

$210

12

$100

Most Likely

$1000

$200

10

$0

Pessimistic

$1150

$175

8

$0

Compute the rate of return for each estimate. If a 10% before-tax minimum attractive rate of

return is required, is the investmentjustified under all three estimates? If it is only justified under

some estimates, how can these results be used.

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Optimistic Estimate

PW of cost=PW of benefit

$950=21O(P/A,IRRopt>12) + 100(P/F,IRRopt, 12)

IRRopt = 19.8%

Most Likely Estimate

$1000=200(P/A,IRRmostlikely,10)

(P/A,IRRmostlikely,10)=1000/200= 5 ~ IRRmostlikely =15.1 %

Pessimistic Estimate

$1150 - 170(P/A, IRRpess,8)

(P/A,IRRpess,8) = 1150/170. 6.76 ~ IRRpess= 3.9%

From the calculations we conclude that the rate of return for this investment is most likely to
be 15.1%, but might range from 3.9%to 19.8%.The investment meets the 10%MARR criterion
for two of the estimates. These estimates can be considered to be scenarios of what may happen
with this project. Since one scenario indicates that the project is not attractive,we need t9 have a
method of weighting the scenarios or considering how likely each is.

Example 10-3 made separate calculations for the sets of optimistic, most likely, and ~il

pessimistic values. The range of scenarios is useful. However,if there are more than a few

uncertain variables it is unlikely that all will prove to be optimistic (best case) or most likely

or pessimistic (worst case). It is more likely that many parameters are the most likely values,

while some are optimistic and some are pessimistic.

This can be addressed by using average or mean values for each parameter, based

on Equation 10-1. Equation 10-1 puts four times the weight on the most likely value