Engineering Economic Analysis

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The Benefit-Cost Ratio 497

Using Annu~ Worth

AW benefits=225,000+300,000(AIF,8%, 30) = $227,600

AW costs = 1,500,000(AI P,8%,30) + 65,000 = $198,200

BICratio = 2,563,000 = 25,790,000 = 227,600 = 1.15. .. ... .......

One can see that the ratio provided by each of these methods produces the sameresult: 1.15.

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An economic analy~is is performed to assist in the objective of making a decision.

When one is using the BICratio, the decision rule is in two parts:

If the BICratio is; 1.0,then the decisionshouldbe to "invest."

If the BICratio is < 100,then the decisionshouldbe "do not invest."

Cases of a BICratiojust equal to1.0 are analogous to the case of a calculated n.etpresent

worth of $0 or an IRR analysis that yieldsi =MARR%. In other words, the decision

measure isjust atthe breakeven criteria. In such cases a detailed analysis of the input

variables and their estimates is necessary, and one should consider the merlts of other

available opportunities for the targeted funds. But, if the BICratio is greater than or less

than 1.0, the recommendation is clear.

TheB/Cratio is a numerator/denominatorrelationship between the equivalentworths

(EW) ofbenefitsandcosts:..

EW of net benefits to whomsoeverthey may accrue

B/Cratio=

EW of costs to the sponsors of the project

The numerator and denominator aspects of the ratio are sometimes interpreted and used

in different fashions. For instance, the conventionalB/C ratio defines the numerator and

denominator as follows:

EW of net benefits

Conventional BICratio=EW of initial costs + EW of operating and maintenance costs

This is the formulation of theB/Cratio used in Example 16-2. However, there is another

version of the ratio, called the modified BIC ratio. Using amodifiedversion, the numerator

and denominator are defined in a different manner: theannual operating and maintenanc~

coststo the users are subtracted in the numerator, whereas they are added as a cost in the

denominator. In this case the ratio becomes:

M d

O

OlefidB/Cratio^0 =EW of net benefits - EW of operating and maintenance costs

EW of initial costs