Engineering Economic Analysis

496 ECONOMICANALYSISIN THE PUBLIC SECTOR

THE BENEFIT-COST RATIO

The benefit-cost ratio was described briefly in Chapter 9 as one of the alternative eco-

nomic analysis methods for evaluating prospective projects. This method is used almost

exclusively in public investment analysis, and because of the magnitude of public dOllars

committed each year through such analysis,the benefit-cost ratio deservesour attentionand

understanding.

One of the primary reasons for the use of the benefit-cost ratio(B/Cratio) in public

decision making is its simplicity. The ratio is formed by calculating the equivalentworth

of the benefits accrued through investment in a project divided by the equivalentworth of

the costs of the project. The benefit-cost ratio can be shown as follows:

B/C

ratio. =Equivalent worth of net benefits

Equivalent worth of costs

PW benefits

PW costs

FW benefits

• FW costs

AW benefits

AW costs

Notice thatanyof the equivalent worth methods (present, future, and annual) can be used

to calculate this ratio. Each formulation of the ratio will produce an identical result, as.

illustrated in Example 16-2.

Demonstrate that for a highway expansion project with data given as follows,the same BICratio

is obtained using the present, future, and annual worth formulations.

Initial costs of expansion

Annual costs for operating/maintenance

Annual savings and benefits to travelers

Scrap value after useful life

Useful life of investment

Interest rate

$1,500,000

65,000

225,000

300,000

30 years

8%

UsingPresentWorth

PW benefits- 225,000(PIA,8%, 30) +300,000(P IF, 8%, 30) =$2,563,000

PW costs - 1,500,QOO+65,000(P IA, 8%, 30) -$2,232,000

U$in~FUtureWorth

FW benefits =225,;00(F IA,=8%,30)+ 300,000- $2{79'0,'Q"bd"= ;:;

FWcosts= 1,500,000(F I P,8%,30) +65,000(FI A,8%,30)- $22,460,000

..