Engineering Economic Analysis

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Benefit-Cost Ratio Analysis 277

benefit-co~t ratios for each machine, they would have been:

MachineX

B 95

- = - =2.38

C 40

MachineY

B 120

C =. 96 = 1.25

Although BIC = 1.25 for MachineY(the higher-cost alternative), we must not use this fact as

the basis for selecting that the more expensive alternative. The incremental.benefibcost ratio,

~BIb. C, clearly shows that Yis a less desirable alternative than X. Also, we must not jump to

the conclusion that the best alternative is always the one with the largest B/Cratio. This, too,

may lead to incorrect decisions-as we shall see when we examine problems with three or JIlor~

alternatives.

I

I

.

Consider the five mutually exclusive alternativesfrom Example 8-8 plus an additional alternative,

F.They have 20-year useful lives and no salvage value. If the minimum attractive rate of return

is 6%, which alternative should be selected?

',-' -.".

SOLUTION.

Incremental analysis is needed to solve the problem. The steps in the solution are the same as the

ones presented for incremental rate of return, except here the criterion is b.B/b.C,and the cutoff

is 1, rather than b.IRR with a cutoff of MARR.

1. Be sure all the alternatives are identified.


2. (Optional) Compute the BICratio for each alternative. Since there are alternatives for
   whichB/C ::::1, we will discard any withB/C < 1. Discard Alt.F.


3. Arrange the remaining alternativesin ascending order of investment.

Cost(=PW of cost)

PW of benefits

B/C

D

$1000

1340

1.34

B

$2000

4700

2.35

A

$4000

7330

1.83

C

$6000

8730

1.46

E

$9000

9000

1.00

~b. Cost

~Benefit

b.BIb.C

Increment B-D

$1060 ~

3360

3.36

Increment A-B

$2006-

2630

J..32 ;

IncrementC-A

: $2000 =~

1400

Q.2J).c

"

il

"_II _ ...__

A B C D E F

Cost $4000 $2000 $6000 $1000 $9000 $10,000

PW of benefit (^73304700873013409000) 9,500
B PW of benefits

- 1.83 2.35 1.46 1.34 1.00 0.95

C PW of cost