Engineering Economic Analysis

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218 RATEOF RETURNANALYSIS

of return (~IRR ~ MARR). When looking at increments of borrowing, we accept the in-

crement when the incremental interest rate is less than or equal to theminimumattractive

rate of return (~IRR ~ MARR). One way to avoid much of the possible confusion is to

organize the solution to any problem so that one is examining increments of investment.

This is illustrated in the next example.

A firm is considering which of two devices to install to reduce costs in a particular situation. Both

devices cost $1000, and both have useful lives of 5 years and no salvage value. DeviceAcan be

expected to result in $300 savings annually. DeviceBwill provide cost savings of $400 the first

year but will decline $50 annually,making the second-year savings $350, the third-year savings

$300, and so forth. For a 7% MARR, which device should the firm purchase?

This problem has been solved by present worth analysis (Example5-1) and annual cost analysis

(Example 6-5). This time we will use rate of return analysis.The examplehas fixedinput ($1000)

and differing outputs (savings).

In determining whether to use an(A- B)or(B- A)differencebetween the alternatives,we

seek an increment of investment.By looking at both(A- B)and(B- A),we find that(A- B)

is the one that represents an increment of investment.

Year

o 1 2 3 4 5

DeviceA

-$1000

+300

+300

+300

+300

+300

DeviceB

-$1000

+400

+350

+300

+250

+200

Difference Between Alternatives:

DeviceA-DeviceB

$0

-100

-50

o

+50

+100

For the difference between the alternatives, write a single equation withias the only unknown.

EUAC=EUAB

[100(P j F, i,1) +50(P j F, i, 2)](Aj P, i,5) [50(Fj P, i,1) +100](Aj F, i, 5)

The equation is cumbersome, but need not be solved. Instead, we observe that the sum of the

costs (-100 and -50) equals the sum of the benefits (+50 and + 100). This indicates that 0% is

ili~IRRA-Bon theA- Bincrement ofinvestment.This is less than the 7% MARR; therefore,

the increment is undesirable. Reject DeviceAand choose DeviceB.

As describedin Example7-8,if theincrel11enteXal1:).inedis(B~ A),'the interestrate would

again be 0%, indicating a desirable, :; =::z' borrowingsituation. We would choose Device==;; :::I B.

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