Engineering Economic Analysis

Rate of Return Analysis 217

:! ....

!1'~.~

Solve Example 7-6 again,but this time compute the interest rate on the increment (Alt. 1- Alt. 2).

How do you interpret the results?

This time the problem is being viewed as follows:

Alt. 1=A1t.2 + [Alt. 1 - Alt. 2]

Year

o

1

Alt. 1

-$10

+15

Alt. 2

-$20

+28

[Alt. 1-Alt. 2]

-$10 - (-$20) =+$10

+15 - (+28) =-13

We can write one equation in one unknown:

NPW=PW of benefit of differences- PW of cost of differences= 0

+lO-13(PIF,i, 1) =0

Thus,

10

(PIF, i,1) = - = 0.7692 13

Once again the interest rate is found to be 30%. The critical question is, what does the 30%
represent? Looking at the increment again:
Year Alt. 1- Alt. 2
o +$10
1 -13
1..,..-r ." -
The cash flowdoesnotrepresent an investment;instead, it represents a loan. It is as if we borrowed
$10 in Year 0 (+$10 represents a receipt of money) and repaid it in Year 1 (-$13 represents a
disbursement). The 30% interest rate means this is the amountwe would payfor the use of the
$10 borrowed in Year 0 and repaid inYear 1..
Is this a desirable borrowing? Since the MARR on investments is 6%, it is reasonable to
assume our maximum interest rate on borrowing would also be 6%. Here the interest rate is
30%, which means the borrowing is undesirable. Since Alt. 1=Alt. 2 + (Alt. 1 -- Alt. 2), and
we do not like the (Alt. 1 - Alt. 2) increment, we should reject Alternative 1, which contains the
undesirable increment. This means we should select Alternative 2-the same conclusion reached
in EXan1ple7-6.

Example 7-8 illustrated that one can analyze either increments of investment or

increments of borrowing. When looking at increments of investment, we accept the in-

crement when the incremental rate of return equals or exceeds the minimum attractive rate

''''~- --- ,.,.,a..II

--- - - - --- - -- ----