Engineering Economic Analysis

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72 INTERESTAND EQUIVALENCE

Aspredicted,at the higher9% interesteach of the repaymentplansof Table3-1 repaysa

present sum less than $5000. But they do not repay thesamepresent sum. Plan 1 would

repay $4877 with 9% interest, while Plan 2 would repay $4806. Thus, with interest at 9%,

Plans 1 and 2 are no longer equivalent, for they will not repay the same present sum. The

two series of payments (Plan 1 and Plan 2) were equivalent at 8%, but not at 9%. This

leads to the conclusion that equivalence is dependent on the interest rate. Changing the

interest rate destroys the equivalencebetween two series of payments.

Could we create revised repayment schemes that would be equivalent to $5000 now

with interest at 9%? Yes, of course we could: to revise Plan I of Table 3-1, we need to

increase the total end-of-year payment in order to pay 9% interest on the outstanding debt.

Year

1

2

3

4

5

Amount Owed at

Beginning of Year

$5000

4000

3000

2000

1000

9% Interest

for Year

$450

360

270

180

90

Total End-of- Year Payment

($1000 plus interest)

$1450

1360

1270

1180

1090

Plan 2 of Table 3-1 is revised for 9% interest by increasing the first four payments to

9% x $5000=$450 and the final payment to $5450. Twoplans that repay $5000 in 5 years

with interest at 9% are:

Revised End-of- Year Payments

Year Plan 1 Plan 2

1 $1450 $ 450

2 1360 450

3 lTIO ~O

4 1180 450

5 1090 5450

Wehave determined that RevisedPlan 1is equivalentto a present sum of $5000 and Revised

Plan 2 is equivalentto $5000 now; it follows that at 9% interest, RevisedPlan 1is equivalent

to Revised Plan 2.

Application of Equivalence Calculations

To understand the usefulness of equivalencecalculations, consider the following:

AlternativeA: AlternativeB:

Lower Initial Cost, Higher Initial Cost,

Higher Operating Cost Lower Operating Cost

-$600 -$850

-115 -80

-115 -80

-115 -80

. Year
o (now)
1
2
3

(^10) -115 -80