Engineering Economic Analysis

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68 INTERESTAND EQUIVALENCE

added to the debt, increasing it further to $5832. At the end of the fifth year, the total sum

due has grown to $7347 and is paid at that time (see Example 3-4).

Note that when the $400 interest was not paid at the end of the first year, it was added

to the debt and, in the second ye~, tilere was interest charged on this unpaid interest. That

is, the $400 of unpaid interest resulted in 8% x $400=$32 of additional interest charge in

the second year. That $32, together with 8% x $5000=$400 interest on the $5000 original

debt, brought the total interest charge at the end of the secondyear to $432. Charging interest

on unpaid interest is called compound interest. We will deal extensively with compound

interestcalculationslaterin thischapter..

With Table 3-1 we have illustrated four different ways of accomplishing the same

task, that is, to repay a debt of $5000 in 5 years with interest at 8%. Having described the

alternatives, we will now use them to present the important concept ofequivalence.

Equivalence

When we are indifferent as to whether we have a quantity of money now or the assurance

of some other sum of money in the future, or series of future sums of money, we say that

the present sum of money is equivalent to the future sum or series of future sums.

If an industrial firm believed 8% was an appropriate interest rate, it would have no

particular preference about whether it received $5000 now or was repaid by Plan 1 of

Table 3-1. Thus $5000 today is equivalent to the series of five end-of-year payments. In

the same fashion, the industrial firm would accept repayment Plan 2 as equivalentto $5000

now. Logic tells us that if Plan 1 is equivalent to $5000 now and Plan 2 is also equivalent

to $5000 now, it must follow that Plan 1 is equivalent to Plan 2. In fact,allfour repayment

plans must be equivalent to each other and to $5000 now.

Equivalence is an essential factor in engineering economic analysis. In Chapter 2, we

saw how an alternativecouldbe representedby a cash flowtable. Howmight two alternatives

with different cash flows be compared? For example, consider the cash flows for Plans 1

and 2:

Year

1

2

3

4

5

Plan 1

-$1400

-1320

-1240

-1160

-1080

-$6200

Plan 2

-$400

-400

-400

-400

-5400

-$7000

If you were given your choice between the two alternatives,which one would you choose?

Obviously the two plans have cash flows that are different. Plan 1 requires that there be.

larger payments in the first 4 years, but the total payments are smaller than the sum of

Plan 2's payments. To make a decision, the cash flows must be altered so that they can be

compared. The technique of equivalence is the way we accomplish this.

Using mathematical manipulation,we can determine an equivalentvalue at some point

in time for Plan 1 and a comparable equivalent value for Plan 2, based on a selected