### TIME VALUE OF MONEY: Equivalence.

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 equivalent to $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 1is equivalent to Plan 2. In fact, all four repayment plans must be equivalent to each other and to $5000 now.

Equivalenceis an essential factor in engineering economic analysis. In Chapter 2, we saw how an alternative could be represented by a cash flow table.How might two alternatives with different cash flows be compared? For example, consider the cash flows for Plans 1 and 2:

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 flowsmust be altered so that they can be compared.The technique of equivalence is theway 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 interest rate. Then we can judge the relative attractiveness of the two alternatives, not from their cash flows,but from comparable equivalentvalues. Since Plan 1, like Plan 2, repays a present sum of $5000with interest at 8%, the plans are equivalentto $5000 now; therefore, the alternatives are equally attractive. This cannot be deduced from the given cash flows alone. It is necessary to learn this by deieimining the equivalent values for each alternative at some point in time,which in this case is "the present."

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