### Application of Equivalence Calculations - Time Value of Money.

To understand the usefulness of equivalencecalculations,consider the following:

Is theleast-cost alternative the one that has the lower initial cost and higher operating costs or the one with higher initial cost and lower continuing costs? Because of the time value of money, one cannot add up sums of money at different points in time directly. This means that alternatives cannot be compared in actual dollars at different points in time; instead comparisons must be made in some equivalent comparable sums of money.

It is not sufficient to compare the initial $600 against $850. Instead, we must compute a value that represents the entire stream of payments. In other words, we want to determine a sum that is equivalent to Alternative A's cash flow; similarly, we need to compute the equivalent sum for Alternative B. By computing equivalent sums at the same point in time ("now"),wewill havevalues thatmaybe validlycompared.Themethods for accomplishing.

Thus far we have discussed computing equivalent present sums for a cash flow. But the technique of equivalence is not limited to a present computation. Instead, we could compute the equivalent sum for a cash flow at any point in time. We could compare alternatives in "Equivalent Year 10" dollars rather than "now" (Year 0) dollars. Further, the equivalence need not be a single sum; it couldbe a seriesof payments or receipts. In Plan 3 of Table3-1, the series of equal payments was equivalent to $5000 now. But the equivalency works both ways. Supposewe ask the question,What is the equivalentequal annualpayment continuing for 5 years, given a present sum of $5000 and interest at 8%? The answer is $1252.

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