INTERST AND EQUIVALENCE: COMPUTING CASH FLOWS.

Installing an expensive piece of machinery in a plant obviously has economic consequences that occur over an extended period of time. If themachinerywereboughtoncredit, the simple process of paying for it may take severalyears.What about the usefulness of the machinery? Certainly it was purchased because it would be a beneficial addition to the plant. These favorable consequencesmay last as long as the equipment performs its useful function.

In these circumstances,we do not add up the various consequences; instead, we describe each alternativeas cash receipts or disbursements at differentpoints in time. In this way, each alternativeis resolved into a set of cash flows. This is illustrated by Examples 3-1 and 3-2.

EXAMPLE 3-1 

The manager has decidedto purchase a new $30,000 mixing machine. The machinemay be paid for in one of two ways:

1. Pay the full price nowminus a 3%discount.
2. Pay $5000 now; at the end of one year, pay $8000; at the end of each of the next four years, pay $6000.

List the alternatives in theform of a table of cash flows.

SOLUTION
In this problem the two alternatives represent different ways to pay for the mixing machine.

While the first plan represents a~lumpsumof $29,100 now, the second one calls for payments continuing until the end of the fifth year.The problemis to convertan alternative into cashreceipts or disbursements andshowthe tirn,ingof each.receipt or disbursement.The result is called a cash flow table or, more simply, a set of cash flows.

The cash flowsfor both the alternativesin this problemare very simple.The cash flowtable, with disbursementsgiven negative signs, is as follows:

EXAMPLE 3-2

Amanborrowed $1000 from a bank at 8% interest. He agreed to repay the loan in twoend-of-year payments. At the end of the first year, he will repay half of the $1000 principal amount plus the interest that is due.At the end of the second year,he will repay the remaining half of the principal amount plus the interest for the second year. Compute the borrower's cash flow.

SOLUTION
In engineeringeconomic analysis,we normallyrefer to the beginningof the firstyear as "time 0."

At this point th eman receives $1000 fromthe bank. (Apositivesignrepresents a receipt of money
and a negative sign, a disbursement.)Thus, at time 0, the cash flowis +$1000.

At the end of the first year, the man pays 8%interest for the use of $1000 for one year.The interest is 0.08 x $1000 = $80. In addition, he repays half the $1000 loan, or $500. Therefore, the end-of-year-1 cash flow is -$580.

At the end of the second year, the payment is 8%for the use of the balance of the principal ($500) for the one-year period, or 0.08 x 500 = $40. The $500 principal is also repaid for a total end-of.;.year-2 cash flowat -$540. The cash flowis:

In this chapter,we will demonstrate techniques for comparing the value of money at different dates, an ability that is essential to engineering economic analysis.We must be able to compare, for example, a low-cost motor with a higher-costmotor. If there were no other consequences, we would obviously prefer the low-cost one. But if the higher-cost motor were more efficient and there by reduced the annual electric power cost, we would want to consider whether to spend more money now on the motor to reduce power costs in the future. This chapter will provide the methods for comparingthe alternatives to determine
which motor is preferred.