10.92. In the evaluation of alternate engineering projects involving the expenditure of funds, incurring of costs, and receipt of revenue, all at different times, a systematic treatment of the effect of the time variable of money is useful. The value of money can be considered to change as it is moved through time. In the present, for example, money has a greater value than it would have at some time in the future because it can be put to a useful purpose in the interim. Some of the terms discussed in the previous section are useful in design comparisons involving expenditures.

10.93. The present-worth concept, for example, provides for the shifting of money from one time level to another with a corresponding shift in value. If r is the effective earning rate or interest rate, then the present worth of 1 dollar due 1 year in the future is 1/(1 + r). This corresponds to shifting backward in time. Similarly, the present worth of 1 dollar in­vested a year previously would be (1 + r), corresponding to a shift forward. In electric utility economics, it is useful to know the present worth of revenue requirements for future years of plant operation. This corresponds to the case of the backward shift. In the case of simple interest (single payment), the present value, P, can be expressed as

(1 + г)"’

where n is the number of years involved.