## Conversion Factor for Geometric Gradient Series

A geometric gradient series is a series of cash flows that increase or decrease by a constant percentage each period. The geometric gradient series may be used to model inflation or deflation, productivity improvement or degradation, and growth or shrinkage of market size, as well as manv other phenomena.

In a geometric series, the base value of the series is A and the "growth" rate in the series (the rate of increase or decrease) is referred to as g. The terms in such a series are given by A, A(l + g), A(l + g)2, ... , A{\ + g)*-1 at the ends of periods 1, 2, 3, . . . , N, respectively. If the rate of growth, g, is positive, the terms are increasing in value. If the rate of growth, g, is negative, the terms are decreasing. Figure 3.7 shows a series of receipts where g is positive. Figure 3.8 shows a series of receipts where v is negative.

The geometric gradient to present worth conversion factor, denoted by (P/A,g,i,N), gives the present worth, P, that is equivalent to a geometric gradient series where the base receipt or disbursement is A, and where the rate of growth is g, the interest rate is i, and the number of periods is X

Figure 3.7 Geometric Gradient Series for Receipts With Positive Growth

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