Sometimes the cash flows may have expenses or incomes being increased by a constant percentage in the successive time periods i.e. in successive years. Such kind of cash flow is known as geometric gradient series. The generalized cash flow diagram involving geometric gradient series with expense or receipt ‘C' at the end of year ‘1' and geometric percentage increase ‘g' is shown in Fig. 1.19.

Fig 1.19 Cash flow diagram involving geometric gradient with ‘unknown P'

The present worth (P) of the geometric gradient series can be calculated by considering each amount as the future worth and then taking sum of these present worth values.

(36)

Equation (36) can be rewritten as follows;

(37)

Dividing both sides of the equation (37) by (1+i) results in the following expression;

(38)

Now multiplying both sides of equation (38) by (1+g) results in the following expression;

(39)