Capital recovery factor (CRF):

The capital recovery factor is generally used to find out the uniform annual amount ‘A' of a uniform series from the known present worth at a given interest rate ‘i' per interest period.

The cash flow diagram is shown in Fig. 1.10. This cash flow diagram indicates, if a person invests a certain amount now, how much he will get as return by an equal amount each year.

Fig 1.10 Cash flow diagram for ‘known P' and ‘unknown A'

From equation (12), the expression for the uniform annual amount (A) can be written as follows;

(17)

The factor within bracket in equation (17) is known as the capital recovery factor (CRF). Thus the uniform annual amount ‘A' at interest rate of ‘i' (per year) can be determined by multiplying the known present worth ‘P' with the capital recovery factor.

It may be noted here that the expressions for uniform series present worth factor and capital recovery factor are derived with present worth ‘P' located one interest period before the occurrence of first ‘A' of the uniform series.