# Meaning, Formula, and Example of the Capital Recovery Factor

To calculate the present value of a sequence of equal payments, the Capital Recovery Factor (or CRF) may be used. It’s up to the individual to decide how often they want to make equal payments. Annuities are the most used term for these payouts. To put it another way, we may argue that the capital recovery factor helps us determine the current value of annuities.

Because of this, the term “capital recovery factor” was coined. Recovery of capital is the process of recouping one’s original investment. Thus, the CRF may be used to estimate the return on investment.

In addition, it is a useful tool for estimating costs. To gauge the success of their investments, start-ups and investors often turn to this tool.

## Factor of Capital Recuperation

The present value of a sequence of payments over a predetermined period of time is converted using CRF. As a result, CRF’s formula is as follows:

This is the CRF formula: I (1+i) n/(+1i) n-1

Annuities received are counted as “n” here, while I am the actual discount rate. There are several similarities between the CRF formula and that of an annuity.

Let’s take a closer look at the notion of CRF using an example.

An annuity with a five-year term (n) is received at a discount rate of 7 percent. CRF equals 0.2439 when the formula is used.

Let’s say a 7%-interest loan of \$1,000 must be repaid over five years. In other words, each of the five-yearly payments is going to come out to be 243.90–\$243.99. The CRF tells us that the five-yearly payments of \$243.90 are worth \$1000 now.

## Sinking Fund Factor Interaction

When compared to the capital recovery factor, the Sinking Fund Factor is the polar opposite. For equal yearly cash flow payments, a sinking fund factor (CRF) may assist establish the present value of the future worth of those payments.

The sinking fund factor may be calculated using the following formula:

[1+i] n – 1

We may calculate the Capital Recovery Factor by adding the interest rate to the Sinking Fund Factor. What do you think?

i*(1+i)n / (1+i)n -1 is the capital recovery factor.

The sinking fund factor is equal to i/((1+i)n – 1)

Adding I to the Sinking Fund Factor formula yields the following result now:

[1+i]n – 1 In other words, the formula is i/(1+i)n -1 = i(1+i)n/(1+i)n -1.

As a result, the Capital Recovery Factor formula is obtained by adding I to the Sinking Fund Factor formula.