Calculator Capital Recovery Factor Solve for N
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Reviewed by Calculator Editorial Team
The Capital Recovery Factor (CRF) is a financial metric used to determine the present value of a series of future cash flows. This calculator helps you solve for N, the number of periods, when you know the annual interest rate, the present value, and the periodic payment.
What is Capital Recovery Factor?
The Capital Recovery Factor (CRF) is a financial ratio that represents the present value of a series of equal periodic payments discounted at a specified rate. It's commonly used in capital budgeting to evaluate the profitability of investments.
When solving for N, we're essentially determining how many periods it will take for a series of equal payments to recover the initial investment, considering the time value of money.
Capital Recovery Factor Formula
Capital Recovery Factor Formula
CRF = (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
- r = annual interest rate (as a decimal)
- n = number of periods
When solving for N, we rearrange the formula to solve for n:
Solving for N
n = log(1 + (CRF * r)) / log(1 + r)
Solving for N (Number of Periods)
To solve for N, you need to know:
- The Capital Recovery Factor (CRF)
- The annual interest rate (r)
The calculator will use the rearranged formula to determine the number of periods required to recover the initial investment based on the given interest rate and CRF.
Important Note
The number of periods calculated represents the time it takes for the series of payments to equal the present value of the investment, considering the discount rate.
Example Calculation
Let's say you have a Capital Recovery Factor of 0.12 and an annual interest rate of 8%. Using the calculator:
- Enter CRF = 0.12
- Enter r = 0.08
- Click Calculate
The calculator will determine that it would take approximately 10 periods to recover the initial investment under these conditions.
| Input | Value |
|---|---|
| Capital Recovery Factor (CRF) | 0.12 |
| Annual Interest Rate (r) | 8% |
| Number of Periods (n) | 10 |
FAQ
What is the difference between CRF and annuity?
The Capital Recovery Factor (CRF) is similar to an annuity factor but specifically used to determine the present value of a series of payments that will recover the initial investment. An annuity is a series of equal payments made at equal intervals.
When would I use the Capital Recovery Factor?
You would use the Capital Recovery Factor when evaluating the profitability of an investment by determining how long it will take for the cash inflows to equal the initial investment, considering the time value of money.
Is the Capital Recovery Factor the same as the annuity factor?
While related, the Capital Recovery Factor is specifically designed to recover the initial investment, whereas the annuity factor is more general and can be used for any series of payments.