What is the Capital Recovery Factor?
The Capital Recovery Factor (CRF), also known as the Capital Charge Factor, is a financial ratio used to calculate the periodic payment amount required to recover an initial capital investment over a specified number of periods at a given interest rate.
This factor is particularly useful in engineering economics, project evaluation, and financial planning where you need to determine the annualized cost of a capital investment or equipment purchase.
Formula for Capital Recovery Factor
The Capital Recovery Factor is calculated using the following formula:
[
\text{CRF} = \frac{i(1+i)^n}{(1+i)^n - 1}
]
Where:
- CRF = Capital Recovery Factor
- i = Interest rate per period (as a decimal)
- n = Number of annuity periods
Calculation Example
Let's say you're evaluating a capital investment with the following parameters:
- Interest Rate: 15% (0.15 as a decimal)
- Number of Annuities: 10 periods
Using the formula:
[
\text{CRF} = \frac{0.15(1+0.15)^{10}}{(1+0.15)^{10} - 1}
]
First, calculate (1 + 0.15)¹⁰:
$$
\text{Result} = 1.15^{10} = 4.0456
$$
Now substitute into the formula:
[
\text{CRF} = \frac{0.15 \times 4.0456}{4.0456 - 1} = \frac{0.6068}{3.0456} = 0.1993
]
The Capital Recovery Factor is approximately 0.20, meaning you need to recover about 20% of the initial investment each period.
Practical Application
If you invested $100,000 in equipment with the parameters above, you would multiply the CRF by your investment:
$$
\text{Annual Payment} = 100{,}000 \times 0.1993 = 19{,}930
$$
This means you would need to recover approximately $19,930 per year to fully recover your $100,000 investment over 10 years at a 15% interest rate.
Why Use the Capital Recovery Factor?
The CRF is valuable for:
- Project Evaluation: Comparing different capital investments by converting them to equivalent annual costs
- Equipment Decisions: Determining whether to purchase or lease equipment
- Budget Planning: Calculating the annual budget allocation needed to recover capital investments
- Break-even Analysis: Understanding the minimum annual revenue needed to justify an investment
By using the Capital Recovery Factor, businesses and engineers can make more informed decisions about capital investments and ensure that projects generate sufficient returns to recover the initial investment plus the cost of capital.