## Payback Reciprocal

The payback reciprocal is simply the reciprocal of the payback period and is sometimes used as an approximation of the project’s internal rate of return (IRR). The formula is:

Payback Reciprocal = 1 / Payback Period

The payback reciprocal can be used as a rough estimate of the internal rate of return when cash flows are relatively uniform over time. This approach has a mathematical foundation because the formula for the payback period is mathematically similar to the formula for the IRR when cash flows are even.

However, it’s crucial to keep in mind that this method is only an approximation and should not replace a proper internal rate of return calculation, especially when cash flows are not consistent. This is because the payback reciprocal does not take into account the time value of money, the size or timing of cash flows after the payback period, or cash flows that fluctuate significantly from year to year.

## Example of Payback Reciprocal

Let’s consider an example to illustrate how to calculate the payback reciprocal:

Let’s say a company invests $100,000 in a new project, and this project is expected to generate an even $20,000 in cash flow each year.

The payback period of this investment would be the initial investment divided by the annual cash inflows, which equals:

Payback Period = Initial Investment / Annual Cash Inflows

Payback Period = $100,000 / $20,000 = 5 years

Then, to calculate the payback reciprocal, you take the reciprocal (1 divided by) of the payback period:

Payback Reciprocal = 1 / Payback Period

Payback Reciprocal = 1 / 5 = 0.2 or 20%

This suggests that the internal rate of return is roughly 20%. However, remember that the payback reciprocal is an approximation and should not replace a full internal rate of return calculation, especially when cash flows are not consistent throughout the life of the investment. It also doesn’t account for any cash flows that occur after the payback period. It provides a rough, quick estimate, but more sophisticated techniques should also be used for a complete analysis.