## 5. Payback reciprocal method

When the useful life of a project is at least twice the payback period and the annual cash flows are uniform each period, the payback period reciprocal gives a quick estimate of the IRR:

 Payback Period Reciprocal = 1 Payback Period

In the example we have previously discussed, Company XYZ is considering an investment of \$100,000. The useful life of the project is 10 years. The cutoff period is 3 years. Alternative B provides equal cash flows of \$35,000 each year. The payback period is 2.86 (i.e., \$100,000 ÷ \$35,000).

The payback period reciprocal for Alternative B is 0.35 or 35% (i.e., 1 ÷ 2.86 = 0.35).

The precise internal rate of return is as follows:

• Useful life 10 years: 33%
• Useful life 20 years: 35%

The table for the present value of ordinary annuity of 1 shows that when the useful life of the project (i.e., periods) is 10 years, the payback period value of 2.86 corresponds to 33%; and when the useful life is 20 years, the IRR is approximately 35%.

Illustration 2: Compound interest table for a present value of ordinary annuity of 1

 (n) Periods 5% 6% 10% 20% 33% 35% 1 0.95238 0.94340 0.90909 0.83333 0.75188 0.74074 2 1.85941 1.83339 1.73554 1.52778 1.31720 1.28944 3 2.72325 2.67301 2.48685 2.10648 1.74226 1.69588 10 7.72173 7.36009 6.14457 4.19247 2.85533 2.71504 15 10.37966 9.71225 7.60608 4.67547 2.98826 2.82545 20 12.46221 11.46992 8.51356 4.86958 3.02020 2.85008

We have previously calculated that the payback period reciprocal equals 35%. This example shows that when the useful life of the investment is at least twice the payback period, the payback period reciprocal is a good approximation of the internal rate of return of the project.

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