What is payback period?
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) |
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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