## 3. Calculation of the payback period

To determine the payback period, divide the initial investment by annual cash flows:

 Payback Period = Original Investment Annual Cash Inflows

The calculation of the payback period depends on the uniformity of annual cash flows. When annual cash flows are not equal (i.e., different each year), there are two steps in calculating the payback period. When annual cash flows are equal, or in other words the company is receiving an annuity, the calculation of the payback period is straightforward: divide the original investment by the annual cash flow.� Let us look at the following example to better understand how the payback period is calculated.

Company XYZ is considering an investment of \$100,000. The useful life of the project is 10 years. The cutoff period is three (3) years. The board of directors has identified two alternatives A and B. The expected annual cash flows are as follows:

 Cost or Cash Flow Alternative A Alternative B Initial cost (\$100,000) (\$100,000) Cash flow year 1 35,000 35,000 Cash flow year 2 28,000 35,000 Cash flow year 3 32,000 35,000 Cash flow year 4 40,000 35,000

The payback period for Alternative A is calculated as follows:

1. \$35,000 + \$28,000 + \$32,000 = \$95,000. In 3 years the company expects to recover \$95,000 of the initial \$100,000 invested. After 3 years the company will need to recover \$5,000 more of the original investment.
2. 2In year 4, the company expects to recover the remaining \$5,000, and the annual cash flow that year is \$40,000. Assuming the cash flow is uniform throughout the year, we can divide \$5,000 by \$40,000 to get 0.125 (or 1.5 months).
3. The payback period for Alternative A is 3.125 years (i.e., 3 years plus 1.5 months).

The payback period for Alternative B is calculated as follows:

1. Divide the initial investment by the annuity: \$100,000 � \$35,000 = 2.86 (or 10.32 months).
2. The payback period for Alternative B is 2.86 years (i.e., 2 years plus 10.32 months).

As mentioned earlier, Company XYZ�s cutoff period is 3 years. Since Alternative B recovers the investment within the cutoff period (i.e., 2.86 is less than 3), Alternative B can be accepted.

This payback method of evaluating two investment alternatives has its limitation: the time value of money is not considered. To incorporate the time value of money concept, the discounted payback period method can be used.

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