## 4. Calculation of the discounted payback period

The discounted payback period calculation is almost the same as the payback period method. The only difference is that the annual cash flows are discounted: in other words, the present value of each year’s cash inflow is used. Because the discounted cash flow values are smaller (i.e., money is worth less overtime) in this case, the discounted payback period is longer than the payback period.

Let us look at the previous example. We will calculate the discounted payback period for Alternative A. To discount each year’s cash flow, we will multiply the annual cash flows by the present value of \$1 for each corresponding year. Let’s assume a cost of capital of 6%.

Illustration 1: Compound interest table for a present value of 1

 (n) Periods 4% 5% 6% 8% 10% 12% 15% 20% 1 0.96154 0.95238 0.94340 0.92593 0.90909 0.89286 0.86957 0.83333 2 0.92456 0.90703 0.89000 0.85734 0.82645 0.79719 0.75614 0.69444 3 0.88900 0.86384 0.83962 0.79383 0.75131 0.71178 0.65752 0.57870 4 0.85480 0.82270 0.79209 0.73503 0.68301 0.63552 0.57175 0.48225

The discounted payback period is calculated as follows:

1. Discount each year’s cash flows:
 Period Annual Cash flow Discount Rate @ 6% Discounted Cash Flow Cumulative Total A B C D = B x C En+1 = D + En Year 0 (100,000) (100,000) Year 1 35,000 0.94340 33,019 (66,981) Year 2 28,000 0.89000 24,920 (42,061) Year 3 32,000 0.83962 26,868 (15,193) Year 4 40,000 0.79209 31,684 16,491

Note that the initial investment does not need to be discounted because the investment takes place at the beginning of the project.

2. We can see from the table above that after 3 years the company still needs to recover \$15,193 of the initial \$100,000 investment. The company will recover the investment in year 4. To calculate the fraction of year 4 it takes to recover the remainder of the investment, divide \$15,193 by the annual cash inflows that year. Because we are calculating the discounted payback period, use the discounted cash flows: \$15,193 ÷ \$31,684 = 0.48 (or 5.76 months).
3. The discounted payback period is 3.48 (i.e., 3 years plus 5.76 months).
4. The discounted payback period is longer than the payback period (i.e., 3.48 is larger than 3.125).

Both the discounted payback period and payback period methods are useful. The payback period can also be used to approximate the internal rate of return (IRR) on an investment. This technique is called the payback reciprocal method.

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