1.5 years results from dividing the total undiscounted cash flows of $300,000 by the initial cash outflow of $200,000. However, this is not the correct way to calculate the payback period.
A payback period of 1.67 years would result if the second year's cash flow were the same as the first year's cash flow. However, that is not the case.
The payback period is, first, the number of the project year in the final year when cumulative cash flow (including the initial investment) is negative, plus a fraction consisting of the positive value of the negative cumulative cash inflow amount from the final negative year divided by the cash flow for the following year. In this case, the final year in which the cumulative cash flow is zero is Year 2, because $(200,000) + $120,000 + $60,000 = $(20,000). In the third year, the cash flow is $40,000. So $20,000 ÷ $40,000 = .5, and the payback period is 2 + .5, or 2.5 years.
This is the discounted payback period, in which all cash flows are discounted and the cumulative discounted cash flow is used to calculate the payback period. Although the discount factors are given in this problem, the problem does not ask for the discounted payback period.
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Assuming that the estimated cash inflows occur evenly during each year, the payback period for the investment is: