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An answer of "over 5 years" could result from using the annual net income amounts instead of the annual after-tax cash flows to calculate the payback period.
An answer of 2.83 years results from using the discounted annual after-tax cash flows to determine the payback period. However, the traditional payback period uses undiscounted cash flows to calculate the payback period.
When cash flows are not constant over the life of the project, we must add up the cash inflows in order to determine when the inflows will equal the outflows. The cash flows are as follows: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Net initial investment (250,000) After-tax cash flows from operations 120,000 108,000 96,000 84,000 72,000 Cumulative cash flows (250,000) (130,000) (22,000) 74,000 158,000 230,000 The cumulative cash flow from the project becomes positive sometime during year 3. If the cash flows are assumed to occur evenly throughout the year, the exact payback period is 2.23 years, calculated as follows: Number of the project year in the final year when cash flow is negative: 2 Plus: a fraction consisting of Numerator = the positive value of the negative cumulative inflow amount from the final negative year: 22,000 Denominator = cash flow for the following year: 96,000 OR: 2 + (22,000/96,000) = 2.23 The initial investment will be recouped after 2.23 years.
An answer of 1.65 years results from adding together the annual after-tax cash flow and the annual net income for each year and using the total to determine the payback period. However, the payback period should be determined using annual after-tax cash flow only.