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The cash flows are as follows: Year 0 Year 1 Year 2 Year 3 Initial Investment (160,000) Depreciation 48,000 64,000 48,000 Depreciation Tax Shield (Depr. * .40) 19,200 25,600 19,200 Cash from disposition RECD @ YEAR END (after tax) 6,000 Operating cash flows 85,000 85,000 85,000 Tax on operating cash flow at 40% (34,000) (34,000) (34,000) Net Cash Flow excluding cash from disposition (160,000) 70,200 76,600 70,200 Cumulative Cash Flow excluding cash from disposition (undiscounted) (160,000) (89,800) (13,200) 57,000 When calculating the payback period, operating cash flows are usually assumed to be received evenly throughout each year of the project's life. However, the $6,000 received from disposition of the asset is not received until the end of the project, which is at the end of Year 3. Therefore, it is handled differently from operating cash flows. It is not included in the calculation of the payback period in this case, because it occurs at the end of the year, while operating cash flows are assumed to occur evenly throughout the year. Thus, the payback period would end before the disposition occurs. Note that it is not a part of the net cash flow used to calculate the payback period. The cumulative cash flow from the project becomes positive during year 3. The payback period is 2.19 years, calculated as follows: Number of the project year in the final year when cash flow is negative, which is 2 Plus: a fraction consisting of Numerator = the positive value of the negative cumulative inflow amount from the final negative year - 13,200 Denominator = cash flow (excluding disposition) for the following year: 70,200 OR : 2 + (13,200/70,200) = 2.19 Since the disposition of the asset occurs after the payback period, it is not a part of the payback period calculation.
Since the useful life of the machine is 3 years, an answer of 3.00 would result from using the annual depreciation as the annual cash flow.
An answer of 1.88 years results from dividing the net investment of $160,000 by the annual operating cash flow of $85,000. However, the operating cash flow of $85,000 is not the only component of cash flow to be used to calculate the payback period. The annual cash flows are not uniform over the life of this project.
An answer of 1.53 years results from using the annual depreciation instead of the depreciation tax shield as an increase to the annual net cash flows.