Choice "A" is correct. Computation of the payback method with uneven cash flows involves using a cumulative approach. Discount and tax rate amounts in the fact pattern are not relevant. The after-tax cash flows are given and the computation of cumulative balances is shown below. | After-tax
Cash Inflows
| Cumulative
after-tax
cash inflows
| Unrecovered
Amount
| |
|---|
Year 1 | $ 35,000 | $ 35,000 | $ 65,000 | (100,000 − 35,000) | Year 2 | 38,000 | 73,000 | 27,000 | (65,000 − 38,000) | Year 3 | 25,000 | 98,000 | 2,000 | (27,000 − 25,000) | Year 4 | 20,000 | 118,000 | (18,000) | (2,000 − 20,000) | Year 5 | 10,000 | 128,000 | (28,000) | |
Amount remaining to be recovered after year 3 | $ 2,000 | Amount received in year 4 | ÷ 20,000 | Percentage of year | .10 | Payback period elapsed before partial year | 3.00 | Payback period | 3.10 |
Note: The candidate can quickly review the first three year's of after-tax cash flows and determine that the amount is $98,000, because payback of the $100,000 investment is slightly more than 3 years. Therefore, the logical answer is 3.1 years. Choice "d" is incorrect. The proposed answer grosses up the cash flows by the tax rate essentially providing the pretax payback. After-tax cash flows are used for capital budgeting.Choice "b" is incorrect. The proposed answer is purely the year in which payback is achieved and does not recognize that only 10% of the year is required.
Choice "c" is incorrect. The proposed answer reduces the after-tax cash flows given in the project by taxes for a second time based upon the after-tax cash flow amounts already provided. Clearly this double counts the tax impact on the cash flows.
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