MacHinery Manufacturing Company is considering a three-year project that has a cost of $75,000. The project will generate after-tax cash flows of $33,100 in Year 1, $31,500 in Year 2, and $31,200 in Year 3. Assume that the appropriate discount rate is 10% and that the firm's tax rate is 40%. What is the project's discounted payback period?
A) 2.81 years
B) 2.33 years
C) 1.22 years
D) The project never reaches payback.

Question

Quizplus · Accepted Answer

The discounted payback period is calculated by discounting the future cash flows back to their present value and then determining how long it takes for these discounted cash flows to pay back the initial investment. Here's the calculation:1. Discount the cash flows at the 10% discount rate:   - Year 1: $33,100 / (1 + 0.10)^1 = $30,090.91   - Year 2: $31,500 / (1 + 0.10)^2 = $26,033.06   - Year 3: $31,200 / (1 + 0.10)^3 = $23,283.192. Calculate the cumulative discounted cash flows:   - End of Year 1: $30,090.91   - End of Year 2: $30,090.91 + $26,033.06 = $56,123.97   - End of Year 3: $56,123.97 + $23,283.19 = $79,407.163. Determine the payback period:   - The initial investment of $75,000 is recovered between Year 2 and Year 3. To find the exact time, we see that at the end of Year 2, we have recovered $56,123.97. We need to recover the remaining $18,876.03 ($75,000 - $56,123.97) in Year 3. The discounted cash flow in Year 3 is $23,283.19, so we calculate the fraction of the year needed to recover the remaining amount: $18,876.03 / $23,283.19 ≈ 0.81 years.Adding this to the 2 years, the discounted payback period is approximately 2.81 years.

MacHinery Manufacturing Company Is Considering a Three-Year Project That Has