Use the following information to answer the following question.
Below are the expected after-tax cash flows for Projects Y and Z.Both projects have an initial cash outlay of $20,000 and a required rate of return of 17%.
Project Y Project Z

-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

Use the following information to answer the following question.
Below are the expected after-tax cash flows for Projects Y and Z.Both projects have an initial cash outlay of $20,000 and a required rate of return of 17%.
Project Y Project Z
 
-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.

Quizplus · Accepted Answer

The discounted payback period is the time it takes for the discounted cash flows to cover the initial investment. To find this, we discount each cash flow back to its present value using the discount rate of 10% and then cumulatively add them until they exceed the initial investment of $75,000.Year 1: $33,100 / (1 + 0.10)^1 = $30,090.91Year 2: $31,500 / (1 + 0.10)^2 = $26,033.06Year 3: $31,200 / (1 + 0.10)^3 = $23,283.19Cumulative discounted cash flows:End of Year 1: $30,090.91End of Year 2: $30,090.91 + $26,033.06 = $56,123.97End of Year 3: $56,123.97 + $23,283.19 = $79,407.16The initial investment of $75,000 is recovered between Year 2 and Year 3. To find the exact time, we calculate how much of Year 3's cash flow is needed to reach $75,000:$75,000 - $56,123.97 = $18,876.03 needed from Year 3's discounted cash flow.$18,876.03 / $23,283.19 = 0.81 (portion of the third year needed).Therefore, the discounted payback period is 2 years + 0.81 = 2.81 years.

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