What is the discounted payback of the following project if the required return is 14%?
A) 2 years
B) 3 years
C) 4 years
D) 5 years
E) It doesn't pay back on a discounted basis.

Question

What is the discounted payback of the following project if the required return is 14%? 
A) 2 years 
B) 3 years 
C) 4 years 
D) 5 years 
E) It doesn't pay back on a discounted basis.

Quizplus · Accepted Answer

To calculate the discounted payback period, we need to determine the present value of each cash inflow and then subtract them from the initial investment until we reach zero or a positive amount.

Year 1: $800 / (1 + 0.14) = $701.75
Year 2: $900 / (1 + 0.14)^2 = $706.19
Year 3: $1,000 / (1 + 0.14)^3 = $681.34
Year 4: $1,100 / (1 + 0.14)^4 = $633.10
Year 5: $1,200 / (1 + 0.14)^5 = $567.08

At the end of year 4, the cumulative present value of the cash inflows is $2,722.38 ($701.75 + $706.19 + $681.34 + $633.10) which is less than the initial investment of $3,000. It is only in year 5 that the cumulative present value exceeds the initial investment.

Therefore, the discounted payback period is between 4 and 5 years, and the best answer is D) 5 years.

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