Scott is considering a project that will produce cash inflows of $2,100 a year for 4 years.The project has a 12 percent required rate of return and an initial cost of $6,000.What is the discounted payback period?
A)3.72 years
B)3.91 years
C)4.26 years
D)4.38 years
E)never

Question

Quizplus · Accepted Answer

The discounted payback period is the time it takes for the discounted cash flows to pay back the initial investment. To find this, we discount each cash inflow at the required rate of return (12% in this case) and then cumulatively add these discounted cash flows until they equal or exceed the initial investment. Year 1: $2,100 / (1 + 0.12)^1 = $1,875.00Year 2: $2,100 / (1 + 0.12)^2 = $1,674.11Year 3: $2,100 / (1 + 0.12)^3 = $1,495.10Year 4: $2,100 / (1 + 0.12)^4 = $1,335.09Cumulative discounted cash flows:End of Year 1: $1,875.00End of Year 2: $3,549.11 ($1,875.00 + $1,674.11)End of Year 3: $5,044.21 ($3,549.11 + $1,495.10)End of Year 4: $6,379.30 ($5,044.21 + $1,335.09)The initial investment of $6,000 is recovered between Year 3 and Year 4. To find the exact time, we interpolate between these two years. The amount needed to recover at the start of Year 3 is $6,000 - $3,549.11 = $2,450.89. The amount available in Year 3 is $1,495.10, leaving $2,450.89 - $1,495.10 = $955.79 to be recovered in Year 4. The fraction of the year needed to recover this in Year 4 is $955.79 / $1,335.09 ≈ 0.72.Therefore, the discounted payback period is approximately 3 years + 0.72 = 3.72 years.

Scott Is Considering a Project That Will Produce Cash Inflows