Your firm is considering an investment that will cost $750,000 today.The investment will produce cash flows of $250,000 in year 1,$300,000 in years 2 through 4,and $100,000 in year 5.What is the investment's discounted payback period if the required rate of return is 10%?
A) 3.33 years
B) 3.16 years
C) 2.67 years
D) 2.33 years

Question

Quizplus · Accepted Answer

To find the discounted payback period, we need to calculate the present value of cash flows until the initial investment is fully recovered.

- Year 1 cash flow = $250,000 / (1 + 10%)^1 = $227,273 
- Year 2-4 cash flows = $300,000 / (1+10%)^2 + $300,000 / (1+10%)^3 + $300,000 / (1+10%)^4 = $772,201
- Year 5 cash flow = $100,000 / (1+10%)^5 = $62,092

Total present value of cash flows = $227,273 + $772,201 + $62,092 = $1,061,567

To find the discounted payback period, we need to figure out the year when the cumulative present value of cash flows equals the initial investment.

Year 1: PV of Year 1 cash flow = $227,273, cumulative PV = $227,273 
Year 2: PV of Year 2 cash flow = $246,047, cumulative PV = $473,320 
Year 3: PV of Year 3 cash flow = $266,157, cumulative PV = $739,477 
Year 4: PV of Year 4 cash flow = $287,671, cumulative PV = $1,027,148 
Year 5: PV of Year 5 cash flow = $62,092, cumulative PV = $1,089,240

The discounted payback period is between year 4 and 5. To find the exact year, we can use linear interpolation:

$1,027,148 + ($1,089,240 - $1,027,148) / $62,092 * 1 = 3.16 years

Therefore, the investment's discounted payback period is approximately 3.16 years. The best choice is B.

Your Firm Is Considering an Investment That Will Cost $750,000