A company is considering a 5-year project with an initial investment of $90,000.Cash inflows will be $30,000 for the first two years and $25,000 for the next 3 years.If the company's required rate of return is 12%, determine its discounted payback.
A)4.40years
B)3.60 years
C)3.80 years
D)4.00 years

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 calculate this, we first need to discount each year's cash inflow to its present value using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (cash inflow), r is the discount rate (12% or 0.12), and n is the year.Year 1: PV = $30,000 / (1 + 0.12)^1 = $26,785.71Year 2: PV = $30,000 / (1 + 0.12)^2 = $23,903.57Year 3: PV = $25,000 / (1 + 0.12)^3 = $17,884.19Year 4: PV = $25,000 / (1 + 0.12)^4 = $15,971.24Year 5: PV = $25,000 / (1 + 0.12)^5 = $14,259.86Adding these up until the initial investment of $90,000 is recovered:Year 1 + Year 2 = $26,785.71 + $23,903.57 = $50,689.28Adding Year 3: $50,689.28 + $17,884.19 = $68,573.47Adding Year 4: $68,573.47 + $15,971.24 = $84,544.71By the end of Year 4, the total discounted cash inflows are $84,544.71, which is less than the initial investment. By Year 5, the total exceeds the initial investment, so the payback happens in Year 5. To find the exact time within Year 5, we calculate how much of the Year 5 inflow is needed to cover the remaining balance of the initial investment.Remaining balance at the start of Year 5 = $90,000 - $84,544.71 = $5,455.29Percentage of Year 5 inflow needed = $5,455.29 / $14,259.86Calculating the exact time: 4 years + (Percentage of Year 5 needed) = 4 + ($5,455.29 / $14,259.86) years = 4.38 years, which rounds to 4.40 years when considering the available choices.

A Company Is Considering a 5-Year Project with an Initial