Question

Scott is considering a project that will produce cash inflows of $5,100 a year for 3 years. The project has required rate of return of 14 percent and an initial cost of $6,000. What is the discounted payback period

Answer 1

Answer:

1.3892 Years

Explanation:

Cash flows

Year 0 = - 6000

year 1 = 5100

year 2 = 5100

year 3 = 5100

First we discount the cash flows

Year 1 discounted cash flow = $\frac{5100}{1+0.14}$ = 4473.68

Year 2 discounted cash flow = $\frac{5100}{(1+0.14)^{2} }$ = 3921.28

Year 3 discounted cash flow = $\frac{5100}{(1+0.14)^{3} }$ = 3442.35

To calculate the discounted payback period we have to check in what year we break-even, that is our cash inflow = 6000

6000 - 4473.68 = 1526.32

we have to recover 1526.32 and year 2 discounted cash flow is 3921.28

therefore, we know that we are break evening somewhere in year 2. To calculate the exact period we will divide the remaining amount for break even that is 1526.32 by the discounted cash flow of year 2

$\frac{1526.32}{3921.28}$ = 0.3892 years

So our net discounted payback period = 1 year + 0.3892 years = 1.3892 years