Your firm has the opportunity to invest $75,000 in a new project opportunity but due to cash flow concerns, your boss wants to know when you can pay back the original investment. Using the discounted payback method, you determine that the project should generate inflows of $30,000, $30,000, $25,000, $20,000, and $20,000 respectively for an expected five years after completion of the project. Your firm's required rate of return is 10%. How long will it take to pay back the initial project investment

It will take the project 3 years 3.6 months to pay back the initial investment.

Explanation:

The discounted payback period is the length of time of time it will take the present value of the cash inflows to recoup its initial cost.

To compute the discounted payback period we will follow the steps below:

Step 1: Compute the present value

Compute the Present Value of the cash inflows

Year                                       Present Value    Cumulative PV

0                                               75,000                (75,000)

1          30,000 × 1.1^(-1)=         27272.72              (47,727.27)

2         30,000 × 1.1^(-2)  =       24793.38            (22,933.88)

3.         25,000 × 1.1^(-3)=      18782.87                (4,151.0)

4.          20,000 × 1.1^(4) =      13,660.26911

5.         20,000 ×  1.1^(-5)=      12,418.42646

Step 2 : compute the payback period using the present value of cash flows

Discounted payback period = 3 years + ( 4,150/13,660)× 12 months

                                               = 3 years 3.6 months

It will take the project 3 years 3.6 months to pay back the initial investment.