Answer and Explanation:
To calculate the Net Present Value (NPV) for the project, we need to discount each cash flow to its present value and then sum them up. The discount rate we'll be using is the required return of 10 percent.
To calculate the present value (PV) of each cash flow, we divide the cash flow by (1 + discount rate) raised to the power of the corresponding year. Let's calculate the present value for each cash flow:
Year 0: PV = -$28,200 / (1 + 0.10)^0 = -$28,200 / 1 = -$28,200
Year 1: PV = $12,200 / (1 + 0.10)^1 = $12,200 / 1.10 = $11,090.91 (rounded to 2 decimal places)
Year 2: PV = $15,200 / (1 + 0.10)^2 = $15,200 / 1.21 = $12,561.98 (rounded to 2 decimal places)
Year 3: PV = $11,200 / (1 + 0.10)^3 = $11,200 / 1.331 = $8,401.80 (rounded to 2 decimal places)
Now, we sum up the present values:
NPV = PV of Year 0 + PV of Year 1 + PV of Year 2 + PV of Year 3
= -$28,200 + $11,090.91 + $12,561.98 + $8,401.80
= $4,854.69 (rounded to 2 decimal places)
The NPV for the project is $4,854.69.
To determine whether the firm should accept or reject the project, we compare the NPV to zero. If the NPV is positive, the project is expected to generate more value than the initial investment and should be accepted. If the NPV is negative, the project is expected to generate less value than the initial investment and should be rejected.
Since the NPV of $4,854.69 is positive, the firm should accept this project.