Final answer:
The Modified Internal Rate of Return (MIRR) for the project is -6.65%.
Step-by-step explanation:
The Modified Internal Rate of Return (MIRR) is a financial metric used to evaluate the profitability of an investment project. It takes into account both the cost of financing (weighted average cost of capital - WACC) and the reinvestment rate for cash flows. To calculate the MIRR, we need to find the future value of all positive cash flows at the reinvestment rate, and the future value of all negative cash flows at the financing rate.
Using the given cash flows and WACC:
- Year 0 (Cash Flow): -$850
- Year 1 (Cash Flow): $300
- Year 2 (Cash Flow): $320
- Year 3 (Cash Flow): $340
- Year 4 (Cash Flow): $360
The future value of the positive cash flows at the reinvestment rate of 4% (WACC - 5%) would be:
- Year 1: 300 * (1 + 0.04)^3 = $333.84
- Year 2: 320 * (1 + 0.04)^2 = $335.74
- Year 3: 340 * (1 + 0.04) = $353.60
- Year 4: 360
The future value of the negative cash flow at the financing rate of 14.25% (WACC) would be:
Next, we calculate the present value of the future cash flows at the financing rate:
- Year 1: 333.84 / (1 + 0.1425) = $292.13
- Year 2: 335.74 / (1 + 0.1425)^2 = $270.23
- Year 3: 353.60 / (1 + 0.1425)^3 = $270.00
- Year 4: 360 / (1 + 0.1425)^4 = $237.08
Finally, we calculate the MIRR by finding the discount rate that makes the present value of the negative cash flow equal to the sum of the present values of the positive cash flows:
- MIRR = [(Present Value of Positive Cash Flows - Present Value of Negative Cash Flow) / Present Value of Negative Cash Flow]^(1/4) - 1
- MIRR = [292.13 + 270.23 + 270.00 + 237.08 - 850] / 850]^(1/4) - 1
- MIRR = -0.0665 or -6.65%
Therefore, the MIRR for the project is -6.65%.