Let’s solve the problem step-by-step: ### **Step 1: Find the Present Value (PV) of All Outflows** **Explanation:** Only one outflow occurs at time 0, so the PV of outflows is simply the initial investment. \[ PV_{outflows} = \$12,500 \] --- ### **Step 2: Find the Future Value (FV) of All Inflows at the End of the Project (Year 4)** **Explanation:** We need to compound each inflow to the end of year 4 using the cost of capital (12%). Formula for compounding: \[ FV = CF_t \times (1 + r)^{n - t} \] where \( n \) is the final year (4), \( t \) is the year of the cash flow. - Year 1: \( \$6,080 \times (1.12)^{3} = \$6,080 \times 1.404928 = \$8,547.98 \) - Year 2: \( \$4,930 \times (1.12)^{2} = \$4,930 \times 1.2544 = \$6,183.19 \) - Year 3: \( \$2,270 \times (1.12)^{1} = \$2,270 \times 1.12 = \$2,542.40 \) - Year 4: \( \$2,750 \) (already at year 4) Sum all future values: \[ FV_{inflows} = 8,547.98 + 6,183.19 + 2,542.40 + 2,750 = \$20,023.57 \] --- ### **Step 3: Calculate MIRR** **Explanation:** MIRR formula: \[ MIRR = \left(\frac{FV_{inflows}}{PV_{outflows}}\right)^{1/n} - 1 \] Where \( n = 4 \): \[ MIRR = \left(\frac{20,023.57}{12,500}\right)^{\frac{1}{4}} - 1 = (1.6018856)^{0.25} - 1 = 1.12443 - 1 = 0.12443 \text{ or } 12.44\% \] --- ## **Final Answer** - **MIRR = 12.44%** - **Decision:** Since the MIRR (12.44%) is slightly higher than the cost of capital (12%), the project should be **accepted**.