Let's solve each part step by step. ### **Given Data** | Year | Cash Flow | |------|-----------| | 0 | -$58,000 | | 1 | $18,400 | | 2 | $24,100 | | 3 | $30,600 | | 4 | $22,400 | | 5 | -$9,500 | - Discount Rate: **11%** - Reinvestment Rate: **8%** --- ## **a. MIRR Using the Discounting Approach** **Steps:** 1. **Discount all negative cash flows (except year 0) to present at 11%.** 2. **Add to year 0 outflow.** 3. **Future value all positive cash flows to year 5 at 8%.** 4. **MIRR formula:** \[ MIRR = \left(\frac{FV_{\text{positive CFs}}}{PV_{\text{negative CFs}}}\right)^{1/n} - 1 \] ### **Step 1: Present Value of Negative Cash Flows** - Year 0: -$58,000 - Year 5: -$9,500 / (1.11)^5 \[ PV_{\text{neg}} = 58,000 + \frac{9,500}{(1.11)^5} \] \[ (1.11)^5 = 1.68506 \] \[ \frac{9,500}{1.68506} = 5,639.26 \] \[ PV_{\text{neg}} = 58,000 + 5,639.26 = 63,639.26 \] ### **Step 2: Future Value of Positive Cash Flows** - Year 1: \(18,400 \times (1.08)^{4}\) - Year 2: \(24,100 \times (1.08)^{3}\) - Year 3: \(30,600 \times (1.08)^{2}\) - Year 4: \(22,400 \times (1.08)^{1}\) Calculate each: - (1.08)^4 = 1.36049 - (1.08)^3 = 1.25971 - (1.08)^2 = 1.1664 - (1.08)^1 = 1.08 \[ FV_{\text{pos}} = 18,400 \times 1.36049 + 24,100 \times 1.25971 + 30,600 \times 1.1664 + 22,400 \times 1.08 \] \[ = 25,046.99 + 30,352.99 + 35,678.4 + 24,192 \] \[ = 115,270.38 \] ### **Step 3: Compute MIRR** \[ MIRR = \left(\frac{115,270.38}{63,639.26}\right)^{1/5} - 1 \] \[ = (1.812)^{0.2} - 1 \] \[ = 1.1262 - 1 \] \[ = 0.1262 = 12.62\% \] --- ## **b. MIRR Using the Reinvestment Approach** **Steps:** 1. **Future value all positive cash flows to year 5 at 8%.** (Already calculated above: **115,270.38**) 2. **Present value all negative cash flows to year 0 at 11%.** (Already calculated above: **63,639.26**) 3. **Apply MIRR formula:** So, it's the same as above: \[ MIRR = 12.62\% \] --- ## **c. MIRR Using the Combination Approach** The combination approach is the same as the above for mixed cash flows (discount all negative at financing, compound all positives at reinvestment). Thus, **MIRR = 12.62%** --- ## **Final Answers** ### a. Discounting Approach MIRR: **12.62%** ### b. Reinvestment Approach MIRR: **12.62%** ### c. Combination Approach MIRR: **12.62%** --- **Let me know if you need the step-by-step calculations for a specific method, or if you need further explanation!**