To determine which machine should be acquired, we can calculate the Net Present Value (NPV) for each machine using the given information. ### Calculating NPV **Machine A:** - Initial Cost: $8.3 million - Cash Inflows: $4.5 million per year for 4 years - Replacement Cost (after 4 years): $9.9 million - New Cash Inflows (after replacement): $4.7 million per year for 4 years - WACC: 9% **Machine B:** - Initial Cost: $13.5 million - Cash Inflows: $4.4 million per year for 8 years - WACC: 9% #### NPV Calculation for Machine A 1. **NPV for initial 4 years:** \[ \text{NPV} = \sum_{t=1}^{4} \frac{4.5}{(1+.09)^t} - 8.3 \] 2. **NPV for next 4 years (after replacement):** \[ \text{NPV} = \sum_{t=5}^{8} \frac{4.7}{(1+.09)^{t-4}} - \frac{9.9}{(1+.09)^4} \] 3. **Total NPV for Machine A = NPV for initial 4 years + NPV for next 4 years** #### NPV Calculation for Machine B \[ \text{NPV} = \sum_{t=1}^{8} \frac{4.4}{(1+.09)^t} - 13.5 \] ### Comparison Calculate the NPVs using the above formulas and compare them: - **Machine A:** Calculate the total NPV. - **Machine B:** Calculate the NPV. The machine with the higher NPV should be chosen as it provides more value to the company. ### Fill in the Blanks 1. Select the machine with the higher NPV. 2. Calculate the increase in NPV for the selected machine compared to the other. 3. Fill in the dollar values in the blanks accordingly. Make sure to round your answers to two decimal places and use millions as the unit.

# Machine Investment Decision for Lesseig Company To make an informed decision about which machine to acquire, we will calculate the Net Present Value (NPV) for both Machine A and Machine B. ## Machine A - **Initial Cost:** $8.3 million - **Cash Inflows (Years 1-4):** $4.5 million per year - **Replacement Cost (after 4 years):** $9.9 million - **New Cash Inflows (Years 5-8):** $4.7 million per year - **WACC:** 9% ### NPV Calculation for Machine A 1. **NPV for First 4 Years:** \[ \text{NPV}_1 = \sum_{t=1}^{4} \frac{4.5}{(1 + 0.09)^t} - 8.3 \] - Cash inflows for years 1-4: - Year 1: \( \frac{4.5}{(1 + 0.09)^1} = 4.13 \) - Year 2: \( \frac{4.5}{(1 + 0.09)^2} = 3.79 \) - Year 3: \( \frac{4.5}{(1 + 0.09)^3} = 3.48 \) - Year 4: \( \frac{4.5}{(1 + 0.09)^4} = 3.20 \) - Total NPV for first 4 years: \[ \text{NPV}_1 = 4.13 + 3.79 + 3.48 + 3.20 - 8.3 = 6.30 \text{ million} \] 2. **NPV for Next 4 Years (Years 5-8):** \[ \text{NPV}_2 = \sum_{t=5}^{8} \frac{4.7}{(1 + 0.09)^{t-4}} - \frac{9.9}{(1 + 0.09)^4} \] - Cash inflows for years 5-8: - Year 5: \( \frac{4.7}{(1 + 0.09)^1} = 4.31 \) - Year 6: \( \frac{4.7}{(1 + 0.09)^2} = 3.96 \) - Year 7: \( \frac{4.7}{(1 + 0.09)^3} = 3.63 \) - Year 8: \( \frac{4.7}{(1 + 0.09)^4} = 3.33 \) - Total NPV for next 4 years: \[ \text{NPV}_2 = 4.31 + 3.96 + 3.63 + 3.33 - \frac{9.9}{(1 + 0.09)^4} = 15.23 - 7.27 = 7.96 \text{ million} \] 3. **Total NPV for Machine A:** \[ \text{Total NPV}_A = \text{NPV}_1 + \text{NPV}_2 = 6.30 + 7.96 = 14.26 \text{ million} \] ## Machine B - **Initial Cost:** $13.5 million - **Cash Inflows (Years 1-8):** $4.4 million per year - **WACC:** 9% ### NPV Calculation for Machine B 1. **NPV Calculation:** \[ \text{NPV}_B = \sum_{t=1}^{8} \frac{4.4}{(1 + 0.09)^t} - 13.5 \] - Cash inflows for years 1-8: - Year 1: \( \frac{4.4}{(1 + 0.09)^1} = 4.02 \) - Year 2: \( \frac{4.4}{(1 + 0.09)^2} = 3.69 \) - Year 3: \( \frac{4.4}{(1 + 0.09)^3} = 3.39 \) - Year 4: \( \frac{4.4}{(1 + 0.09)^4} = 3.11 \) - Year 5: \( \frac{4.4}{(1 + 0.09)^5} = 2.85 \) - Year 6: \( \frac{4.4}{(1 + 0.09)^6} = 2.62 \) - Year 7: \( \frac{4.4}{(1 + 0.09)^7} = 2.41 \) - Year 8: \( \frac{4.4}{(1 + 0.09)^8} = 2.21 \) - Total NPV for Machine B: \[ \text{NPV}_B = 4.02 + 3.69 + 3.39 + 3.11 + 2.85 + 2.62 + 2.41 + 2.21 - 13.5 = 1.29 \text{ million} \] ## Conclusion - **Total NPV for Machine A:** 14.26 million - **Total NPV for Machine B:** 1.29 million ### Final Decision - Select **Machine A** as it has a higher NPV, providing greater value to the company. ### Increase in Company Value The increase in value from selecting Machine A over Machine B is: \[ \Delta \text{NPV} = 14.26 - 1.29 = 12.97 \text{ million} \] **Final Answer:** - Machine A: 14.26 million - Machine B: 1.29 million - Increase in company value: 12.97 million