To determine which machine should be acquired, we need to calculate the Net Present Value (NPV) of both Machine A and Machine B using the given cash flows and the Weighted Average Cost of Capital (WACC) of 9%. The NPV helps in evaluating the profitability of an investment. ### Steps to Calculate NPV 1. **Identify Cash Flows:** - **Machine A:** - Initial Cost: $8.3 million - Yearly Inflows: $4.5 million for 4 years - Replacement Cost: $9.9 million (with inflows of $4.7 million for 4 more years) - **Machine B:** - Initial Cost: $13.5 million - Yearly Inflows: $4.4 million for 8 years 2. **Calculate NPV for Machine A:** - **Years 1-4:** \[ NPV_A1 = \sum_{t=1}^{4} \frac{4.5}{(1+.09)^t} \] - **Years 5-8 (Replacement):** \[ NPV_A2 = \sum_{t=5}^{8} \frac{4.7}{(1+.09)^t} - \frac{9.9}{(1+.09)^4} \] - **Total NPV for A:** \[ NPV_A = -8.3 + NPV_A1 + NPV_A2 \] 3. **Calculate NPV for Machine B:** \[ NPV_B = -13.5 + \sum_{t=1}^{8} \frac{4.4}{(1+.09)^t} \] 4. **Compare NPVs:** - The machine with the higher NPV is the better investment. ### Calculation #### Machine A: - **Years 1-4:** \[ NPV_A1 = \frac{4.5}{1.09} + \frac{4.5}{1.09^2} + \frac{4.5}{1.09^3} + \frac{4.5}{1.09^4} = 15.53 \] - **Years 5-8 (Replacement):** \[ NPV_A2 = \frac{4.7}{1.09^5} + \frac{4.7}{1.09^6} + \frac{4.7}{1.09^7} + \frac{4.7}{1.09^8} - \frac{9.9}{1.09^4} = 6.49 \] - **Total NPV for A:** \[ NPV_A = -8.3 + 15.53 + 6.49 = 13.72 \] #### Machine B: - \[ NPV_B = -13.5 + \frac{4.4}{1.09} + \frac{4.4}{1.09^2} + \frac{4.4}{1.09^3} + \ldots + \frac{4.4}{1.09^8} = 12.82 \] ### Conclusion - **Machine A** has a higher NPV of **$13.72 million** compared to Machine B's **$12.82 million**. - **Machine A** is the better project and will increase the company's value by **$13.72 million**, rather than the **$12.82 million** created by Machine B.