Certainly! Let's break the problem into two steps: --- ## **Step 1: Calculate the Firm's Weighted Average Cost of Capital (WACC)** Given: - Debt outstanding = $1,500 million - Book value of equity = $4,000 million - Cost of debt = 6.5% - Cost of equity = 12% - Tax rate = 35% **Formula for WACC:** \[ \text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{D}{V} \times r_d \times (1-T) \right) \] Where: - \( E \) = Market value of equity ($4,000M) - \( D \) = Market value of debt ($1,500M) - \( V \) = Total value = $4,000M + $1,500M = $5,500M - \( r_e \) = Cost of equity (12%) - \( r_d \) = Cost of debt (6.5%) - \( T \) = Tax rate (35%) \[ \frac{E}{V} = \frac{4,000}{5,500} = .7273 \] \[ \frac{D}{V} = \frac{1,500}{5,500} = .2727 \] \[ \text{After-tax cost of debt} = 6.5\% \times (1 - .35) = 4.225\% \] \[ \text{WACC} = (.7273 \times 12\%) + (.2727 \times 4.225\%) \] \[ = 8.7276\% + 1.1511\% \] \[ = 9.88\% \] **Explanation:** We calculated the weighted average cost of capital (WACC) using the proportions and after-tax costs of debt and equity. --- ## **Step 2: Calculate the NPV of the Project** Given: - Initial investment = $100 million - Annual after-tax operating cash flow = $15 million (for 10 years) - Depreciation per year = $5.75 million (straight-line for 10 years, fully recovered at end) - Salvage value = $24 million (book value at end) - WACC = 9.88% ### Cash Flows: - Year : Outflow of $100 million - Year 1-10: Inflow of $15 million each year - Year 10: Additional inflow of $24 million (salvage value) ### NPV Formula: \[ \text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1 + WACC)^t} + \frac{\text{Salvage value}}{(1 + WACC)^{10}} - \text{Initial Investment} \] \[ \text{NPV} = \left[ \sum_{t=1}^{10} \frac{15}{(1.0988)^t} \right] + \frac{24}{(1.0988)^{10}} - 100 \] The present value of an annuity (years 1-10): \[ PV_{\text{annuity}} = C \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] \] \[ PV_{\text{annuity}} = 15 \times \left[ \frac{1 - (1.0988)^{-10}}{.0988} \right] \] \[ (1.0988)^{-10} \approx .3936 \] \[ PV_{\text{annuity}} = 15 \times \left[ \frac{1 - .3936}{.0988} \right] \] \[ PV_{\text{annuity}} = 15 \times \left[ \frac{.6064}{.0988} \right] \] \[ PV_{\text{annuity}} = 15 \times 6.137 = 92.06 \] Present value of salvage value: \[ PV_{\text{salvage}} = \frac{24}{(1.0988)^{10}} = \frac{24}{2.543} = 9.44 \] Total present value: \[ NPV = 92.06 + 9.44 - 100 = 1.50 \] **Explanation:** We calculated the present value of the project's cash flows and salvage value, then subtracted the initial investment to get the NPV. --- ## **Final Answer** **The NPV of the project is approximately $1.50 million.**