Cost of Capital: Advanced Topics

Correct Answer: 7.45%

To determine the most appropriate discount rate for evaluating the project, we need to calculate the project's weighted average cost of capital (WACC) using the given inputs. **Step 1: Calculate the Cost of Equity (Re)** Using the Capital Asset Pricing Model (CAPM): Re = Risk-free rate + Beta × Market risk premium Given: - Risk-free rate (Rf) = 2.5% - Beta (β) = 1.8 - Market risk premium (Rm - Rf) = 4.5% Re = 2.5% + 1.8 × 4.5% = 2.5% + 8.1% = **10.6%** **Step 2: Calculate the After-tax Cost of Debt (Rd)** Rd = Pre-tax cost of debt × (1 - Tax rate) Given: - Pre-tax cost of debt = 5% - Tax rate (T) = 28% or 0.28 Rd = 5% × (1 - 0.28) = 5% × 0.72 = **3.6%** **Step 3: Calculate the Weighted Average Cost of Capital (WACC)** Using the target capital structure of 55% equity and 45% debt: WACC = (E/V) × Re + (D/V) × Rd Where: - E/V = Proportion of equity = 55% - D/V = Proportion of debt = 45% WACC = 0.55 × 10.6% + 0.45 × 3.6% = 5.83% + 1.62% = **7.45%** **Conclusion:** The most appropriate discount rate to use when evaluating this project is **7.45%**.

Correct Answer: The project-specific cost of equity should be used as the discount rate, as the project's cash flows are uncorrelated with the company's existing assets.

The most appropriate discount rate to use when evaluating this project is the project-specific cost of equity. This is because the project's cash flows are expected to be highly volatile and uncorrelated with the company's existing assets. Using the company's weighted average cost of capital (WACC) or the company's cost of equity based on its equity beta would not be appropriate in this case. These discount rates are suitable for projects with cash flows that are correlated with the company's existing assets and overall risk profile. However, since this project's cash flows are uncorrelated with the company's existing assets, it should be evaluated using a discount rate that reflects its unique risk characteristics. The project-specific cost of equity takes into account the project's unique risk profile and is the most appropriate discount rate to use in this situation.

Correct Answer: The project's cash flows are highly correlated with the company's existing assets, so the company's weighted average cost of capital (WACC) should be used as the discount rate.

The most appropriate discount rate to use when evaluating this project is the company's weighted average cost of capital (WACC). This is because the project's cash flows are highly correlated with the company's existing assets, indicating that the project has the same risk profile as the company's overall operations. The WACC takes into account the cost of both debt and equity financing, weighted by their respective proportions in the capital structure. In this case, the project will be financed with 50% debt and 50% equity. The cost of debt is given as 5% pre-tax, and with a marginal tax rate of 25%, the after-tax cost of debt is 3.75% (5% × (1 - 0.25)). The cost of equity can be calculated using the Capital Asset Pricing Model (CAPM): Risk-free rate + (Beta × Market risk premium) = 3% + (1.4 × 4%) = 8.6%. Therefore, the WACC is: (0.5 × 3.75%) + (0.5 × 8.6%) = 6.175%. Using the project-specific equity beta or the average of the cost of debt and cost of equity would not accurately reflect the project's risk and the company's overall financing mix.