21 Chapter 10 Cost of Capital
Conceptual Questions
1. Explain the role of WACC in investment decision-making. Why is it important to use a firm’s WACC as the discount rate when evaluating new projects?
WACC represents the average return required by investors. Using it as the discount rate ensures that the project’s return exceeds the firm’s cost of financing, thereby creating value.
2. Why does the after-tax cost of debt differ from the pre-tax cost of debt? Provide an example.
The after-tax cost of debt is lower because interest payments are tax-deductible. For example, if the pre-tax cost of debt is 6% and the tax rate is 30%, the after-tax cost is 6\% \times (1 – 0.3) = 4.2\% .
3. What is the primary benefit of using the weighted average in WACC calculations?
It accurately reflects the proportional cost of each financing source, ensuring the overall cost aligns with the firm’s actual capital structure.
4. Explain the significance of beta in determining the cost of equity using the CAPM.
Beta measures a stock’s sensitivity to market movements. A higher beta indicates higher risk and expected return, while a lower beta suggests lower risk and return.
5. How do project-specific costs of capital improve decision-making in acquisitions? Provide an example.
They account for the unique risk profile of the project. For example, acquiring a tech firm with a high beta would require a higher cost of capital than a low-risk manufacturing project.
Short Calculations
1. WACC Calculation
[latex]WACC = \left(\frac{400}{1,000} \times 10\%\right) + \left(\frac{600}{1,000} \times 6\% \times (1 - 0.3)\right)[/latex]
[latex]WACC = (0.4 \times 0.10) + (0.6 \times 0.06 \times 0.7)[/latex]
[latex]WACC = 0.04 + 0.0252 = 0.0652 \text{ or } 6.52\%[/latex]
2. Cost of Debt
[latex]r_D = 7\% \times (1 - 0.25) = 5.25\%[/latex]
3. Cost of Equity (CAPM)
[latex]r_E = 3\% + 1.2 \times 5\% = 3\% + 6\% = 9\%[/latex]
4. Preferred Stock Cost
[latex]r_P = \frac{6}{60} = 0.10 \text{ or } 10\%[/latex]
Scenario-Based Problems
1. WACC and Investment Decision
[latex]PV = \frac{1.2}{1.09} + \frac{1.2}{1.09^2} + \frac{1.2}{1.09^3} + \frac{1.2}{1.09^4} + \frac{1.2}{1.09^5}[/latex]
[latex]PV = 1.10 + 1.01 + 0.93 + 0.85 + 0.78 = 4.67 \text{ million}[/latex]
[latex]NPV = 4.67 - 5 = -0.33 \text{ million}[/latex]
Decision: The project has a negative NPV, so the firm should not proceed.
2. Project-Specific Cost of Capital
[latex]r_E = 3\% + 1.4 \times 6\% = 3\% + 8.4\% = 11.4\%[/latex]
[latex]WACC = (0.5 \times 11.4\%) + (0.5 \times 5\% \times 0.75)[/latex]
[latex]WACC = 5.7\% + 1.875\% = 7.575\%[/latex]
3. Divisional WACC
•Healthcare:
[latex]r_E = 4\% + 1.1 \times 5\% = 4\% + 5.5\% = 9.5\%[/latex]
[latex]WACC = (0.714 \times 9.5\%) + (0.286 \times 5\% \times 0.7)[/latex]
[latex]WACC = 6.785\% + 1\% = 7.785\%[/latex]
•Consumer Goods:
[latex]r_E = 4\% + 0.9 \times 5\% = 4\% + 4.5\% = 8.5\%[/latex]
[latex]WACC = (0.625 \times 8.5\%) + (0.375 \times 5\% \times 0.7)[/latex]
[latex]WACC = 5.3125\% + 1.3125\% = 6.625\%[/latex]
Interactive Challenge
1. WACC for Firm
[latex]WACC = (0.615 \times 11\%) + (0.385 \times 5\% \times 0.75)[/latex]
[latex]WACC = 6.765\% + 1.4438\% = 8.2088\%[/latex]
2. Acquisition-Specific WACC
[latex]r_E = 4\% + 1.5 \times 6\% = 4\% + 9\% = 13\%[/latex]
[latex]WACC = (0.6 \times 13\%) + (0.4 \times 5\% \times 0.7)[/latex]
[latex]WACC = 7.8\% + 1.4\% = 9.2\%[/latex]
3. Stock Valuation Using CAPM
[latex]CAPM Required Return = 3\% + 1.3 \times (6\%) = 3\% + 7.8\% = 10.8\%[/latex]
The stock’s expected return (12%) exceeds the CAPM-required return (10.8%), so it is undervalued.
