Part A: Calculate the Capital Structure Weights

The capital structure weights represent the proportion of each component (debt, preferred shares, and common equity) in the firm's total market value. The total market value of the firm is the sum of the market values of debt, preferred shares, and common equity.

1. Market Values:

   • Debt: $D = \$260 \text{ million}$
   • Preferred Shares: $P = \$95 \text{ million}$
   • Common Equity: $E = \$325 \text{ million}$

2. Total Market Value: $V = D + P + E = 260 + 95 + 325 = 680 \text{ million dollars}$

3. Capital Structure Weights:

   • Weight of Debt: $W_D = \frac{D}{V} = \frac{260}{680} = 0.3824 \text{ or } 38.24\%$
   • Weight of Preferred Shares: $W_P = \frac{P}{V} = \frac{95}{680} = 0.1397 \text{ or } 13.97\%$
   • Weight of Common Equity: $W_E = \frac{E}{V} = \frac{325}{680} = 0.4779 \text{ or } 47.79\%$

Part B: Calculate the Costs of Debt, Preferred Equity, and Common Equity

1. Cost of Debt (Pre-tax):

   • The yield to maturity (YTM) on the debt is given as 6.0%, which is compounded semi-annually. Therefore, the effective annual rate (EAR) for the cost of debt is: $\text{Cost of Debt} = 6.0\%$

2. Cost of Preferred Equity:

   • The cost of preferred equity is calculated as the dividend yield: $\text{Cost of Preferred Equity} = \frac{\text{Dividend}}{\text{Price}} = \frac{1.95}{24.36} = 0.0801 \text{ or } 8.01\%$

3. Cost of Common Equity:

   • The cost of common equity can be estimated using the Capital Asset Pricing Model (CAPM): $\text{Cost of Common Equity} = R_f + \beta \times (R_m - R_f)$ Where:
     • $R_f = 3.5\%$ (risk-free rate)
     • $\beta = 0.85$ (equity beta)
     • $R_m - R_f = 5.9\%$ (market risk premium) $\text{Cost of Common Equity} = 3.5\% + 0.85 \times 5.9\% = 8.515\% \text{ or } 8.52\%$

Part C: Calculate the WACC (After-tax)

The Weighted Average Cost of Capital (WACC) is calculated as follows: $\text{WACC} = W_D \times (1 - T) \times \text{Cost of Debt} + W_P \times \text{Cost of Preferred Equity} + W_E \times \text{Cost of Common Equity}$ Where:

• $T = 22.5\%$ (tax rate)

1. WACC Calculation: $\text{WACC} = 0.3824 \times (1 - 0.225) \times 6.0\% + 0.1397 \times 8.01\% + 0.4779 \times 8.52\%$ $\text{WACC} = 0.3824 \times 4.65\% + 0.1397 \times 8.01\% + 0.4779 \times 8.52\%$ $\text{WACC} = 1.78\% + 1.12\% + 4.08\% = 6.98\%$

Final Answers:

Part A: Capital Structure Weights

• Weight of Debt: 38.24%
• Weight of Preferred Shares: 13.97%
• Weight of Common Equity: 47.79%

Part B: Cost of Capital

• Cost of Debt (Pre-tax): 6.00%
• Cost of Preferred Equity: 8.01%
• Cost of Common Equity: 8.52%

Part C: WACC (After-tax)

• WACC: 6.98%

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Would you like more details or have any questions? Here are some follow-up questions you might consider:

1. How does changing the tax rate affect the WACC?
2. What happens if the company issues more debt?
3. How would a change in the market risk premium impact the cost of equity?
4. What is the impact of a different equity beta on WACC?
5. How does the semi-annual compounding of debt affect its effective cost?
6. What if the company plans to increase its preferred shares? How would WACC change?
7. Can WACC be used to evaluate all investment projects of the company?
8. How does the company's capital structure influence its financial risk?

Tip: Always consider the impact of taxes when calculating the cost of debt, as it directly affects the WACC.