To calculate the Weighted Average Cost of Capital (WACC), we need to consider the cost of each component of the company's capital structure: debt, preferred stock, and common equity. We will also need to determine the proportions of each component in the overall capital structure.

Step 1: Determine the Market Values and Costs of Each Component

Before the New Bond Issue

1. Secured Bonds:

   • Amount: $15 million
   • Interest Rate: 6.5%
   • After-tax Cost of Debt (since interest is tax-deductible): $r_d = 6.5\% \times (1 - 0.30) = 6.5\% \times 0.70 = 4.55\%$

2. Preferred Stock:

   • Amount: $10 million
   • Dividend: $3.80 per share
   • Par Value: $50 per share
   • Cost of Preferred Stock: $r_p = \frac{3.80}{50} = 7.6\%$

3. Common Equity:

   • Book Value: $75 million
   • Cost of Equity: 12%

After the New Bond Issue

1. New Debentures:
   • Amount: $10 million
   • Interest Rate: 7.5%
   • After-tax Cost of Debt: $r_d = 7.5\% \times (1 - 0.30) = 7.5\% \times 0.70 = 5.25\%$

Step 2: Calculate the Proportions of Each Component

Before the New Bond Issue

Total Capital Before: $\text{Total Capital} = \text{Debt} + \text{Preferred Stock} + \text{Common Equity} = 15 + 10 + 75 = 100 \text{ million}$

Proportions: $w_d = \frac{15}{100} = 0.15$ $w_p = \frac{10}{100} = 0.10$ $w_e = \frac{75}{100} = 0.75$

After the New Bond Issue

Total Capital After: $\text{Total Capital} = \text{Old Debt} + \text{New Debt} + \text{Preferred Stock} + \text{Common Equity} = 15 + 10 + 10 + 75 = 110 \text{ million}$

Proportions: $w_{d_{\text{old}}} = \frac{15}{110} \approx 0.1364$ $w_{d_{\text{new}}} = \frac{10}{110} \approx 0.0909$ $w_p = \frac{10}{110} \approx 0.0909$ $w_e = \frac{75}{110} \approx 0.6818$

Step 3: Calculate the WACC

Before the New Bond Issue

$\text{WACC} = w_d \times r_d + w_p \times r_p + w_e \times r_e$ $\text{WACC} = 0.15 \times 4.55\% + 0.10 \times 7.6\% + 0.75 \times 12\%$ $\text{WACC} = 0.6825\% + 0.76\% + 9\% = 10.4425\%$

After the New Bond Issue

$\text{WACC} = w_{d_{\text{old}}} \times r_d + w_{d_{\text{new}}} \times r_d + w_p \times r_p + w_e \times r_e$ $\text{WACC} = 0.1364 \times 4.55\% + 0.0909 \times 5.25\% + 0.0909 \times 7.6\% + 0.6818 \times 12\%$ $\text{WACC} = 0.62012\% + 0.477225\% + 0.69084\% + 8.1816\% = 9.969785\%$

Final Results

• Before the new bond issue: WACC ≈ 10.44%
• After the new bond issue: WACC ≈ 9.97%

Would you like further details or have any questions? Here are some related questions:

1. What are the implications of a lower WACC for the company?
2. How does issuing new debt affect the company's risk profile?
3. What factors can influence the cost of equity for a company?
4. How is the cost of preferred stock calculated if the dividend changes?
5. What are the benefits of using WACC in capital budgeting decisions?
6. How can a company optimize its capital structure to minimize WACC?
7. How does the tax rate affect the after-tax cost of debt?
8. What is the impact of fluctuating interest rates on WACC?

Tip: Regularly reviewing and optimizing the capital structure can help a company maintain a lower WACC, improving its overall financial health.