The Expanding Capital Corporation has a current capital structure of $15 million in secured bonds paying 6.5% annual interest, $10 million in preferred stock with a par value of $50 per share and an annual dividend of $3.80 per share, and common stock with a book value of $75 million.  It is about to issue new debentures in the amount of $10 million paying 7.5% annual interest.  Its CFO says its marginal tax rate is 30% and its cost of common equity capital is 12%.  Calculate the company’s Weighted Average Costs of Capital for the following:

Before the new bond issue
After the new bond issue

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.

Learn how to calculate the Weighted Average Cost of Capital (WACC) for a company with existing and new bond issues. Includes detailed calculations of cost of debt, preferred stock, and cost of equity. Suitable for financial analysts and professionals.

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