A firm has two classes of securities: long-term bonds and common stock. The bonds have 15 years to maturity, a coupon rate of 4%, semi-annual coupon payments, a yield-to-maturity of 6.2%, and $373 million of total par value. The stock has 33 million shares outstanding and a current market price of $36. When computing the WACC, what weight should the firm assign to its cost of debt? Enter your answer as a decimal and show two decimal places.

To find the weight the firm should assign to its cost of debt when calculating the Weighted Average Cost of Capital (WACC), we need to determine the total market value of the debt and the equity. Then, we use these values to calculate the proportion of the firm's capital structure that is debt.

### Step 1: Calculate the Market Value of Debt
The market value of debt can be calculated using the par value of the bonds and the yield-to-maturity. However, since we’re calculating weight, we assume the par value approximately represents the market value here.

- **Total Par Value of Debt** = $373 million

### Step 2: Calculate the Market Value of Equity
The market value of equity is found by multiplying the current market price per share by the number of shares outstanding.

\[
\text{Market Value of Equity} = \text{Shares Outstanding} \times \text{Price per Share}
\]
\[
\text{Market Value of Equity} = 33,000,000 \times 36 = 1,188,000,000
\]

### Step 3: Calculate the Total Market Value of the Firm
Add the market values of debt and equity to get the total market value of the firm.

\[
\text{Total Market Value} = \text{Market Value of Debt} + \text{Market Value of Equity}
\]
\[
\text{Total Market Value} = 373,000,000 + 1,188,000,000 = 1,561,000,000
\]

### Step 4: Calculate the Weight of Debt
The weight assigned to the cost of debt is the proportion of the market value of debt in the total market value of the firm.

\[
\text{Weight of Debt} = \frac{\text{Market Value of Debt}}{\text{Total Market Value}}
\]
\[
\text{Weight of Debt} = \frac{373,000,000}{1,561,000,000}
\]
\[
\text{Weight of Debt} \approx 0.24
\]

### Final Answer
The weight the firm should assign to its cost of debt is approximately **0.24** (or 24%).

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Would you like to go over the equity calculation or any other part in more detail?

Here are five related questions:
1. How is yield-to-maturity used in determining the market value of debt?
2. What is the significance of the weight in the WACC formula?
3. How would changes in stock price affect the WACC?
4. Why is the coupon rate not used directly in calculating the WACC?
5. How would adding more debt impact the firm's capital structure and WACC?

**Tip:** Remember, when calculating WACC, weights should reflect the current market values, not just the book or par values, to represent the firm's actual cost structure more accurately.

Learn how to calculate the weight of debt in the WACC formula using the market values of debt and equity. This problem involves determining the market value of debt ($373 million) and the equity ($1,188 million), and calculating the debt weight in the firm's capital structure. Suitable for students in Grades 11-12.

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