Titan Mining Corporation has 6.4 million shares of common stock outstanding and 175,000 (units of) 6 percent semiannual bonds outstanding, par value $1,000 each. (Hint: the coupon payment every 6 months is $30.) The common stock currently sells for $53 per share and has a beta of 1.15; the bonds have 5 years to maturity and sell for $1,060 per unit. The market risk premium is 6.8 percent, T-bills are yielding 3.1 percent, and the company's tax rate is 21 percent. a. What is the market leverage of the company?

To calculate the **market leverage** of Titan Mining Corporation, we need to determine the proportion of the company's total market value that comes from debt relative to equity. Leverage is the ratio of the firm's debt to the sum of its debt and equity, using **market values** rather than book values.

### Step 1: Calculate the **Market Value of Equity (E)**
The market value of equity (also called market capitalization) is calculated as:

\[
\text{Market Value of Equity (E)} = \text{Number of Shares} \times \text{Price per Share}
\]

Given:
- Number of shares = 6.4 million = 6,400,000 shares
- Price per share = \$53

\[
E = 6,400,000 \times 53 = 339,200,000 \, (\$339.2 \, \text{million})
\]

### Step 2: Calculate the **Market Value of Debt (D)**
The market value of debt is calculated as:

\[
\text{Market Value of Debt (D)} = \text{Number of Bonds} \times \text{Market Price per Bond}
\]

Given:
- Number of bonds = 175,000 units
- Market price per bond = \$1,060

\[
D = 175,000 \times 1,060 = 185,500,000 \, (\$185.5 \, \text{million})
\]

### Step 3: Calculate the **Market Leverage**
Market leverage is the ratio of the market value of debt to the total market value (debt + equity).

\[
\text{Market Leverage} = \frac{D}{D + E}
\]

Substitute the values:

\[
\text{Market Leverage} = \frac{185,500,000}{185,500,000 + 339,200,000}
\]

\[
\text{Market Leverage} = \frac{185,500,000}{524,700,000} \approx 0.3536
\]

### Final Answer:
The **market leverage** of the company is approximately **35.36%**.

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Would you like more details or further clarifications on any part of the calculation? 

Here are 5 related questions you may want to explore:
1. How does market leverage impact the risk profile of a company?
2. What is the effect of tax on the leverage ratio calculation?
3. How do we compute the cost of debt for the company?
4. How would the leverage ratio change if bond prices fluctuated?
5. What role does beta play in determining the firm's cost of equity?

**Tip**: Remember that using market values instead of book values for leverage provides a more accurate and up-to-date financial snapshot of the company.

Learn how to calculate the market leverage of Titan Mining Corporation, including step-by-step instructions to find the market value of equity and debt. This problem involves key corporate finance concepts such as leverage ratios and market capitalization, suitable for undergraduate-level finance courses.

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