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. c. What is the cost of equity for the company?


To calculate the cost of equity, we will use the **Capital Asset Pricing Model (CAPM)**. The CAPM formula is:

\[
\text{Cost of Equity} = R_e = R_f + \beta \times (R_m - R_f)
\]

Where:
- $R_e$ is the cost of equity.
- $R_f$ is the risk-free rate (T-bill rate).
- $\beta$ is the stock's beta.
- $R_m - R_f$ is the market risk premium (MRP).

### Given Data:
- **Risk-free rate (T-bill rate), $R_f$**: 3.1% or 0.031
- **Beta, $\beta$**: 1.15
- **Market risk premium, $R_m - R_f$**: 6.8% or 0.068

### Step-by-Step Calculation:
1. Substitute the given values into the CAPM formula:

\[
R_e = 0.031 + 1.15 \times (0.068)
\]

2. Calculate the excess market return ($R_m - R_f$):

\[
R_m - R_f = 0.068
\]

3. Multiply the beta by the market risk premium:

\[
1.15 \times 0.068 = 0.0782
\]

4. Now, add the risk-free rate:

\[
R_e = 0.031 + 0.0782 = 0.1092
\]

So, the cost of equity is:

\[
R_e = 0.1092 \text{ or } 10.92\%
\]

### Final Answer:
The cost of equity for Titan Mining Corporation is **10.92%**.

Do you need more details or have any other questions?

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Here are 5 related questions to expand on this:

1. How is the cost of equity used in calculating the Weighted Average Cost of Capital (WACC)?
2. What impact would a higher beta have on the cost of equity?
3. How does the market risk premium influence the cost of equity?
4. What are alternative methods for calculating the cost of equity besides CAPM?
5. How does the choice of risk-free rate affect the cost of equity calculation?

**Tip:** The CAPM model assumes that the only risk investors are concerned with is systematic (market) risk, measured by beta. Unsystematic risk is assumed to be diversified away.

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. 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. What is the cost of equity for the company?

Learn how to calculate the cost of equity for Titan Mining Corporation using the Capital Asset Pricing Model (CAPM). This example includes real-world data such as stock prices, bond details, risk-free rate, market risk premium, and beta. Ideal for finance students or professionals looking to understand equity valuation.

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