The Francis Company is expected to pay a dividend of D1 = $1.25 per share at the end of the year, and that dividend is expected to grow at a constant rate of 6.00% per year in the future. The company's beta is 0.80, the market risk premium is 5.50%, and the risk-free rate is 4.00%. What is the company's current stock price? Do not round intermediate calculations.

a. $52.08

b. $35.71

c. $55.21

d. $20.83

e. $14.88

To determine the current stock price of The Francis Company, we can use the Gordon Growth Model (Dividend Discount Model) and the Capital Asset Pricing Model (CAPM) to find the required rate of return.

### Step 1: Calculate the Required Rate of Return using CAPM
The CAPM formula is:

\[ \text{Required Rate of Return} (r_s) = r_f + \beta (r_m - r_f) \]

Where:
- $ r_f $ is the risk-free rate
- $ \beta $ is the beta of the stock
- $ r_m $ is the expected market return
- $ r_m - r_f $ is the market risk premium

Given:
- $ r_f = 4.00\% $ or 0.04
- $ \beta = 0.80 $
- Market risk premium $ r_m - r_f = 5.50\% $ or 0.055

Plugging in the values:

\[ r_s = 0.04 + 0.80 \times 0.055 \]
\[ r_s = 0.04 + 0.044 \]
\[ r_s = 0.084 \text{ or } 8.40\% \]

### Step 2: Use the Gordon Growth Model to find the Current Stock Price
The Gordon Growth Model formula is:

\[ P_0 = \frac{D_1}{r_s - g} \]

Where:
- $ P_0 $ is the current stock price
- $ D_1 $ is the dividend at the end of the year
- $ r_s $ is the required rate of return
- $ g $ is the growth rate of dividends

Given:
- $ D_1 = \$1.25 $
- $ r_s = 8.40\% $ or 0.084
- $ g = 6.00\% $ or 0.06

Plugging in the values:

\[ P_0 = \frac{1.25}{0.084 - 0.06} \]
\[ P_0 = \frac{1.25}{0.024} \]
\[ P_0 = 52.0833 \]

So, the company's current stock price is approximately $52.08.

Therefore, the correct answer is:

a. $52.08

Would you like details or have any questions? Here are 5 numbered questions you can ask next:

1. How does a change in the market risk premium affect the stock price?
2. What assumptions does the Gordon Growth Model make about dividend growth?
3. Can the CAPM be used for companies without a constant dividend growth rate?
4. How does the beta of a stock influence its required rate of return?
5. What are the limitations of using the Dividend Discount Model for valuing stocks?

**Tip:** Always check the assumptions of the valuation model being used to ensure they fit the company's financial situation.

Learn how to calculate the current stock price of The Francis Company using dividend growth and the Capital Asset Pricing Model (CAPM). Includes step-by-step solution with specific data points. Suitable for advanced finance students and professionals.

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