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.