We will calculate the discount rate and the price Sally Buffit should be willing to pay for the stock today using the Capital Asset Pricing Model (CAPM) and the dividend discount model.

Step 1: Calculate the Discount Rate

The Capital Asset Pricing Model (CAPM) formula is as follows:

$r = r_f + \beta \times (r_m - r_f)$

Where:

• $r$ is the discount rate or required return.
• $r_f$ is the risk-free rate.
• $\beta$ is the stock's beta (since it's the same as the market, $\beta = 1$).
• $r_m$ is the expected market return.
• $(r_m - r_f)$ is the market risk premium.

From the problem:

• $r_f = 1.9\%$ (risk-free Treasury rate).
• The market risk premium $(r_m - r_f) = 7.7\%$.

Now, applying the CAPM formula:

$r = 1.9\% + 1 \times 7.7\% = 1.9\% + 7.7\% = 9.6\%$

So, the discount rate is:

$r = 9.60\%$

Step 2: Calculate the Price of the Stock Today

Using the dividend discount model (DDM) for a stock that pays dividends:

$P_0 = \frac{D_1 + P_1}{1 + r}$

Where:

• $P_0$ is the price today.
• $D_1 = 2.00$ (dividend at year-end).
• $P_1 = 44.00$ (expected price at year-end).
• $r = 9.6\%$ (discount rate, as calculated above).

Now, let's substitute the values:

$P_0 = \frac{2.00 + 44.00}{1 + 0.096} = \frac{46.00}{1.096}$

$P_0 = 41.97$

Final Answers:

• The discount rate is 9.60%.
• The price Sally Buffit should be willing to pay for the stock today is $41.97.

Would you like to explore further details or ask any questions?

Here are 5 related questions:

1. How does changing the market risk premium affect the stock price?
2. What would happen to the price if the dividend were expected to grow annually?
3. Can you calculate the stock price with a different beta value?
4. How does the CAPM model compare with other models for stock pricing?
5. What is the relationship between the risk-free rate and stock valuations?

Tip: The CAPM assumes that all risk is systematic; diversifiable risks are ignored. Always check if this assumption holds when using CAPM.