Let's tackle each part of the problem step by step.

Part A: Cost of Equity

To calculate the cost of equity, we can use the Capital Asset Pricing Model (CAPM) formula:

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

Where:

• $R_f$ is the risk-free rate (4.8% or 0.048),
• $\beta$ is the beta of the stock (0.85),
• $R_m$ is the market return (13.7% or 0.137).

Substituting the values:

$\text{Cost of Equity} = 0.048 + 0.85 \times (0.137 - 0.048)$

Let's calculate it.

$\text{Cost of Equity} = 0.048 + 0.85 \times 0.089 = 0.048 + 0.07565 = 0.12365$

The cost of equity is 12.37%.

Part B: Fair Price Today

The fair price of the share today can be found by discounting the expected price one year from now and the dividend to the present value using the cost of equity:

$\text{Fair Price} = \frac{\text{Expected Price + Dividend}}{(1 + \text{Cost of Equity})^1}$

Given:

• Expected Price = $49.66
• Expected Dividend = $7.29
• Cost of Equity = 12.37% or 0.1237

$\text{Fair Price} = \frac{49.66 + 7.29}{(1 + 0.1237)^1} = \frac{56.95}{1.1237}$

Let's calculate it.

$\text{Fair Price} = \frac{56.95}{1.1237} \approx 50.69$

So, the fair price today is $50.69.

Part C: New Fair Price with Negative News

With the negative news, the price target of $49.66 will only be reached 2 years from now, and there will be no dividends. We need to calculate the present value of the $49.66 price target in 2 years.

$\text{New Fair Price} = \frac{\text{Expected Price in 2 years}}{(1 + \text{Cost of Equity})^2}$

Given:

• Expected Price = $49.66
• Cost of Equity = 12.37% or 0.1237

$\text{New Fair Price} = \frac{49.66}{(1 + 0.1237)^2} = \frac{49.66}{1.2677}$

Let's calculate it.

$\text{New Fair Price} = \frac{49.66}{1.2677} \approx 39.17$

So, the new fair price today is $39.17.

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Summary:

• Part A: The cost of equity is 12.37%.
• Part B: The fair price for shares today is $50.69.
• Part C: The new fair price with the updated news is $39.17.

Do you want details or have any questions?

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1. What other models can be used to estimate the cost of equity?
2. How does beta affect the cost of equity in the CAPM formula?
3. What is the significance of the risk-free rate in the CAPM model?
4. How would a higher market return affect the fair price of the shares today?
5. What impact does dividend payments have on the fair value of a stock?
6. How does the time horizon affect the fair price calculation?
7. What are the implications of a company reporting no dividends on its stock price?
8. How might the company's beta change after reporting negative news?

Tip: Understanding how different financial metrics interact in pricing models can help you make more informed investment decisions.