Question

4B. The required return on Mountain Brook stock is 13.8 percent

and the dividend growth rate is 3.64 percent. The stock is
currently selling for $32.80 a share. What is the dividend
yield?

Answer 1

To find the dividend yield for Mountain Brook stock, one must first calculate the annual dividend using the Gordon Growth Model, given the required return and the dividend growth rate. The dividend is then divided by the current stock price of $32.80 to find the dividend yield.

Step-by-step explanation:

To calculate the dividend yield on Mountain Brook stock, we use the formula for dividend yield which is Dividend Yield = (Annual Dividends Per Share / Price Per Share). However, the question does not provide the amount of the annual dividend, but gives us the required return (also known as the discount rate) and the dividend growth rate. We can derive the dividend from the Gordon Growth Model which states that Price = Dividend / (Required Return - Growth Rate). Using the information provided, we can rearrange the formula to solve for the dividend: Dividend = Price × (Required Return - Growth Rate). So the dividend is $32.80 × (0.138 - 0.0364).

After calculating the dividend, we then divide that number by the current stock price of $32.80 to get the dividend yield. This is the percentage of the stock's price that is returned to shareholders in the form of dividends. Remember, the dividend yield does not account for any potential capital gains or losses from price fluctuations in the stock itself.

Answer 2

The closest option is 11.75 percent.

The dividend yield is calculated by dividing the annual dividend by the current stock price. The formula is:


`\[ \text{Dividend Yield} = \left( \frac{\text{Dividend per Share}}{\text{Stock Price per Share}} \right) * 100 \]`

Given that the required return is 13.8 percent and the dividend growth rate is 3.64 percent, you can use the Gordon Growth Model to find the dividend per share:


`\[ \text{Dividend per Share} = \text{Dividend} * (1 + \text{Dividend Growth Rate}) \]\\`

`\[ \text{Dividend per Share} = \frac{\text{Required Return}}{\text{Dividend Growth Rate}} \]`

Substituting the values:


`\[ \text{Dividend per Share} = (13.8\%)/(3.64\%) \approx 3.7912 \]`

Now, the dividend yield is:


`\[ \text{Dividend Yield} = \left( (3.7912)/(32.80) \right) * 100 \approx 11.56\% \]`