To find the current stock price, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a constantly growing dividend), which is given by:

$P_0 = \frac{D_1}{r - g}$

Where:

• $P_0$ is the current stock price.
• $D_1$ is the dividend expected next year.
• $r$ is the required rate of return.
• $g$ is the growth rate of the dividend.

Step 1: Calculate the dividend growth rate (g)

The growth rate of dividends ($g$) can be calculated using the formula:

$g = ROE \times \text{Retention Ratio}$

The retention ratio is the portion of earnings that is not paid out as dividends, so:

$\text{Retention Ratio} = 1 - \text{Payout Ratio}$

Given that the payout ratio is 48%, the retention ratio is:

$\text{Retention Ratio} = 1 - 0.48 = 0.52$

Now calculate $g$:

g = 0.113 \times 0.52 = 0.05876 \quad \text{(or 5.876% growth rate)}

Step 2: Calculate $D_1$ (Next year's dividend)

The dividend just paid (i.e., $D_0$) is $6.10. The dividend for next year ($D_1$) will be:

$D_1 = D_0 \times (1 + g) = 6.10 \times (1 + 0.05876) = 6.10 \times 1.05876 = 6.46$

Step 3: Calculate the stock price using the Gordon Growth Model

Now, plug in the values into the formula for the current stock price:

$P_0 = \frac{6.46}{0.107 - 0.05876} = \frac{6.46}{0.04824} = 133.88$

So, the current stock price is $133.88.

Answer:

(a) $133.88

Would you like more details or have any questions?

Here are five related questions:

1. How does the retention ratio affect the dividend growth rate?
2. What happens to the stock price if the required rate of return increases?
3. How would the stock price change if the payout ratio was 60% instead of 48%?
4. Why do we use the Gordon Growth Model for valuing stocks with constant dividend growth?
5. How is the required rate of return determined for a stock?

Tip: The Gordon Growth Model is only valid if the required rate of return is higher than the dividend growth rate.