To find the required rate of return for the stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth). The model is represented by the formula:
\[ P = \frac{D_1}{r - g} \]
Where:
- \( P \) is the current price of the stock ($46.36 in this case),
- \( D_1 \) is the expected dividend next year ($3.82),
- \( r \) is the required rate of return,
- \( g \) is the growth rate of the dividend (3.55% or 0.0355).
We will rearrange the formula to solve for \( r \):
\[ r = \frac{D_1}{P} + g \]
Now we can substitute the values into the equation:
- First, we calculate \( \frac{D_1}{P} \):
\[ \frac{D_1}{P} = \frac{3.82}{46.36} \approx 0.0824 \text{ (or 8.24%)} \]
- Next, we add the growth rate \( g \):
\[ r = 0.0824 + 0.0355 = 0.1179 \text{ (or 11.79%)} \]
Therefore, the required rate of return for the stock is approximately 11.79%.