To calculate the expected growth rate of the dividend (g), we can use the Gordon Growth Model (Dividend Discount Model), which describes the relationship between the price of a stock, its dividend, the required rate of return, and the growth rate of the dividend. The formula is:
\[ P = \frac{D_1}{r - g} \]
Where:
- \( P \) = Price of the stock ($23.86)
- \( D_1 \) = Expected dividend next year ($1.31)
- \( r \) = Required rate of return (11.56% or 0.1156)
- \( g \) = Growth rate of the dividend
Rearranging the formula to solve for \( g \):
\[ g = r - \frac{D_1}{P} \]
Substituting in the given values:
\[ g = 0.1156 - \frac{1.31}{23.86} \]
Calculating \( \frac{1.31}{23.86} \):
\[ \frac{1.31}{23.86} \approx 0.0549 \]
Now substituting back into the growth rate equation:
\[ g = 0.1156 - 0.0549 \] \[ g \approx 0.0607 \]
Converting to a percentage:
\[ g \approx 6.07% \]
Thus, the expected growth rate of the dividend is approximately 6.07%.
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