To determine the expected growth rate of the dividend for the given stock, we can utilize the Gordon Growth Model (also known as the Dividend Discount Model). The formula for this model is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) is the current stock price,
- \( D_1 \) is the expected dividend next year,
- \( r \) is the required rate of return, and
- \( g \) is the growth rate of the dividend.
Given:
- Current stock price \( P_0 = 24.64 \)
- Recently paid dividend \( D_0 = 1.16 \)
- Required rate of return \( r = 11.63% = 0.1163 \)
First, we need to calculate \( D_1 \), which is the expected dividend next year. This can be expressed in terms of the most recent dividend and the growth rate as follows:
\[ D_1 = D_0 \times (1 + g) \]
Now substitute \( D_1 \) back into the Gordon Growth Model formula:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
To find the growth rate \( g \), we rearrange the equation:
\[ P_0 (r - g) = D_0 \times (1 + g) \]
Expanding this gives:
\[ P_0 r - P_0 g = D_0 + D_0 g \]
Now we can isolate \( g \):
\[ P_0 r - D_0 = P_0 g + D_0 g \]
\[ P_0 r - D_0 = g(P_0 + D_0) \]
\[ g = \frac{P_0 r - D_0}{P_0 + D_0} \]
Now plug in the values:
- Calculate \( P_0 r \):
\[ P_0 r = 24.64 \times 0.1163 = 2.864992 \]
- Now substitute into the equation for \( g \):
\[ D_0 = 1.16 \]
\[ g = \frac{2.864992 - 1.16}{24.64 + 1.16} \]
\[ g = \frac{1.704992}{25.8} \]
\[ g \approx 0.0661 \text{ or } 6.61% \]
Thus, the expected growth rate of the dividend is approximately 6.61%.