To find the expected growth rate of the dividend, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model can be expressed as:
\[ P_0 = \frac{D_1}{r - g} \]
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
Given the information:
- Current stock price \( P_0 = 24.91 \)
- The most recent dividend \( D_0 = 1.89 \)
- Required rate of return \( r = 0.1160 \) (or 11.60%)
First, we need to determine \( D_1 \), the expected dividend for next year. Since \( D_1 \) can be found as:
\[ D_1 = D_0 \times (1 + g) \]
We can substitute \( D_1 \) into the Gordon Growth Model equation:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
Rearranging this equation to solve for \( g \) gives:
\[ P_0 (r - g) = D_0 \times (1 + g) \]
Expanding and rearranging:
\[ P_0 \cdot r - P_0 \cdot g = D_0 + D_0 \cdot g \]
\[ P_0 \cdot r - D_0 = P_0 \cdot g + D_0 \cdot g \]
\[ P_0 \cdot r - D_0 = g (P_0 + D_0) \]
Thus, we can solve for \( g \):
\[ g = \frac{P_0 \cdot r - D_0}{P_0 + D_0} \]
Now substituting the known values:
\[ g = \frac{24.91 \cdot 0.1160 - 1.89}{24.91 + 1.89} \]
Calculating the numerator:
\[ 24.91 \cdot 0.1160 = 2.89276 \]
Now substituting this value into the formula:
\[ g = \frac{2.89276 - 1.89}{24.91 + 1.89} \]
Calculating the numerator:
\[ 2.89276 - 1.89 = 1.00276 \]
Calculating the denominator:
\[ 24.91 + 1.89 = 26.8 \]
Now substituting the numerator and denominator:
\[ g = \frac{1.00276}{26.8} \approx 0.0374 \]
Expressing this as a percentage:
\[ g \approx 0.0374 \cdot 100 = 3.74% \]
Therefore, the expected growth rate of the dividend is approximately 3.74%.
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