Bot GPT 4-o mini To find the expected growth rate of the dividend, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth), which is given by the formula:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = Current stock price
- \( D_1 \) = Dividend in the next period
- \( r \) = Required rate of return
- \( g \) = Growth rate of the dividend
We know the following:
- \( P_0 = 21.80 \)
- \( D_0 = 1.86 \) (this is the dividend just paid)
- \( r = 0.1125 \) (11.25%)
First, we need to calculate \( D_1 \), which is the expected dividend next year. Since we are looking for growth \( g \), we can express \( D_1 \) in terms of the current dividend (\( D_0 \)) and the growth rate (\( g \)):
\[ D_1 = D_0 \cdot (1 + g) = 1.86 \cdot (1 + g) \]
Substituting \( D_1 \) back into the Gordon Growth Model equation:
\[ 21.80 = \frac{1.86 \cdot (1 + g)}{0.1125 - g} \]
To solve for \( g \), we can rearrange and simplify the equation. Multiply both sides by \( 0.1125 - g \):
\[ 21.80(0.1125 - g) = 1.86(1 + g) \]
Expanding both sides gives:
\[ 2.44875 - 21.80g = 1.86 + 1.86g \]
Now, combine the terms involving \( g \):
\[ 2.44875 - 1.86 = 21.80g + 1.86g \]
\[ 0.58875 = 23.66g \]
Now, solve for \( g \):
\[ g = \frac{0.58875}{23.66} \approx 0.02487 \]
Converting this to a percentage:
\[ g \approx 0.02487 \times 100 \approx 2.487% \]
Thus, the expected growth rate of the dividend is approximately 2.49%.
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