To calculate the new price of the stock after the announcement of the dividend decrease and the change in growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = Price of the stock today
- \( D_1 \) = Dividend in the next year
- \( r \) = Required rate of return
- \( g \) = Growth rate of dividends
Step 1: Identify the inputs
- Next Year Dividend (\( D_1 \)): The dividend will be $2.10 per share.
- Growth Rate (\( g \)): The new growth rate is 3.90% or 0.039.
- To use the Gordon Growth Model, we also need the required return (\( r \)). We can assume it remains constant based on its original price.
Step 2: Calculate the required return (\( r \))
The original dividend was $3.01, and the stock was priced at $18.66 with an expected growth rate of 2.50%. We can find the required return using the original data:
\[ P_0 = \frac{D_1}{r - g} \]
We can rearrange this to solve for \( r \):
\[ r = \frac{D_1}{P_0} + g \]
Using \( D_1 = 3.01 \), \( P_0 = 18.66 \), and \( g = 0.025 \):
\[ r = \frac{3.01}{18.66} + 0.025 \]
Calculating \( \frac{3.01}{18.66} \):
\[ \frac{3.01}{18.66} \approx 0.1613 \]
So,
\[ r \approx 0.1613 + 0.025 \approx 0.1863 = 18.63% \]
Step 3: Use the new growth rate to find the new stock price
Now that we have \( r \) and the new \( g \), we can calculate the new price using \( D_1 = 2.10 \) and \( g = 0.039 \):
\[ P_0 = \frac{2.10}{0.1863 - 0.039} \]
Calculating \( r - g \):
\[ 0.1863 - 0.039 = 0.1473 \]
Now, substituting into the Price formula:
\[ P_0 = \frac{2.10}{0.1473} \approx 14.24 \]
Final Result
The new price of the stock after the announcement is approximately $14.24 per share.
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