To calculate the new price of the stock after the announcement of the dividend cut and the new growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model states that the price of a stock is equal to the next year's dividend divided by the difference between the required rate of return and the growth rate of the dividend.
The formula for the Gordon Growth Model is:
\[ P = \frac{D_1}{r - g} \]
Where:
- \(P\) = Price of the stock
- \(D_1\) = Dividend in the next year
- \(r\) = Required rate of return
- \(g\) = Growth rate of dividends
Given Data:
- New Dividend (\(D_1\)) = $2.05
- New Growth Rate (\(g\)) = 3.81% = 0.0381
To use the formula, we need to know the required rate of return (\(r\)). We can estimate \(r\) using the previous stock price and dividend given before the announcement.
Since we have:
- Previous Stock Price = $18.79
- Previous Dividend = $3.02
- Previous Growth Rate (\(g_{old}\)) = 2.50% = 0.025
Using the Gordon Growth Model before the announcement to find \(r\):
\[ 18.79 = \frac{3.02}{r - 0.025} \]
Now, rearranging and solving for \(r\):
\[ r - 0.025 = \frac{3.02}{18.79} \] \[ r - 0.025 = 0.160 \] \[ r = 0.160 + 0.025 \] \[ r = 0.185 \text{ or } 18.5% \]
Now that we have \(r\), we can use it to find the new price after the announcement:
Using the new dividend and growth rate:
\[ P_{new} = \frac{2.05}{0.185 - 0.0381} \]
Calculating the denominator:
\[ 0.185 - 0.0381 = 0.1469 \]
Then calculating the stock price:
\[ P_{new} = \frac{2.05}{0.1469} \approx 13.95 \]
Conclusion:
The new price of the stock after the announcement is approximately $13.95.
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