To find the new price of the stock after the announcement, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The model states that the price of a stock is equal to the expected dividend in the next period divided by the difference between the required rate of return and the dividend growth rate:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = price of the stock today
- \( D_1 \) = dividend expected next year
- \( r \) = required rate of return
- \( g \) = growth rate of dividends
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Determine the new expected dividend (D1): The new dividend announced is $2.05.
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Use the new growth rate (g): The new growth rate after the announcement is 3.99% (or 0.0399 as a decimal).
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Calculate the required rate of return (r): To find \( r \), we need to rearrange the formula and use the price before the announcement and the prior expected dividend growth rate to find the implied required rate of return:
Prior dividend growth rate = 2.50% (0.025)
The stock price before the announcement can be evaluated with the old dividend of $3.08:
\[ 16.98 = \frac{3.08 \times (1 + 0.025)}{r - 0.025} \]
This means:
\[ 16.98 = \frac{3.08 \times 1.025}{r - 0.025} \]
Thus, we can calculate:
\[ 16.98 = \frac{3.15}{r - 0.025} \]
Rearranging gives:
\[ r - 0.025 = \frac{3.15}{16.98} \] \[ r - 0.025 = 0.185 \] \[ r = 0.210 \text{ or } 21.0% \]
- Now apply this to find the new stock price using the new dividend and growth rate:
Using the new \( D_1 \), which is $2.05, and the new growth rate \( g = 0.0399 \) (3.99%).
Now we substitute into the Gordon Growth Model:
\[ P_0 = \frac{2.05}{0.210 - 0.0399} \] \[ P_0 = \frac{2.05}{0.1701} \] \[ P_0 \approx 12.06 \]
So, the new price of the stock after the announcement is approximately $12.06.
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