To calculate the new price of the stock after the announcement, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model provides a way to value a stock based on the expected future dividends that grow at a constant rate.
The formula for the Gordon Growth Model is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = price of the stock
- \( D_1 \) = expected dividend next year
- \( r \) = required rate of return
- \( g \) = growth rate of the dividend
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Identify the values:
- The new dividend \( D_1 \) for year 1 is $2.17.
- The new growth rate \( g \) is 3.91% or 0.0391.
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Determine the required rate of return \( r \): To estimate the required rate of return, we will first compute it using the previous information. Prior to the announcement, the dividend was $3.01 and was expected to grow at 2.5%. The stock price was $18.15, so we can set up the equation:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
Rearranging the terms to find \( r \):
\[ r = \frac{D_0 \times (1 + g)}{P_0} + g \]
Here:
- \( D_0 = 3.01 \), the previous dividend
- \( g = 0.025 \)
Now we compute \( D_1 \):
\[ D_1 = 3.01 \times (1 + 0.025) = 3.01 \times 1.025 = 3.08025 \]
Substitute these values into the formula:
\[ r = \frac{3.08025}{18.15} + 0.025 \] \[ r = 0.1692 + 0.025 \] \[ r = 0.1942 \] or 19.42%
Now, we will use this required rate of return \( r \) to find the new stock price with the updated dividend and growth rate.
- Calculate the new stock price using the new dividend and growth rate:
Using the new dividend \( D_1 = 2.17 \) and the growth rate \( g = 0.0391 \):
\[ P_0 = \frac{D_1}{r - g} \] \[ P_0 = \frac{2.17}{0.1942 - 0.0391} \] \[ P_0 = \frac{2.17}{0.1551} \] \[ P_0 \approx 14.0 \]
Thus, the new price of the stock after the announcement is approximately $14.00.
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