To calculate the new price of the stock after the announcement, we can use the Gordon Growth Model (Dividend Discount Model), which is given by the formula:
\[ P = \frac{D_1}{r - g} \]
where:
- \( P \) = price of the stock
- \( D_1 \) = dividend in year 1
- \( r \) = required rate of return
- \( g \) = growth rate of dividends
Here are the steps to find the new price of the stock:
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Calculate the required rate of return (r): Since we have the previous stock price, dividend, and growth rate, we can rearrange the formula to find \( r \) before the announcement:
\[ P = \frac{D_0(1 + g)}{r - g} \]
Before the dividend cut, the dividend was $3.01 per share, and \( g \) was 2.50% or 0.025.
Calculating \( D_1 \) (the dividend for year 1 before the cut):
\[ D_1 = D_0(1 + g) = 3.01 \times (1 + 0.025) = 3.01 \times 1.025 = 3.08025 \]
Now using the original stock price ($18.73):
\[ 18.73 = \frac{3.08025}{r - 0.025} \]
Rearranging gives:
\[ r - 0.025 = \frac{3.08025}{18.73} \]
\[ r - 0.025 = 0.164 \]
\[ r = 0.164 + 0.025 = 0.189 = 18.9% \]
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Calculate the new price after the announcement: The new dividend \( D_1 \) after the cut is $2.19 per share, and the new growth rate \( g \) is 3.56% or 0.0356.
Now, using the Gordon Growth Model again with the new parameters:
\[ P = \frac{D_1}{r - g} = \frac{2.19}{0.189 - 0.0356} \]
First, compute \( r - g \):
\[ r - g = 0.189 - 0.0356 = 0.1534 \]
Now substitute back into the formula:
\[ P = \frac{2.19}{0.1534} \approx 14.27 \]
Thus, the new price of the stock after the announcement is approximately $14.27.
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