To determine 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 calculates the price of a stock based on the expected future dividends that will 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 today
- \(D_1\) = dividend expected in the next year
- \(r\) = required rate of return
- \(g\) = growth rate of the dividend
Given:
- New dividend (\(D_1\)) = $2.20
- Expected growth rate after the announcement (\(g\)) = 3.65% = 0.0365
- Previous growth rate = 2.50% = 0.025 (not needed for the calculation after the announcement)
- Stock price before the announcement = $15.42 (not needed for the calculation after the announcement, but gives context)
To calculate the new stock price, we need to first estimate the required rate of return (\(r\)). We can use the previous stock price and dividend to work backwards to find the required rate of return before the announcement:
\[ 15.42 = \frac{3.02}{r - 0.025} \]
Now we can solve this equation for \(r\):
- Rearrange the equation: \[ 15.42(r - 0.025) = 3.02 \] \[ 15.42r - 15.42 \times 0.025 = 3.02 \] \[ 15.42r - 0.3855 = 3.02 \] \[ 15.42r = 3.02 + 0.3855 \] \[ 15.42r = 3.4055 \] \[ r = \frac{3.4055}{15.42} \] \[ r \approx 0.2201 \text{ or } 22.01% \]
Now that we have estimated \(r\) (in percentage terms) to be approximately 22.01%, we can use this to calculate the new stock price with the new dividend and new growth rate.
New Stock Price Calculation
Now, substituting the values into the Gordon Growth Model with \(D_1 = 2.20\), \(g = 0.0365\), and \(r = 0.2201\):
\[ P_0 = \frac{2.20}{0.2201 - 0.0365} \]
Calculate \(r - g\):
\[ r - g = 0.2201 - 0.0365 = 0.1836 \]
Now substitute back in for \(P_0\):
\[ P_0 = \frac{2.20}{0.1836} \] \[ P_0 \approx 11.99 \]
Thus, the new price of the stock after the announcement is approximately $11.99.
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