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), which estimates the price of a stock based on its expected dividends and growth rate. The formula is given by:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( P_0 \) = current price of the stock
- \( D_1 \) = dividend in the next year
- \( r \) = required rate of return
- \( g \) = growth rate of dividends
First, we need to find the new expected dividend \( D_1 \) and the required rate of return \( r \).
Step 1: Determine \( D_1 \)
The new dividend \( D_1 \) for Year 1 is already provided as \( 2.04 \).
Step 2: Determine the required rate of return \( r \)
To find \( r \), we can use the old growth rate and price information. Before the announcement, the expected growth rate was 2.50%, and the price was $17.79 with a dividend of $3.06.
Using the Gordon Growth Model before the announcement, we can set up the equation: \[ 17.79 = \frac{3.06}{r - 0.025} \]
Rearranging to find \( r \): \[ r - 0.025 = \frac{3.06}{17.79} \] \[ r - 0.025 = 0.171 \] \[ r = 0.171 + 0.025 = 0.196 \text{ or } 19.6% \]
Step 3: Calculate the new price after the growth rate changes to 3.97%
Now that we know \( D_1 = 2.04 \) and \( r = 0.196 \) and that the new growth rate \( g = 0.0397 \) (or 3.97%), we can calculate the new price \( P_0 \):
Substituting into the Gordon Growth Model: \[ P_0 = \frac{2.04}{0.196 - 0.0397} \] \[ P_0 = \frac{2.04}{0.1563} \] \[ P_0 \approx 13.06 \]
Conclusion
The new price of the stock after the announcement is approximately $13.06.
3 answers