To find the new price of the stock after Big Time Cell Phone Corporation announced the cut in dividends and the new growth rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model), which is given by the formula:
\[ P = \frac{D_1}{r - g} \]
where:
- \( P \) = price of the stock
- \( D_1 \) = the expected dividend next year
- \( r \) = required rate of return
- \( g \) = growth rate of dividends
Step 1: Identify the new \( D_1 \) (dividend next year)
From the announcement, the new dividend for year 1 \( D_1 \) is $2.15.
Step 2: Identify the new growth rate \( g \)
The new growth rate after the announcement is 3.85% or 0.0385 in decimal form.
Step 3: Determine the required rate of return \( r \)
To find \( r \), we can use the information from before the announcement. Before the announcement, dividends were expected to grow at 2.50%. First, we need to compute the required return using the old price and old growth.
Using the old price ($18.74) and old dividend ($3.10):
Using the Gordon Growth Model with the previous parameters:
\[ 18.74 = \frac{3.10}{r - 0.025} \]
Rearranging to find \( r \):
\[ r - 0.025 = \frac{3.10}{18.74} \]
Calculating \( \frac{3.10}{18.74} \):
\[ r - 0.025 = 0.1653 \quad (\text{approximately}) \]
Adding \( 0.025 \):
\[ r \approx 0.1653 + 0.025 = 0.1903 \quad (\text{approximately}) \]
So, the required rate of return \( r \) is approximately 19.03% or 0.1903 in decimal form.
Step 4: Calculate the new stock price \( P \)
Now, we can use the new dividend, the required return, and the new growth rate to find the new price of the stock:
\[ P = \frac{D_1}{r - g} = \frac{2.15}{0.1903 - 0.0385} \]
Calculating the denominator:
\[ r - g = 0.1903 - 0.0385 = 0.1518 \]
Now substituting back into the formula:
\[ P = \frac{2.15}{0.1518} \approx 14.17 \]
Thus, the new price of the stock after the announcement is approximately $14.17.
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