To calculate the value of a stock that pays dividends growing at a constant rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth). The formula for the stock price \( P_0 \) is:
\[ P_0 = \frac{D_1}{r - g} \]
Where:
- \( D_1 \) = Dividend expected next year
- \( r \) = Required rate of return
- \( g \) = Growth rate of the dividend
Step 1: Calculate \( D_1 \)
Given that the most recent dividend \( D_0 \) is $4.66 and it is expected to grow at a rate \( g \) of 3.69%, we can calculate \( D_1 \):
\[ D_1 = D_0 \times (1 + g) = 4.66 \times (1 + 0.0369) = 4.66 \times 1.0369 \approx 4.83 \]
Step 2: Substitute values into the Gordon Growth Model
Now we have:
- \( D_1 \approx 4.83 \)
- \( r = 10.09% = 0.1009 \)
- \( g = 3.69% = 0.0369 \)
Plugging in the values:
\[ P_0 = \frac{4.83}{0.1009 - 0.0369} \]
Calculating the denominator:
\[ 0.1009 - 0.0369 = 0.0640 \]
Now substituting back into the formula:
\[ P_0 = \frac{4.83}{0.0640} \approx 75.47 \]
Final Answer
Thus, the value of the stock is approximately $75.47.
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