To calculate the required rate of return for the stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth). The model formula is:
\[ P = \frac{D_1}{r - g} \]
where:
- \( P \) = price of the stock ($57.80)
- \( D_1 \) = the next year's dividend
- \( r \) = required rate of return
- \( g \) = growth rate of the dividend (3.44% or 0.0344)
Since we know the most recent dividend (\( D_0 \)) is $5.26, we can calculate next year's dividend (\( D_1 \)) as follows:
\[ D_1 = D_0 \times (1 + g) = 5.26 \times (1 + 0.0344) = 5.26 \times 1.0344 \approx 5.45 \]
Now we can substitute the known values into the Gordon Growth Model equation to find \( r \):
\[ 57.80 = \frac{5.45}{r - 0.0344} \]
We can rearrange this equation to isolate \( r \):
\[ 57.80(r - 0.0344) = 5.45 \]
Expanding the left side:
\[ 57.80r - 1.98932 = 5.45 \]
Now, add \( 1.98932 \) to both sides:
\[ 57.80r = 5.45 + 1.98932 \]
\[ 57.80r = 7.43932 \]
Now, divide both sides by \( 57.80 \):
\[ r \approx \frac{7.43932}{57.80} \approx 0.12854 \]
Finally, convert the decimal to a percentage:
\[ r \approx 0.12854 \times 100 \approx 12.85% \]
Thus, the required rate of return for the stock is approximately 12.85%.
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