To determine 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 formula is given by:
\[ P = \frac{D_0 \times (1 + g)}{r - g} \]
Where:
- \( P \) = current stock price
- \( D_0 \) = dividend just paid
- \( g \) = growth rate of the dividend
- \( r \) = required rate of return
We need to rearrange this formula to solve for \( r \):
\[ r = \frac{D_0 \times (1 + g)}{P} + g \]
Substituting the values we have:
- \( P = 56.63 \) (market price of the stock)
- \( D_0 = 5.68 \) (dividend just paid)
- \( g = 0.0285 \) (growth rate of 2.85%)
Now, let's calculate \( D_0 \times (1 + g) \):
\[ D_0 \times (1 + g) = 5.68 \times (1 + 0.0285) = 5.68 \times 1.0285 \approx 5.84 \]
Next, we can plug everything back into the rearranged equation for \( r \):
\[ r = \frac{5.84}{56.63} + 0.0285 \]
Calculating \( \frac{5.84}{56.63} \):
\[ \frac{5.84}{56.63} \approx 0.1037 \]
Now, adding the growth rate:
\[ r \approx 0.1037 + 0.0285 \approx 0.1322 \]
To express this as a percentage:
\[ r \approx 0.1322 \times 100 \approx 13.22% \]
Thus, the required rate of return for the stock is approximately 13.22%.
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