To find the value of a stock that pays dividends growing at a constant rate, you can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:
\[ P = \frac{D_1}{r - g} \]
Where:
- \( P \) = Price of the stock
- \( D_1 \) = Dividend in the next period
- \( r \) = Required rate of return
- \( g \) = Growth rate of the dividend
Given that the firm just paid a dividend (\( D_0 \)) of $3.34 and that it is expected to grow at a constant rate of 3.30% forever, we first need to find \( D_1 \):
\[ D_1 = D_0 \times (1 + g) = 3.34 \times (1 + 0.033) = 3.34 \times 1.033 = 3.45 \]
Now we can use the required rate of return (\( r = 12.24% = 0.1224 \)) and the growth rate (\( g = 3.30% = 0.033 \)) to find the stock price (\( P \)):
\[ P = \frac{D_1}{r - g} = \frac{3.45}{0.1224 - 0.033} = \frac{3.45}{0.0894} \]
Calculating the denominator:
\[ 0.1224 - 0.033 = 0.0894 \]
Now calculating the final stock price:
\[ P \approx \frac{3.45}{0.0894} \approx 38.63 \]
So, the value of the stock is approximately $38.63.