Final answer:
Using the Gordon Growth Model and the given market price of $22.49, an expected dividend of $1.69, and a required rate of return of 11.56%, the expected growth rate of the dividend is calculated to be 4.05%.
Step-by-step explanation:
To calculate the expected growth rate of the dividend for a stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model). This model expresses the price of a stock (P0) as the present value of all future dividends that are expected to grow at a constant rate (g). The formula for this model is P0 = D1 / (r - g), where P0 is the current stock price, D1 is the expected dividend next year, r is the required rate of return, and g is the expected growth rate.
In this scenario, the market price of the stock is $22.49, expected to pay a dividend of $1.69 next year, and the required rate of return is 11.56%. By rearranging the formula to solve for the growth rate, we get g = r - (D1 / P0). Substituting the given values, we find the expected growth rate, g:
g = 0.1156 - (1.69 / 22.49)
After performing the calculations:
g = 0.1156 - 0.0751
g = 0.0405 or 4.05%
The expected growth rate of the dividend for the stock is therefore 4.05%.