The market price of a stock is $23.70 and it is expected to pay a dividend of $1.82 next year. The required rate of return is 11.41%. What is the expected growth rate of the dividend?

Answer 1

To find the expected growth rate of the dividend, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is given by:

$$P=\frac{D_1}{r-g}$$

Where:

• $P$ is the price of the stock,
• $D_1$ is the expected dividend next year,
• $r$ is the required rate of return,
• $g$ is the growth rate of the dividend.

Plugging in the values we have:

• $P=23.70$
• $D_1=1.82$
• $r=11.41$

Rearranging the formula to solve for $g$:

$$g=r-\frac{D_1}{P}$$

Now we can substitute the values into the equation:

$$g=0.1141-\frac{1.82}{23.70}$$

Calculating $\frac{1.82}{23.70}$:

$$\frac{1.82}{23.70}\approx 0.0767$$

Now substituting this value back into the equation for $g$:

$$g=0.1141-0.0767\approx 0.0374$$

To express $g$ as a percentage, we multiply by 100:

$$g\approx 3.74$$

Thus, the expected growth rate of the dividend is approximately 3.74%.