Question

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:

- \( P = 23.70 \)
- \( D_1 = 1.82 \)
- \( r = 11.41\% = 0.1141 \)

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%**.