Question

The market price of a stock is $30.00 and it is expected to pay a dividend of $2.50 next year. The required rate of return is 13.00%. What is the expected growth rate of the dividend?

Answer 1

To find the expected growth rate of the dividend (g), we can use the Gordon Growth Model (also known as the Dividend Discount Model), which states that the price of the stock (P) is equal to the next year's dividend (D1) divided by the difference between the required rate of return (r) and the growth rate (g):

\[
P = \frac{D_1}{r - g}
\]

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

Given:
- \( P = 30.00 \)
- \( D_1 = 2.50 \)
- \( r = 0.13 \)

We can rearrange the formula to solve for \( g \):

\[
g = r - \frac{D_1}{P}
\]

Substituting the values into the equation:

\[
g = 0.13 - \frac{2.50}{30.00}
\]

Calculating \( \frac{2.50}{30.00} \):

\[
\frac{2.50}{30.00} = 0.0833 \text{ (approximately)}
\]

Now substitute that value back into the equation for \( g \):

\[
g = 0.13 - 0.0833
\]

\[
g = 0.0467
\]

Converting to percentage:

\[
g \approx 4.67\%
\]

Thus, the expected growth rate of the dividend is approximately **4.67%**.