Question

The market price of a stock is $23.86 and it is expected to pay a dividend of $1.31 next year. The required rate of return is 11.56%. What is the expected growth rate of the dividend?

Answer 1

To calculate the expected growth rate of the dividend (g), we can use the Gordon Growth Model (Dividend Discount Model), which describes the relationship between the price of a stock, its dividend, the required rate of return, and the growth rate of the dividend. The formula is:

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

Where:
- \( P \) = Price of the stock ($23.86)
- \( D_1 \) = Expected dividend next year ($1.31)
- \( r \) = Required rate of return (11.56% or 0.1156)
- \( g \) = Growth rate of the dividend

Rearranging the formula to solve for \( g \):

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

Substituting in the given values:

\[
g = 0.1156 - \frac{1.31}{23.86}
\]

Calculating \( \frac{1.31}{23.86} \):

\[
\frac{1.31}{23.86} \approx 0.0549
\]

Now substituting back into the growth rate equation:

\[
g = 0.1156 - 0.0549
\]
\[
g \approx 0.0607
\]

Converting to a percentage:

\[
g \approx 6.07\%
\]

Thus, the expected growth rate of the dividend is approximately **6.07%**.