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?

1 answer

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%.