Question

The market price of a stock is $24.91 and it just paid a dividend of $1.89. The required rate of return is 11.60%. 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 model can be expressed as:

\[
P_0 = \frac{D_1}{r - g}
\]

Where:
- \( P_0 \) is the current stock price
- \( D_1 \) is the dividend expected next year
- \( r \) is the required rate of return
- \( g \) is the growth rate of the dividend

Given the information:
- Current stock price \( P_0 = 24.91 \)
- The most recent dividend \( D_0 = 1.89 \)
- Required rate of return \( r = 0.1160 \) (or 11.60%)

First, we need to determine \( D_1 \), the expected dividend for next year. Since \( D_1 \) can be found as:

\[
D_1 = D_0 \times (1 + g)
\]

We can substitute \( D_1 \) into the Gordon Growth Model equation:

\[
P_0 = \frac{D_0 \times (1 + g)}{r - g}
\]

Rearranging this equation to solve for \( g \) gives:

\[
P_0 (r - g) = D_0 \times (1 + g)
\]

Expanding and rearranging:

\[
P_0 \cdot r - P_0 \cdot g = D_0 + D_0 \cdot g
\]

\[
P_0 \cdot r - D_0 = P_0 \cdot g + D_0 \cdot g
\]

\[
P_0 \cdot r - D_0 = g (P_0 + D_0)
\]

Thus, we can solve for \( g \):

\[
g = \frac{P_0 \cdot r - D_0}{P_0 + D_0}
\]

Now substituting the known values:

\[
g = \frac{24.91 \cdot 0.1160 - 1.89}{24.91 + 1.89}
\]

Calculating the numerator:

\[
24.91 \cdot 0.1160 = 2.89276
\]

Now substituting this value into the formula:

\[
g = \frac{2.89276 - 1.89}{24.91 + 1.89}
\]

Calculating the numerator:

\[
2.89276 - 1.89 = 1.00276
\]

Calculating the denominator:

\[
24.91 + 1.89 = 26.8
\]

Now substituting the numerator and denominator:

\[
g = \frac{1.00276}{26.8} \approx 0.0374
\]

Expressing this as a percentage:

\[
g \approx 0.0374 \cdot 100 = 3.74\%
\]

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