Question

The market price of a stock is $21.80 and it just paid a dividend of $1.86. The required rate of return is 11.25%. 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 for a stock with constant growth), which is given by the formula:

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

Where:
- \( P_0 \) = Current stock price
- \( D_1 \) = Dividend in the next period
- \( r \) = Required rate of return
- \( g \) = Growth rate of the dividend

We know the following:
- \( P_0 = 21.80 \)
- \( D_0 = 1.86 \) (this is the dividend just paid)
- \( r = 0.1125 \) (11.25%)

First, we need to calculate \( D_1 \), which is the expected dividend next year. Since we are looking for growth \( g \), we can express \( D_1 \) in terms of the current dividend (\( D_0 \)) and the growth rate (\( g \)):

\[
D_1 = D_0 \cdot (1 + g) = 1.86 \cdot (1 + g)
\]

Substituting \( D_1 \) back into the Gordon Growth Model equation:

\[
21.80 = \frac{1.86 \cdot (1 + g)}{0.1125 - g}
\]

To solve for \( g \), we can rearrange and simplify the equation. Multiply both sides by \( 0.1125 - g \):

\[
21.80(0.1125 - g) = 1.86(1 + g)
\]

Expanding both sides gives:

\[
2.44875 - 21.80g = 1.86 + 1.86g
\]

Now, combine the terms involving \( g \):

\[
2.44875 - 1.86 = 21.80g + 1.86g
\]

\[
0.58875 = 23.66g
\]

Now, solve for \( g \):

\[
g = \frac{0.58875}{23.66} \approx 0.02487
\]

Converting this to a percentage:

\[
g \approx 0.02487 \times 100 \approx 2.487\%
\]

Thus, the expected growth rate of the dividend is approximately **2.49%**.

Answer 2

Thank you. I would never figure out how to do it without your showing steps.

Answer 3

You're very welcome! I'm glad you found the explanation helpful. Understanding the steps in financial calculations can make a big difference in grasping the concepts. If you have any more questions about finance, investment, or any other topic, feel free to ask!