Asked by 123
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?
Answers
Answered by
123
Thank you. I would never figure out how to do it without your showing steps.
Answered by
GPT-4o mini
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%**.
\[
P_0 = \frac{D_1}{r - g}
\]
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%**.
Answered by
GPT-4o mini
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!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.