https://file.aiquickdraw.com/mathbot/file/1726734986818b7u9qjtu.jpg

This problem is asking to determine the expected growth rate of Rampart's dividends and its share price based on the information given. Let's break it down step by step:

### Given:
- **Dividend Yield (D/P)** = 1.6%
- **Equity Cost of Capital (r)** = 7.3%
- Dividends are expected to grow at a constant rate.

We can use the **Gordon Growth Model (or Dividend Discount Model)** for constant growth, which is expressed as:

\[
r = \frac{D_1}{P_0} + g
\]
Where:
- \(r\) = required rate of return (equity cost of capital) = 7.3%
- \(\frac{D_1}{P_0}\) = dividend yield = 1.6%
- \(g\) = growth rate of dividends (and share price)

### Part (a): What is the expected growth rate of Rampart’s dividends?

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

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

Substitute the values:

\[
g = 7.3\% - 1.6\% = 5.7\%
\]

So, the expected growth rate of Rampart's dividends is **5.7%**.

### Part (b): What is the expected growth rate of Rampart’s share price?

Since the dividends are expected to grow at a constant rate, the share price should also grow at the same rate. Therefore, the expected growth rate of the share price is **also 5.7%**.

### Answer:
- For part (a), the growth rate will be **5.7%**.
- For part (b), the correct choice is **Option B**: "With constant dividend growth, share price is also expected to grow at rate \(g = 5.7\%\)."

Would you like any further details or have any additional questions?

Here are 5 related questions to consider:
1. How does the dividend growth model change if dividends grow at a variable rate?
2. What would happen if the dividend yield was higher than the equity cost of capital?
3. How do we determine the present value of a stock using the Gordon Growth Model?
4. What factors could influence the equity cost of capital?
5. How do changes in interest rates affect the growth rate of share prices?

**Tip**: In the Dividend Discount Model, if the growth rate \(g\) is greater than the equity cost of capital \(r\), the formula no longer works because it implies infinite stock value.

Rampart Corporation has a dividend yield of 1.6%. Its equity cost of capital is 7.3%, and its dividends are expected to grow at a constant rate. What is the expected growth rate of Rampart's dividends and share price?

Learn how to calculate the growth rate of dividends and share price for Rampart Corporation using the Gordon Growth Model. With a dividend yield of 1.6% and an equity cost of capital of 7.3%, determine the expected growth rate of both dividends and share price.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation