You have 1 share of stock A and 1 share of stock B. The total value of the two holdings is $388.51. Stock A is expected to pay annual dividends forever. The first dividend for stock A is expected to be $11.77 and all subsequent dividends are expected to increase by 2.84 percent per year forever. The expected return for stock A is 6.66 percent per year and the first dividend will be paid in 1 year. Stock B is expected to pay annual dividends forever. The first dividend for stock B is expected to be $6.11 and all subsequent dividends are expected to increase by X percent per year forever. The expected return for stock B is 10.95 percent per year and the first dividend will be paid in 1 year. What is X?



To find the dividend growth rate $ X $ for stock B, we will use the Gordon Growth Model (Dividend Discount Model) to value both stocks. This model expresses the price of a stock as:

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

where:
- $ P $ is the price of the stock,
- $ D_1 $ is the first dividend to be paid in 1 year,
- $ r $ is the expected return (discount rate),
- $ g $ is the dividend growth rate.

### Step 1: Solve for the price of Stock A using the given information.
For Stock A:
- $ D_1 = 11.77 $,
- $ r = 6.66\% = 0.0666 $,
- $ g = 2.84\% = 0.0284 $.

Applying the formula for Stock A:

\[
P_A = \frac{11.77}{0.0666 - 0.0284} = \frac{11.77}{0.0382} = 308.11
\]

So, the price of Stock A is approximately $308.11.

### Step 2: Solve for the price of Stock B.
Let $ P_B $ represent the price of Stock B. Since the total value of the two stocks is $388.51, we know:

\[
P_A + P_B = 388.51
\]

Thus:

\[
308.11 + P_B = 388.51
\]

\[
P_B = 388.51 - 308.11 = 80.40
\]

The price of Stock B is $80.40.

### Step 3: Solve for the dividend growth rate $ X $ for Stock B.
For Stock B:
- $ D_1 = 6.11 $,
- $ P_B = 80.40 $,
- $ r = 10.95\% = 0.1095 $,
- $ g = X $ (the growth rate we are solving for).

Using the formula for Stock B:

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

Substitute the known values:

\[
80.40 = \frac{6.11}{0.1095 - g}
\]

Solving for $ g $:

\[
80.40 (0.1095 - g) = 6.11
\]

\[
8.804 - 80.40g = 6.11
\]

\[
80.40g = 8.804 - 6.11 = 2.694
\]

\[
g = \frac{2.694}{80.40} \approx 0.0335
\]

Thus, $ g = 3.35\% $.

### Final Answer:
The dividend growth rate $ X $ for Stock B is approximately **3.35%**.

Would you like any further details or have any questions?

Here are 5 related questions to consider:
1. How does the expected return affect the price of a stock?
2. What is the significance of perpetual dividends in stock valuation?
3. How would the stock price change if the dividend growth rate increased?
4. What are the limitations of the Gordon Growth Model in stock valuation?
5. How does risk influence the expected return of a stock?

**Tip**: The Gordon Growth Model assumes a constant growth rate for dividends. In reality, growth rates may fluctuate due to market conditions.

You have 1 share of stock A and 1 share of stock B. The total value of the two holdings is $388.51. Stock A is expected to pay annual dividends forever. The first dividend for stock A is expected to be $11.77 and all subsequent dividends are expected to increase by 2.84 percent per year forever. The expected return for stock A is 6.66 percent per year and the first dividend will be paid in 1 year. Stock B is expected to pay annual dividends forever. The first dividend for stock B is expected to be $6.11 and all subsequent dividends are expected to increase by X percent per year forever. The expected return for stock B is 10.95 percent per year and the first dividend will be paid in 1 year. What is X?

Discover how to calculate the dividend growth rate X for Stock B when given the values and returns for Stocks A and B. This example uses the Gordon Growth Model and provides a detailed breakdown of each calculation step. Total value of the holdings is $388.51.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation