WG Inc. just paid a dividend of $6.10 per share. The dividend is expected to grow at a constant rate forever. The company has a dividend policy of paying out 48% of its earnings every year. The ROE (return on equity) of reinvestments is 11.30%. The required rate of return is 10.70%. What is the current stock price?

Question 4

Answer

a.

$133.88

b.

$70.25

c.

$105.38

d.

$126.45

e.

$160.66


To find the current stock price, we can use the **Gordon Growth Model** (also known as the Dividend Discount Model for a constantly growing dividend), which is given by:

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

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.

### Step 1: Calculate the dividend growth rate (g)
The growth rate of dividends ($g$) can be calculated using the formula:

\[
g = ROE \times \text{Retention Ratio}
\]

The retention ratio is the portion of earnings that is not paid out as dividends, so:

\[
\text{Retention Ratio} = 1 - \text{Payout Ratio}
\]

Given that the payout ratio is 48%, the retention ratio is:

\[
\text{Retention Ratio} = 1 - 0.48 = 0.52
\]

Now calculate $g$:

\[
g = 0.113 \times 0.52 = 0.05876 \quad \text{(or 5.876% growth rate)}
\]

### Step 2: Calculate $D_1$ (Next year's dividend)
The dividend just paid (i.e., $D_0$) is $6.10. The dividend for next year ($D_1$) will be:

\[
D_1 = D_0 \times (1 + g) = 6.10 \times (1 + 0.05876) = 6.10 \times 1.05876 = 6.46
\]

### Step 3: Calculate the stock price using the Gordon Growth Model

Now, plug in the values into the formula for the current stock price:

\[
P_0 = \frac{6.46}{0.107 - 0.05876} = \frac{6.46}{0.04824} = 133.88
\]

So, the current stock price is **$133.88**.

### Answer: 
**(a) $133.88**

Would you like more details or have any questions?

Here are five related questions:
1. How does the retention ratio affect the dividend growth rate?
2. What happens to the stock price if the required rate of return increases?
3. How would the stock price change if the payout ratio was 60% instead of 48%?
4. Why do we use the Gordon Growth Model for valuing stocks with constant dividend growth?
5. How is the required rate of return determined for a stock?

**Tip:** The Gordon Growth Model is only valid if the required rate of return is higher than the dividend growth rate.

WG Inc. just paid a dividend of $6.10 per share. The dividend is expected to grow at a constant rate forever. The company has a dividend policy of paying out 48% of its earnings every year. The ROE (return on equity) of reinvestments is 11.30%. The required rate of return is 10.70%. What is the current stock price?

Learn to calculate the current stock price of WG Inc. using the Gordon Growth Model, given a dividend of $6.10, a payout ratio of 48%, an ROE of 11.3%, and a required rate of return of 10.7%. This example demonstrates the Dividend Discount Model and the calculation of dividend growth rate, suitable for finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation