A security is expected to pay a dividend of $1.50 in one year.  This dividend is expected to increase at an annual rate of 3% forever.  If the required return is 15%, what is a fair value of this security today?




Group of answer choices

$12.50

$14.38

$10.00

$12.88

$50.00

To find the fair value of the security today, we can use the Gordon Growth Model (or Dividend Discount Model), which is commonly used for valuing a stock that pays dividends that grow at a constant rate. The formula for this model is:

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

Where:

- $ P_0 $ = Present value or fair price of the stock today
- $ D_1 $ = Dividend expected in one year
- $ r $ = Required rate of return
- $ g $ = Growth rate of the dividend

Given values:

- $ D_1 = 1.50 $
- $ r = 0.15 $ (15%)
- $ g = 0.03 $ (3%)

Substituting these values into the formula:

\[
P_0 = \frac{1.50}{0.15 - 0.03}
\]

Let's calculate the fair value.The fair value of the security today is **$12.50**.

**Correct answer: $12.50**

Would you like more details or have any questions? Here are some related questions to consider:

1. How does the required rate of return affect the valuation of a stock?
2. What happens to the stock price if the growth rate of the dividend increases?
3. How does the Gordon Growth Model differ from other stock valuation methods?
4. What would the fair value be if the required return were 18% instead of 15%?
5. How would a non-constant dividend growth rate affect the valuation?

**Tip:** The Gordon Growth Model is most accurate for stocks with stable and predictable dividend growth rates.

A security is expected to pay a dividend of $1.50 in one year. This dividend is expected to increase at an annual rate of 3% forever. If the required return is 15%, what is a fair value of this security today? Group of answer choices: $12.50, $14.38, $10.00, $12.88, $50.00

Learn how to calculate the fair value of a dividend-paying security expected to pay $1.50 next year, with a 3% annual dividend growth rate and a 15% required return. This step-by-step solution uses the Gordon Growth Model, perfect for finance students at the college level.

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