A firm will pay a dividend of $2.29 next year. The dividend is expected to grow at a constant rate of 3.98% forever and the required rate of return is 13.74%. What is the value of the stock?

Answer 1

To find the value of the stock based on the dividend discount model (DDM), specifically the Gordon Growth Model (also known as the Dividend Discount Model), we use the following formula:

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

Where:

• \( P_0 \) = price of the stock today
• \( D_1 \) = the dividend to be paid next year ($2.29)
• \( r \) = required rate of return (13.74% or 0.1374)
• \( g \) = growth rate of the dividend (3.98% or 0.0398)

Substituting the given values into the formula:

\[ P_0 = \frac{2.29}{0.1374 - 0.0398} \]

First, we calculate the denominator:

\[ 0.1374 - 0.0398 = 0.0976 \]

Now, substitute this value back into the formula:

\[ P_0 = \frac{2.29}{0.0976} \approx 23.43 \]

Therefore, the value of the stock is approximately $23.43.