Question

A stock will pay a dividend of $3.8 exactly one year from now. Future dividends will grow at a constant 2.6% every year thereafter. If the stock's required rate of return is 10.2%, what is a fair price for the stock today? Round your answer to the nearest penny.

Answer 1

Using the Gordon Growth Model, the fair price for a stock that will pay a $3.8 dividend in one year with dividends growing at 2.6% annually and a required return of 10.2% is calculated to be $50.

Step-by-step explanation:

To calculate the fair price of a stock today given that it will pay a dividend of $3.8 exactly one year from now and future dividends will grow at a constant rate of 2.6% every year thereafter, we utilize the Gordon Growth Model (also known as the Dividend Discount Model). This model takes into account the next dividend payment, the constant growth rate of dividends, and the required rate of return. The formula to determine the fair price of a stock is:

P = D1 / (k - g)

Where:

• P is the current stock price.
• D1 is the value of the next year’s dividend.
• k is the required rate of return.
• g is the growth rate of dividends.

By plugging in the values provided:

P = 3.8 / (0.102 - 0.026) = 3.8 / 0.076 = $50

Therefore, the fair price for the stock today, rounded to the nearest penny, would be $50.