Question

What is the value of a stock expected to be in 12 years if the dividend is expected to remain unchanged forever at $1.09 per quarter, the expected rate of return is 14.89% per year, and the next dividend is expected in one quarter?(Round the value to 100th decimal)

Answer 1

The value of a stock with a constant dividend of $1.09 per quarter and an expected rate of return of 14.89% is calculated using the Perpetuity formula and is approximately $29.28.

Step-by-step explanation:

To calculate the value of a stock that pays a constant dividend, we can use the dividend discount model, specifically the Perpetuity formula, since the dividend is expected to remain unchanged forever. This model assumes that the stock price is equal to the dividend per period divided by the required rate of return minus the growth rate. In this case, the growth rate of dividends is zero because the dividend is constant. Given that the dividend is $1.09 per quarter, the annual dividend is $1.09 × 4 = $4.36. The expected rate of return is 14.89% per year, or 0.1489 in decimal form.

Using the formula, the value of the stock is:

Stock Value = Dividend per share / Required rate of return = $4.36 / 0.1489 = $29.28.

Therefore, the expected stock value in 12 years, assuming a constant dividend and required rate of return, is approximately $29.28.