Question

A stock currently pays no dividends. You expect it to pay its first dividend of $5.69 exactly 10 years from now. You also expect the stock to pay that same dividend every year thereafter. If the stock's required rate of return is 14.4%, what is a fair price for the stock foday? Round your answer to the nearest penny.

Answer 1

The fair price of a stock expected to pay a perpetual annual dividend of $5.69 starting in 10 years with a required rate of return of 14.4% is approximately $12.16 today.

Step-by-step explanation:

To calculate the fair price of a stock that will pay its first dividend 10 years from now at $5.69 per year, we should use the dividend discount model for perpetual dividends, also known as the Gordon Growth Model, since the stock is expected to pay the same dividend indefinitely after 10 years.

The formula for the present value of a perpetuity is Dividend / (Required Rate of Return). Since the dividends will start 10 years from now, the present value we find needs to be discounted back to today, which requires dividing by (1 + r)^t, where r is the required rate of return and t is the number of years until the first dividend payment.

Using the given information:

• Dividend (D): $5.69
• Required Rate of Return (r): 14.4%
• Years until first dividend (t): 10

The present value of the stock can be calculated as follows:

1. Calculate the perpetuity value in year 10: $5.69 / 0.144 = $39.51
2. Discount the perpetuity back to today's value: $39.51 / (1 + 0.144)^10
3. The fair price of the stock today is therefore approximately $12.16