This morning, you purchased a stock that will pay an annual dividend of $1.90 per share next year. You require a 12 percent rate of return and the annual dividend increases at 3.5 percent annually. What will your capital gain be on this stock if you sell it three years from now?

Question

This morning, you purchased a stock that will pay an annual dividend of $1.90 per share next year. You require a 12 percent rate of return and the annual dividend increases at 3.5 percent annually. What will your capital gain be on this stock if you sell it three years from now?

Answer 1

To calculate the capital gain on the stock when sold after three years, we need to find the future dividend payments and the future selling price.

First, let's find the future dividend payments using the given information. The dividend increases at a rate of 3.5 percent annually. So, the dividend next year will be $1.90 multiplied by (1 + 0.035), which is $1.9665 per share.

In the second year, the dividend will increase again by 3.5 percent. Thus, the dividend in the second year will be $1.9665 multiplied by (1 + 0.035), which is $2.033025 per share.

In the third year, the dividend will increase by 3.5 percent as well. So, the dividend in the third year will be $2.033025 multiplied by (1 + 0.035), which equals $2.10158 per share.

Next, we need to calculate the selling price of the stock after three years. The selling price can be determined using the price-earnings (P/E) ratio, which depends on the required rate of return.

The P/E ratio is the price per share divided by the earnings per share (EPS). In this case, the earnings per share would be the future dividend in the third year, which is $2.10158, so the P/E ratio can be calculated as:

P/E ratio = Price per share / Earnings per share

Given that the required rate of return is 12 percent, we can use this rate to estimate the P/E ratio. A commonly used approximation formula for the P/E ratio is:

P/E ratio = 1 / (rate of return - growth rate)

P/E ratio = 1 / (0.12 - 0.035)

Now, we can calculate the price per share after three years using the P/E ratio:

Price per share = Earnings per share * P/E ratio

Price per share = $2.10158 * P/E ratio

To find the capital gain, subtract the initial purchase price from the selling price. However, the initial purchase price is not provided in the question, so we cannot calculate the exact capital gain with the given information.

I have explained the process and calculations involved in finding the future dividend payments, the selling price, and the capital gain. To obtain the exact capital gain, we would need the initial purchase price or additional information.