The price of a stock is currently $750 and the stock will pay a $43 dividend. The interest rate is 7.5%. Based on the dividend-discount model, what is the expected price of this stock for next year?

Question

Quizplus · Accepted Answer

The expected price of the stock for next year can be calculated using the dividend-discount model formula: $ P_0 = \frac{D_1}{r-g} $, where $P_0$ is the current stock price, $D_1$ is the dividend next year, $r$ is the required rate of return (interest rate in this case), and $g$ is the growth rate of the dividend, which is assumed to be 0 here since no growth rate is provided. However, to find the expected price next year, we adjust the formula to account for the received dividend and the unchanged expected return: $ P_1 = P_0 + D - P_0 \times r $. Substituting the given values: $ P_1 = 750 + 43 - 750 \times 0.075 = 793 - 56.25 = 736.75 $. This result does not match any of the provided options directly, indicating a need to revisit the calculation or the interpretation of the model. The correct approach is to consider the price one year from now, which should include the dividend received and the expected price appreciation. The correct formula reflecting the expected price next year actually simplifies to considering the dividend received and the expected growth in price due to the interest rate, which is a misunderstanding in the initial explanation. The correct calculation should be based on the formula for the expected price next year considering the dividend received and the capital gain, which is $ P_1 = \frac{D + P_0}{1 + r} $. However, this approach also seems to misinterpret the application of the dividend-discount model for predicting future stock prices directly. The correct application involves understanding that the price next year would inherently account for the next period's dividend and growth expectations, which in a zero-growth model simplifies to $ P_1 = \frac{D}{r} $ added to the current price adjusted for the dividend paid out and interest effects. Given the confusion and the incorrect application of formulas, the correct answer relies on understanding that the dividend-discount model with a zero growth assumption essentially values the stock based on its dividend yield and the required rate of return, and the expected price next year would be the current price adjusted for the dividend payout and the required return, which is not directly calculated through the provided formulas. The correct answer, therefore, involves recognizing the mistake in the calculation process and identifying that none of the provided options directly match the expected outcome based on a correct application of the dividend-discount model principles for a zero-growth scenario.

The Price of a Stock Is Currently $750 and the Stock