Talon Corp. just paid a dividend of $1.50 per share. The dividends have been growing at 5% per year. If the required return is 12%, what was the price of the stock three years ago?
A) $15.84
B) $16.74
C) $17.64
D) $18.54
E) $19.44

Question

Quizplus · Accepted Answer

To find the price of the stock three years ago, we first calculate the present value of the dividends. The dividend just paid is $1.50, growing at 5% per year. The dividend next year (D1) will be $1.50 * (1 + 0.05) = $1.575. The price of the stock today (P0) can be calculated using the Gordon Growth Model: P0 = D1 / (r - g), where r is the required return (12% or 0.12) and g is the growth rate (5% or 0.05). So, P0 = $1.575 / (0.12 - 0.05) = $22.50. To find the price three years ago, we discount this price back three years using the required return of 12%. The price three years ago (P-3) = P0 / (1 + r)^3 = $22.50 / (1 + 0.12)^3 = $22.50 / 1.404928 = $16.01, which is not an option provided. However, the correct approach to find the price three years ago directly from the dividend three years before the current dividend would involve calculating the dividend three years ago and then applying the Gordon Growth Model formula. Given the mistake in the initial calculation, let's correctly calculate the price three years ago based on the dividend growth model, considering the dividend growth and the time frame correctly:First, find the dividend three years ago, which would be D0 / (1 + g)^3. However, since we started with the dividend that was just paid (D0), we need to adjust our approach to find the price directly three years ago based on the given information and the correct formula application.The correct calculation should involve adjusting the dividend back three years and then applying the Gordon Growth Model or correctly applying the formula based on the future value of the dividends and discounting it back to the present value three years ago. Given the error in the initial explanation and calculation, the correct answer should involve recalculating based on the dividend growth rate and the required return, properly applying the dividend discount model (DDM) for a growing dividend, which is P = D / (r - g). However, without recalculating based on the initial mistake, the correct process involves understanding the growth rate, the required return, and how they impact the stock price calculation over time, which was not accurately reflected in the initial response. The correct calculation directly from the dividend paid three years ago or correctly applying the growth rates and discounting back would lead to the correct answer, but the initial explanation failed to accurately calculate or provide the correct formula application for the scenario described.