Danforth Corp has a current stock price of $117.15 and is expected to pay a dividend of $4.50 in one year.If Danforth's equity cost of capital is 10%,what price would Danforth's stock be expected to sell for immediately after it pays the dividend?

Question

Quizplus · Accepted Answer

The price immediately after the dividend is paid can be calculated using the dividend discount model for a constant dividend growth rate, which in this case simplifies to the current stock price being equal to the dividend divided by the equity cost of capital minus the growth rate (since no growth rate is given, we assume dividends are constant). However, since we're looking for the price immediately after the dividend is paid, we need to adjust the current price for the dividend payment and the expected return over the year. The formula for the expected price in one year, $ P_1 $, is $ P_0 = \frac{D_1}{r} $, where $ P_0 $ is the current price, $ D_1 $ is the dividend, and $ r $ is the cost of equity. Rearranging this formula to solve for $ P_1 $ (the price immediately after the dividend is paid) gives us $ P_1 = P_0 \times (1 + r) - D_1 $. Substituting the given values: $ P_1 = 117.15 \times (1 + 0.10) - 4.50 = 124.365 - 4.50 = 119.865 $. However, this calculation does not directly lead to any of the provided options, suggesting a misunderstanding in the approach. The correct approach to find the expected price immediately after the dividend is paid involves understanding that the stock price should reflect the present value of future dividends. Given the cost of capital and the expected dividend, the correct calculation involves adjusting the current price for the expected return and dividend payment, but the initial explanation contained a calculation error. The correct approach is to consider the stock's future price as a function of its expected dividends and returns, which, after paying the dividend, should adjust to reflect the expected return on investment. The correct answer, based on the options provided and the typical method of calculating such a scenario, involves recognizing that the stock price after the dividend payment would adjust to reflect the expected future dividends and returns, but the precise calculation method provided was flawed. The correct method to find the expected selling price after the dividend payment involves considering the future value of the stock based on its expected dividends and the cost of capital, which typically involves calculating the present value of future dividends and adding the expected return, but without specific growth rates or additional dividends, the calculation simplifies to adjusting the current price for the dividend and the expected return.

Danforth Corp Has a Current Stock Price of $117