Choc Hut, Inc. normally pays a annual dividend. The last such dividend paid was $1.50, all future annual dividends are expected to grow at 6 percent, and the firm faces a required rate of return on equity of 18 percent. If the firm just announced that the next dividend will be an extraordinary dividend of $5.00 per share that is not expected to affect any other future dividends, what should the stock price be?

Question

Quizplus · Accepted Answer

The stock price can be calculated using the dividend discount model (DDM) for a growing dividend, adjusted for the extraordinary dividend. The formula for the price of a stock with growing dividends is P0 = D1 / (r - g), where D1 is the dividend next year, r is the required rate of return, and g is the growth rate. The extraordinary dividend requires an adjustment.First, calculate the normal dividend for next year, which would be $1.50 * (1 + 0.06) = $1.59. Then, apply the DDM formula: P0 = $1.59 / (0.18 - 0.06) = $1.59 / 0.12 = $13.25.However, this does not include the extraordinary dividend. The total value of the stock should include the present value of the extraordinary dividend plus the present value of all future dividends. Since the extraordinary dividend of $5.00 does not affect future dividends and is paid immediately, it does not need to be discounted. Therefore, the total stock price should be the sum of the extraordinary dividend and the present value of future dividends: $5.00 + $13.25 = $18.25.It seems there was a mistake in my explanation regarding the final calculation. Let's correct that:Given the extraordinary dividend does not affect the calculation of the normal dividend growth model directly, the correct approach is to calculate the present value of the normal dividends moving forward and then add the extraordinary dividend since it's a one-time payment.The correct calculation for the stock price using the dividend growth model, considering the normal growth of dividends, is as follows:$$ P_0 = \frac{D_0 \times (1 + g)}{r - g} $$Where $D_0$ is the last dividend paid ($1.50), $g$ is the growth rate (6% or 0.06), and $r$ is the required rate of return (18% or 0.18). Plugging in the numbers:$$ P_0 = \frac{1.50 \times (1 + 0.06)}{0.18 - 0.06} = \frac{1.59}{0.12} = 13.25 $$This calculation gives us the present value of all future normal dividends. Since the extraordinary dividend of $5.00 is a one-time event and does not affect the calculation of future dividends, it should not be added to the stock price derived from the dividend growth model. Therefore, the correct answer to the stock price, considering the growth of dividends and the required rate of return, is $13.25, which corresponds to option C. My previous explanation mistakenly suggested adding the extraordinary dividend to this calculation, which was incorrect.