AC Electric just paid its annual dividend of $2.42. The firm plans to increase its dividend by 2.5 percent for the next 3 years and then maintain a constant 2 percent rate of dividend growth. The required return is 12.5 percent. What is the current value per share of this stock?

Question

Quizplus · Accepted Answer

To find the current value per share of the stock, we use the dividend discount model for a stock with a changing growth rate. First, calculate the dividends for the next three years, then calculate the present value of these dividends and the present value of the stock price at the end of year 3, discounted back to the present.1. Calculate future dividends:- Year 1: $2.42 * (1 + 2.5%) = $2.4805- Year 2: $2.4805 * (1 + 2.5%) = $2.5425- Year 3: $2.5425 * (1 + 2.5%) = $2.60612. Calculate the stock price at the end of year 3 using the Gordon Growth Model, assuming dividends grow at a constant 2% after year 3:$$ P_3 = \frac{D_4}{r - g} = \frac{2.6061 \times (1 + 2\%)}{0.125 - 0.02} = \frac{2.6582}{0.105} = 25.3162 $$3. Calculate the present value of the dividends and the stock price at the end of year 3:$$ PV = \frac{2.4805}{(1 + 0.125)} + \frac{2.5425}{(1 + 0.125)^2} + \frac{2.6061 + 25.3162}{(1 + 0.125)^3} $$$$ PV = \frac{2.4805}{1.125} + \frac{2.5425}{1.2656} + \frac{27.9223}{1.4227} $$$$ PV = 2.2044 + 2.0081 + 19.6237 = 23.8362 $$Rounding to two decimal places, the current value per share of the stock is approximately $23.82.

AC Electric Just Paid Its Annual Dividend of $2