The Felix Corp.will pay an annual dividend of $1.00 next year.The dividend will increase by 12 percent a year for the following two years before growing at 4 percent indefinitely thereafter.If the required rate of return is 10 percent,what is the stock's current value?
A)$13.38
B)$14.05
C)$19.11
D)$9.80
E)$10.38

Question

Quizplus · Accepted Answer

The stock's current value can be calculated using the dividend discount model for a stock with changing growth rates. First, calculate the dividends for the first three years and then calculate the present value of the stock at the beginning of the third year, which will then grow indefinitely at 4%.1. Dividend in Year 1 (D1) = $1.002. Dividend in Year 2 (D2) = D1 * (1 + 12%) = $1.00 * 1.12 = $1.123. Dividend in Year 3 (D3) = D2 * (1 + 12%) = $1.12 * 1.12 = $1.25444. Dividend in Year 4 (D4) = D3 * (1 + 4%) = $1.2544 * 1.04 = $1.3046The value of the stock at the beginning of Year 3, considering the dividends will grow at 4% indefinitely from Year 4 onwards, can be calculated using the Gordon Growth Model (also known as the Dividend Growth Model for a perpetuity):$$ P_3 = \frac{D4}{r - g} = \frac{1.3046}{0.10 - 0.04} = \frac{1.3046}{0.06} = 21.7433 $$Now, discount P3 and the dividends received in Years 1, 2, and 3 back to the present value:$$ PV = \frac{1.00}{(1+0.10)^1} + \frac{1.12}{(1+0.10)^2} + \frac{1.2544 + 21.7433}{(1+0.10)^3} $$$$ PV = \frac{1.00}{1.10} + \frac{1.12}{1.21} + \frac{22.9977}{1.331} $$$$ PV = 0.9091 + 0.9256 + 17.2763 $$$$ PV = 19.111 $$Therefore, the current value of the stock is approximately $19.11.