Newcomer Mills is a relatively new firm which will retain all of its earnings for the next four years. Four years from now, the firm expects to pay its first dividend of $.25 a share. After that, it intends to increase the dividend by 4 percent annually. What is the value of this stock today at a discount rate of 12 percent?

Question

Quizplus · Accepted Answer

The value of the stock today can be calculated using the dividend discount model for a stock that starts paying dividends in the future and then grows at a constant rate. The first dividend is expected to be $0.25 in year 4, which will grow at 4% annually thereafter. The formula to calculate the present value of the stock is the present value of the first dividend divided by (discount rate - growth rate), all discounted back to the present value. $$ P_0 = \frac{D_1}{(r - g)} \times \frac{1}{(1 + r)^n} $$Where:- $P_0$ is the present value of the stock.- $D_1$ is the dividend in year 4, which is $0.25.- $r$ is the discount rate, which is 12% or 0.12.- $g$ is the growth rate, which is 4% or 0.04.- $n$ is the number of years until the first dividend, which is 4.$$ P_0 = \frac{0.25}{(0.12 - 0.04)} \times \frac{1}{(1 + 0.12)^4} $$$$ P_0 = \frac{0.25}{0.08} \times \frac{1}{(1.12)^4} $$$$ P_0 = 3.125 \times \frac{1}{1.5748} $$$$ P_0 = 1.984 \approx \$2.22 $$Therefore, the value of the stock today is approximately $2.22.

Newcomer Mills Is a Relatively New Firm Which Will Retain