Bradley Broadcasting expects to pay dividends of $1.10, $1.21, and $1.331 in one, two, and three years, respectively. After that, dividends are expected to grow at a constant rate of 4% forever. Stocks of similar risk yield 10%.

The price of Bradley Broadcasting stock today should be:

Question

The price of Bradley Broadcasting stock today should be:

Quizplus · Accepted Answer

The price of Bradley Broadcasting stock today can be calculated using the dividend discount model for a stock that pays dividends for a finite period and then grows at a constant rate indefinitely. The formula to calculate the present value of dividends for the first three years is:$$ P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{D_3 \times (1+g)}{r-g} \times \frac{1}{(1+r)^3} $$Where:- $P_0$ is the price of the stock today.- $D_1$, $D_2$, $D_3$ are the dividends for years 1, 2, and 3 respectively.- $r$ is the required rate of return (10% or 0.10).- $g$ is the constant growth rate of dividends after year 3 (4% or 0.04).Plugging in the given values:- $D_1 = $1.10$- $D_2 = $1.21$- $D_3 = $1.331$- $r = 0.10$- $g = 0.04$$$ P_0 = \frac{1.10}{(1+0.10)^1} + \frac{1.21}{(1+0.10)^2} + \frac{1.331}{(1+0.10)^3} + \frac{1.331 \times (1+0.04)}{0.10-0.04} \times \frac{1}{(1+0.10)^3} $$$$ P_0 = \frac{1.10}{1.10} + \frac{1.21}{1.21} + \frac{1.331}{1.331} + \frac{1.331 \times 1.04}{0.06} \times \frac{1}{1.331} $$$$ P_0 = 1 + 1 + 1 + \frac{1.38424}{0.06} $$$$ P_0 = 3 + 23.07067 $$$$ P_0 \approx 20.33 $$Therefore, the correct answer is $20.33, which corresponds to choice C.

Bradley Broadcasting Expects to Pay Dividends of $1