Question

determine the value of a stock with the following variables using the constant growth model: • current annual dividend: $1.30 per share • required return rate: 7% • constant growth rate: 5% options: $63.75, $65.00, $68.25, $69.55

Explanation:

Step1: Recall the constant growth model formula

The formula for the constant growth model (Gordon Growth Model) is $P_0 = \frac{D_1}{r - g}$, where $D_1$ is the next - year's dividend, $r$ is the required return rate, and $g$ is the constant growth rate. Also, $D_1=D_0(1 + g)$, where $D_0$ is the current annual dividend.

Step2: Calculate $D_1$

Given $D_0 = 1.30$ and $g=0.05$, we calculate $D_1$ as follows:
$D_1=D_0(1 + g)=1.30\times(1 + 0.05)=1.30\times1.05 = 1.365$

Step3: Calculate the stock price $P_0$

We know that $r = 0.07$ and $g = 0.05$. Substitute $D_1$, $r$, and $g$ into the formula $P_0=\frac{D_1}{r - g}$:
$P_0=\frac{1.365}{0.07-0.05}=\frac{1.365}{0.02}=68.25$

Answer:

$\$68.25$