Question

The market price of a stock is $46.36 and it is expected to pay a $3.82 dividend next year. The dividend is expected to grow at 3.55% forever. What is the required rate of return for the stock?

Answer 1

To find the required rate of return for the stock, we can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth). The model is represented by the formula:

\[
P = \frac{D_1}{r - g}
\]

Where:
- \( P \) is the current price of the stock ($46.36 in this case),
- \( D_1 \) is the expected dividend next year ($3.82),
- \( r \) is the required rate of return,
- \( g \) is the growth rate of the dividend (3.55% or 0.0355).

We will rearrange the formula to solve for \( r \):

\[
r = \frac{D_1}{P} + g
\]

Now we can substitute the values into the equation:

1. First, we calculate \( \frac{D_1}{P} \):

\[
\frac{D_1}{P} = \frac{3.82}{46.36} \approx 0.0824 \text{ (or 8.24%)}
\]

2. Next, we add the growth rate \( g \):

\[
r = 0.0824 + 0.0355 = 0.1179 \text{ (or 11.79%)}
\]

Therefore, the required rate of return for the stock is approximately **11.79%**.