Question

The market price of a stock is $32.68 and it is expected to pay a $3.65 dividend next year. The dividend is expected to grow at 4.24% forever. What is the required rate of return for the stock?

Answer 1

To calculate 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 formula for the required rate of return (\( r \)) is:

\[
r = \frac{D_1}{P_0} + g
\]

Where:
- \( D_1 \) = Dividend expected next year
- \( P_0 \) = Current market price of the stock
- \( g \) = Growth rate of the dividend

Given:
- \( D_1 = 3.65 \)
- \( P_0 = 32.68 \)
- \( g = 4.24\% = 0.0424 \)

Now, we can substitute the values into the formula:

\[
r = \frac{3.65}{32.68} + 0.0424
\]

First, calculate \( \frac{3.65}{32.68} \):

\[
\frac{3.65}{32.68} \approx 0.111
\]

Now add the growth rate:

\[
r \approx 0.111 + 0.0424 = 0.1534
\]

To express this as a percentage:

\[
r \approx 15.34\%
\]

Thus, the required rate of return for the stock is approximately **15.34%**.