Question

The market price of a stock is $44.58 and it is expected to pay a $3.79 dividend next year. The dividend is expected to grow at 4.76% forever. What is the required rate of return for the stock?

Answer 1

To calculate the required rate of return for the stock, you can use the Gordon Growth Model (also known as the Dividend Discount Model for a stock with constant growth). The formula is as follows:

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

Where:
- \( P_0 \) = current stock price ($44.58)
- \( D_1 \) = dividend expected next year ($3.79)
- \( r \) = required rate of return
- \( g \) = growth rate of the dividend (4.76% or 0.0476)

Rearranging the formula to solve for \( r \):

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

Now plug in the values:

1. Calculate \( \frac{D_1}{P_0} \):
\[
\frac{D_1}{P_0} = \frac{3.79}{44.58} \approx 0.08493 \text{ or } 8.493\%
\]

2. Add the growth rate \( g \):
\[
r = 0.08493 + 0.0476 \approx 0.13253 \text{ or } 13.253\%
\]

Thus, the required rate of return for the stock is approximately **13.25%**.