Question

The market price of a stock is $57.80 and it just paid $5.26 dividend. The dividend is expected to grow at 3.44% 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 model formula is:

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

where:
- \( P \) = price of the stock ($57.80)
- \( D_1 \) = the next year's dividend
- \( r \) = required rate of return
- \( g \) = growth rate of the dividend (3.44% or 0.0344)

Since we know the most recent dividend (\( D_0 \)) is $5.26, we can calculate next year's dividend (\( D_1 \)) as follows:

\[
D_1 = D_0 \times (1 + g) = 5.26 \times (1 + 0.0344) = 5.26 \times 1.0344 \approx 5.45
\]

Now we can substitute the known values into the Gordon Growth Model equation to find \( r \):

\[
57.80 = \frac{5.45}{r - 0.0344}
\]

We can rearrange this equation to isolate \( r \):

\[
57.80(r - 0.0344) = 5.45
\]

Expanding the left side:

\[
57.80r - 1.98932 = 5.45
\]

Now, add \( 1.98932 \) to both sides:

\[
57.80r = 5.45 + 1.98932
\]

\[
57.80r = 7.43932
\]

Now, divide both sides by \( 57.80 \):

\[
r \approx \frac{7.43932}{57.80} \approx 0.12854
\]

Finally, convert the decimal to a percentage:

\[
r \approx 0.12854 \times 100 \approx 12.85\%
\]

Thus, the required rate of return for the stock is approximately **12.85%**.