Question

If the market price of a stock is $56.63 and it just paid $5.68 dividend The dividend is expected to grow at 2.85% forever. What is the required rate of return for the sock?

Answer 1

To determine 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 is given by:

\[
P = \frac{D_0 \times (1 + g)}{r - g}
\]

Where:
- \( P \) = current stock price
- \( D_0 \) = dividend just paid
- \( g \) = growth rate of the dividend
- \( r \) = required rate of return

We need to rearrange this formula to solve for \( r \):

\[
r = \frac{D_0 \times (1 + g)}{P} + g
\]

Substituting the values we have:

- \( P = 56.63 \) (market price of the stock)
- \( D_0 = 5.68 \) (dividend just paid)
- \( g = 0.0285 \) (growth rate of 2.85%)

Now, let's calculate \( D_0 \times (1 + g) \):

\[
D_0 \times (1 + g) = 5.68 \times (1 + 0.0285) = 5.68 \times 1.0285 \approx 5.84
\]

Next, we can plug everything back into the rearranged equation for \( r \):

\[
r = \frac{5.84}{56.63} + 0.0285
\]

Calculating \( \frac{5.84}{56.63} \):

\[
\frac{5.84}{56.63} \approx 0.1037
\]

Now, adding the growth rate:

\[
r \approx 0.1037 + 0.0285 \approx 0.1322
\]

To express this as a percentage:

\[
r \approx 0.1322 \times 100 \approx 13.22\%
\]

Thus, the required rate of return for the stock is approximately **13.22%**.