Question

A firm just paid a dividend of $4.66. The dividend is expected to grow at a constant rate of 3.69% forever and the required rate of return is 10.09%. What is the value of the stock?

Answer 1

To calculate the value of a stock that pays dividends growing at a constant rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth). The formula for the stock price \( P_0 \) is:

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

Where:
- \( D_1 \) = Dividend expected next year
- \( r \) = Required rate of return
- \( g \) = Growth rate of the dividend

### Step 1: Calculate \( D_1 \)

Given that the most recent dividend \( D_0 \) is $4.66 and it is expected to grow at a rate \( g \) of 3.69%, we can calculate \( D_1 \):

\[
D_1 = D_0 \times (1 + g) = 4.66 \times (1 + 0.0369) = 4.66 \times 1.0369 \approx 4.83
\]

### Step 2: Substitute values into the Gordon Growth Model

Now we have:
- \( D_1 \approx 4.83 \)
- \( r = 10.09\% = 0.1009 \)
- \( g = 3.69\% = 0.0369 \)

Plugging in the values:

\[
P_0 = \frac{4.83}{0.1009 - 0.0369}
\]

Calculating the denominator:

\[
0.1009 - 0.0369 = 0.0640
\]

Now substituting back into the formula:

\[
P_0 = \frac{4.83}{0.0640} \approx 75.47
\]

### Final Answer
Thus, the value of the stock is approximately **$75.47**.