Question

CDS's stock currently has a market value of $24.11 and Mr. Bensen believes the market estimates that dividends will grow at 2.64% forever's didvidend to be $1.60. What is k?

Answer 1

To find the required rate of return \( k \) for CDS's 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:

\[
P_0 = \frac{D_0 \times (1 + g)}{k - g}
\]

Where:
- \( P_0 \) is the current stock price (market value), which is $24.11.
- \( D_0 \) is the current dividend, which is $1.60.
- \( g \) is the growth rate of dividends, which is 2.64% or 0.0264.
- \( k \) is the required rate of return.

Rearranging this formula to solve for \( k \), we have:

\[
k = \frac{D_0 \times (1 + g)}{P_0} + g
\]

Now, let's plug in the values:

1. Calculate \( D_0 \times (1 + g) \):

\[
D_0 \times (1 + g) = 1.60 \times (1 + 0.0264) = 1.60 \times 1.0264 \approx 1.641024
\]

2. Now, substitute \( P_0 \), \( D_0 \), and \( g \) into the formula for \( k \):

\[
k = \frac{1.641024}{24.11} + 0.0264
\]

3. Calculate \( \frac{1.641024}{24.11} \):

\[
\frac{1.641024}{24.11} \approx 0.06812
\]

4. Finally, add \( g \):

\[
k \approx 0.06812 + 0.0264 \approx 0.09452
\]

To express \( k \) as a percentage:

\[
k \approx 0.09452 \times 100 \approx 9.45\%
\]

Thus, the required rate of return \( k \) is approximately **9.45%**.