Asked by 123
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. Next year's dividend is projected to be $1.60. What is k?
Answers
Answered by
GPT-4o mini
To find the required rate of return \( k \) on CDS's stock using the Gordon Growth Model (also known as the Dividend Discount Model), we can utilize the formula:
\[
P_0 = \frac{D_1}{k - g}
\]
Where:
- \( P_0 \) is the current stock price ($24.11).
- \( D_1 \) is the dividend expected next year ($1.60).
- \( g \) is the growth rate of dividends (2.64% or 0.0264).
- \( k \) is the required rate of return, which we want to solve for.
Rearranging the formula to solve for \( k \):
\[
k = \frac{D_1}{P_0} + g
\]
Now, substituting the values into the formula:
1. Calculate \( \frac{D_1}{P_0} \):
\[
\frac{D_1}{P_0} = \frac{1.60}{24.11} \approx 0.0664 \text{ or } 6.64\%
\]
2. Now, adding the growth rate \( g \):
\[
k = 0.0664 + 0.0264 = 0.0928 \text{ or } 9.28\%
\]
Thus, the required rate of return \( k \) is approximately **9.28%**.
\[
P_0 = \frac{D_1}{k - g}
\]
Where:
- \( P_0 \) is the current stock price ($24.11).
- \( D_1 \) is the dividend expected next year ($1.60).
- \( g \) is the growth rate of dividends (2.64% or 0.0264).
- \( k \) is the required rate of return, which we want to solve for.
Rearranging the formula to solve for \( k \):
\[
k = \frac{D_1}{P_0} + g
\]
Now, substituting the values into the formula:
1. Calculate \( \frac{D_1}{P_0} \):
\[
\frac{D_1}{P_0} = \frac{1.60}{24.11} \approx 0.0664 \text{ or } 6.64\%
\]
2. Now, adding the growth rate \( g \):
\[
k = 0.0664 + 0.0264 = 0.0928 \text{ or } 9.28\%
\]
Thus, the required rate of return \( k \) is approximately **9.28%**.