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?

Answer 1

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%.