Question
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Suppose you know that a company's stock currently sells for \( \$ 65.90 \) per share and the required return on the stock is 12 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Dividend per share

Ask by Lawson Kelly. in the United States
Mar 10,2025

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Answer

The current dividend per share is \$3.95.

Solution

Let \( P_0 = 65.90 \) be the current stock price, and \( r = 0.12 \) be the required return. Since the total return is divided evenly between the capital gains yield and the dividend yield, the dividend yield is \[ \text{Dividend Yield} = \frac{r}{2} = \frac{0.12}{2} = 0.06. \] By definition, the dividend yield is given by \[ \text{Dividend Yield} = \frac{D}{P_0}, \] where \( D \) is the current dividend per share. Solving for \( D \): \[ D = P_0 \times \text{Dividend Yield} = 65.90 \times 0.06 = 3.954. \] Rounded to 2 decimal places, the current dividend per share is \[ \boxed{3.95}. \]

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To find the current dividend per share, we need to understand that the total required return consists of both the dividend yield and the capital gains yield. Given that the required return is 12 percent and it's evenly divided, the dividend yield and the capital gains yield will each be 6 percent (12% / 2). Using the formula for dividend yield, we can express it as: \[ \text{Dividend Yield} = \frac{\text{Dividend per Share}}{\text{Stock Price}} \] From this, we can derive the current dividend per share: \[ 0.06 = \frac{\text{Dividend per Share}}{65.90} \] Solving for the dividend per share: \[ \text{Dividend per Share} = 0.06 \times 65.90 = 3.95 \] Thus, the current dividend per share is **$3.95**.

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