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Suppose you know that a company’s stock currently sells for $56 per share and the required return on the stock is 10 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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Answer:

Current dividend per share =$2.67

Explanation:

[tex]Total Return = Div yield + Capital gain yield = 10%\\[/tex]

But from the question

[tex]Dividend yield = Capital gains yield[/tex]

therefore [tex]Dividend yield =\frac{0.1}{2} = 0.05[/tex]

[tex]Dividend yield = \frac{D1}{P0}[/tex]

therefore: [tex]D1=P0*Dividend yield = 56*0.05=$2.80\\[/tex]

the question however is not asking for D1 but D0.

and [tex] D1= D0(1+g)[/tex]

[tex]g=ke-\frac{D1}{P0} = 0.1 - \frac/{2.8}{56} = 0.05[/tex]

therefore [tex]D0=\frac{2.8}{1.05} = $2.67[/tex]

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