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3 October, 13:41

You consider buying a share of stock. The stock is expected to pay a dividend of $1.50 next year, and dividends are expected to grow by 5% per year forever. What is the stock price now if the stock's beta is 1.1, rf is 6%, and E[rm]

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  1. 3 October, 14:51
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    Question

    The question is incomplete. The complete question is given as follows:

    You consider buying a share of stock. The stock is expected to pay a dividend of $1.50 next year, and dividends are expected to grow by 5% per year forever. What is the stock price now if the stock's beta is 1.1, rf is 6%, and E[rm] = 16%.

    Answer

    Stock price = $12.5

    Explanation:

    Using the dividend valuation model, the value of a stock can be determined using this model:

    Price = D (1+g) / (r-g)

    D - dividend payable now, g - growth rate in dividend, r-return on equity

    Return on equity

    Re = Rf + β (Rm - Rf)

    Rf - risk-free rate, Rm - Return on market portfolio, β - Beta factor

    To determine the Stock price we follow the steps below

    Step 1

    Determine the cost of equity

    r = 6% + 1.1 * (16%-6%)

    = 17%

    Step 2

    Determine the stock price

    Stock price = 1.50 / (0.17-0.05)

    = $12.5

    Stock price = $12.5

    Note

    D * (1+g) = Dividend next year. And this has been given as $1.50. So there is no need to apply the growth rate.
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