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25 January, 06:02

A share of stock sells for $36 today. The beta of the stock is 1.1 and the expected return on the market is 15 percent. The stock is expected to pay a dividend of $0.90 in one year. If the risk-free rate is 3.5 percent, what should the share price be in one year?

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  1. 25 January, 06:27
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    First, use CAPM formula to find the rate of return on this stock;

    CAPM; r = risk free + beta (market return - risk free)

    r = 0.035 + 1.1 (0.15-0.035)

    r = 0.035 + 0.115

    r = 0.15 or 15%

    Next, use dividend discount model to find growth rate of the dividends;

    Price (yr0) = Div1 / (r-g)

    36 = 0.90 / (0.15-g)

    then cross-multiply to get;

    5.4 - 36g = 0.90

    5.4 - 0.90 = 36g

    4.5 = 36g

    g = 4.5/36

    g = 0.125 or 12.5%

    Price next year (P1) = Current price (1+g)

    P1 = 36 * (1+0.125)

    P1 = 40.5

    Therefore in one year, this stock will be valued at $40.50
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