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14 January, 00:51

New Gadgets, Inc., currently pays no dividend but is expected to pay its first annual dividend of $5.30 per share exactly 9 years from today. After that, the dividends are expected to grow at 3.9 percent forever. If the required return is 12.1 percent, what is the price of the stock today?

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  1. 14 January, 01:19
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    The multiple choices are:

    $64.63 '

    $23.12

    $30.24

    $47.59

    $25.92

    The correct option is $25.92

    Explanation:

    The price of the stock today is the present of dividend of $5.30 payable in nine years' time and present value of the dividend terminal value:

    present of dividend=dividend/discount factor

    where discount factor = (1+r) ^n

    r is the required rate of return of 12.1%

    n is the number of years which is 9

    present value of dividend=$5.30 / (1+12.1%) ^9=$ 1.90

    Terminal value=dividend * (1+g) / (r-g)

    g is the dividend growth rate of 3.9%

    r is the required return of 12.1%

    terminal value=$5.3 * (1+3.9%) / (12.1%-3.9%) = $ 67.15

    Present value of terminal value=$ 67.15 / (1+12.1%) ^9=$ 24.02

    Sum of both present values=$ 24.02 + $1.90=$25.92
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