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Math Help - Stock Valuation with Constant Growth Rate

  1. #1
    Newbie CaesarXXIV's Avatar
    Joined
    Mar 2010
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    Question Stock Valuation with Constant Growth Rate

    Hi,

    This is my first time posting on this forum. If a company pays a quarterly dividend of $0.75, with a dividend growth rate of 6% per year (indefinitely), and with a required rate of return of 14%, what is the price of the stock?

    I know I have to use the formula which states: Po=Do(1+g)/(r-g), where g=dividend growth rate, and r=required rate of return. Except I have to calculate the equivalent annual dividend of the 4 quarterly dividends.

    I calculated that using:

    Deq=0.75 [(1+0.14/4)^3+(1+0.14/4)^2+(1+0.14/4)+1)

    And then I plugged Deq as Do. I used 6% as g and 14% as r. I got $41.89 as the answer, but the textbook has $41.78 as the answer.

    Where did I go wrong?
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  2. #2
    Junior Member
    Joined
    Jan 2010
    Posts
    65
    Your error is here:

    Quote Originally Posted by CaesarXXIV View Post

    Deq=0.75 [(1+0.14/4)^3+(1+0.14/4)^2+(1+0.14/4)+1)
    You should not be using .14/4 as your rate. You need to find the equivalent quarterly rate that yields an annual rate of 14%:

    (1+.14)=(1+r)^4

    Thus the rate you should use in your Deq equation is r=.033299484759
    Then your Deq should be 3.15320194171 and your answer should follow from there.
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