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Math Help - Constant and nonconstant growth valuation

  1. #1
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    Constant and nonconstant growth valuation

    Can someone please help me, i am stumped on these 2 problems? Thanks.

    1-A company currently pays dividnd of $2 per share. It is estimated that the conpnay's divivend will grow at a rate of 20% per year for the next 2 years and then grow at a constant 7% therafter. The compnay's stock has a beta equal to 1.2, the risk-free rate is 7.5% and the narket risk premium is 4%. What s your estimate of tyhe stock's current price?

    2- The risk-free rate of return is 11%, the requires rate of return on the market is 14% and Schuler Compnay's stock has a beta coefficent of 1.5.

    a. If the dividend expected during the coming year is $2.25 and g= a constant 5%, at what price should Schuler's stock sell?

    b. Now, suppose the Federal Reserve Baord increses the money supply, causing the risk-free rate to drop to 9% and the rate on the market falls to 12%. what would this do to the price of the stock?
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  2. #2
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    It has been a little while since I did these type of questions... so hopefully I haven't done anything incorrectly.
    1- by the CAPM, the discount rate for the company is
    i=r_{f}+\beta \left( r_{m}-r_{f} \right) = 0.075+1.2(0.04)=0.123 or 12.3\%

    Given that the company receives a current divdend of $2, the dividend in year 1 will be $2.40 which gets discounted 1 year, and $2.88 in year 2 which gets discounted 2. In year three, the dividend grows by 7% and grows indefinitly at this rate. Using the PV of a perputiuty formula will discount these future cash flows into year 2, so they then need to be discounted back a further 2 years to get the PV.
    So the current share price is equal to the discounted value of these cashflows;
     <br />
PV = \frac{2.40}{1+0.123}+\frac{2.88}{(1+0.123)^2}+\fra  c{\left[\frac{2.88(1+0.07)}{0.123-0.07}\right]}{(1+0.123)^2}=\$50.52504<br />

    edit: i made a mistake when i discounted the PV of the growing dividends... Something doesn't look right now?
    Last edited by Robb; September 21st 2009 at 06:15 PM.
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