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21 May, 20:07

Anderson Corp just issued a stock dividend of$2.00 yesterday. The company plans on increasing the dividend by 6% per year for the next 5 years. After which, the dividend will grow at 3% forever. The required rate of return is 10%.

A) Calculate the current price of the stock

B) Calculate what the price of the stock should be in 1 year

C) Calculate the Dividend yield and capital gains yield during the first year.

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  1. 21 May, 23:43
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    A). The current price of stock=$38.24

    B). The price of the stock at year 1=$30.29

    C). The dividend yield=7%

    D). Capital gains yield=6%

    Explanation:

    A). Determine the current price of the stock using the formula;

    Required rate of return = (expected dividend payment/current stock price) + expected dividend growth rate

    where;

    Expected dividend payments for years 1-5 is given by the formula;

    dividend payment (1+dividend growth rate). Substituting;

    year 1=2 (1+0.06) = 2.12

    year 2=2.12 (1+0.06) = 2.2472

    year 3=2.2472 (1+0.06) = 2.3820

    year 4=2.3820 (1+0.06) = 2.5250

    year 5=2.5250 (1+0.06) = 2.6765

    Expected dividend payments after 5 years=2.6765

    Current stock price=unknown=C

    Expected dividend growth rate=3%=3/100=0.03

    Required rate of return=10%=10/100=0.1

    replacing;

    0.1 = (2.6765/C) + 0.03

    (2.6765/C) = 0.1-0.03=0.07

    0.07 C=2.6765

    C=2.6765/0.07=38.24

    The current price of stock=$38.24

    B). Price of the stock at 1 year

    Using the expression above and substituting the following;

    Expected dividend payments after 1 year=2.12

    Current stock price=unknown=C

    Expected dividend growth rate=3%=3/100=0.03

    Required rate of return=10%=10/100=0.1

    replacing;

    0.1=2.12/C+0.03

    2.12/C=0.1-0.03=0.07

    0.07 C=2.12

    C=2.12/0.07=30.29

    The price of the stock at year 1=$30.29

    C). The dividend yield is calculated as;

    dividend yield=annual dividend/share price

    where;

    annual dividend=2.12

    share price=30.29

    replacing;

    dividend yield=2.12/30.29=0.07=7%

    The dividend yield=7%

    D). The Capital gains yield is calculated as;

    capital gains yield={ (Current price-original price) / original price}*100

    Current price at year 1=$30.29

    Original price=O

    0.1=2/O+0.03

    2/O=0.07

    O=2/0.07=28.57

    Original price=$28.57

    Capital gains yield={ (30.29-28.57) / 28.57}*100=6%

    Capital gains yield=6%
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