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10 June, 19:23

Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i. e., years 2 through 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%?

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  1. 10 June, 19:25
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    At 10 percent capitalization rate the price of the stock is $104.49

    At 7 percent capitalization rate the price of the stock is $156.48

    Explanation:

    D1 = 5

    D2 = 5 x 1.2 = 6

    D3 = 5 x 1.2^2 = 7.2

    D4 = 5 x 1.2^3 = 8.64

    D5 = 5 x 1.2^4 = 10.37

    D6 = 5 x 1.2^5 = 12.44

    At 10 percent capitalization rate the price of the stock can be computed by first calculating the present value of the dividends computed above

    5/1.1 = 4.54

    6/1.1^2 = 4.96

    7.2/1.1^3 = 5.41

    8.64/1.1^4 = 5.90

    10.37/1.1^5 = 6.44

    12.44/1.1^6 = 7.02

    Price after six years when the stock will experience zero growth should be

    P = 12.44/0.1 = 124.4

    The present value of the price six years after should be

    124.4 / 1.1^6 = 70.22

    Adding up all the p[resent values gives us the price of the stock today

    4.54 + 4.96 + 5.41 + 5.90 + 6.44 + 7.02 + 70.22 = $104.49

    At 7 percent capitalization rate the price of the stock can be computed by first calculating the present value of the dividends computed above

    5/1.07 = 4.67

    6/1.07^2 = 5.24

    7.2/1.07^3 = 5.88

    8.64/1.07^4 = 6.59

    10.37/1.07^5 = 7.39

    12.44/1.07^6 = 8.29

    Price after six years when the stock will experience zero growth should be

    P = 12.44/0.07 = 177.71

    The present value of the price six years after should be

    177.71 / 1.07^6 = 118.42

    Adding up all the p[resent values gives us the price of the stock today

    4.67 + 5.24 + 5.88 + 6.59 + 7.39 + 8.29 + 118.42 = 156.48
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