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31 August, 00:04

A common stock pays dividends at the end of each year into perpetuity. Assume that the dividend increases by 2% each year. Using an annual effective interest rate of 5%, calculate the Macaulay duration of the stock in years

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  1. 31 August, 01:10
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    35 years

    Explanation:

    Data given in the question

    Increase in dividend = 2%

    Annual effective interest rate = 5%

    So by considering the above information, the duration of the stock in years is

    = 1 : (Annual effective interest rate - increase in dividend)

    = 1 : (5% - 2%)

    = 1 : 3%

    = 33.33

    Now the duration of the stock in years is

    = (1 + interest rate) ^ 33.33

    = (1 + 0.05) ^33.33

    = 1.05^33.33

    = 34.999 years i. e 35 years
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