Question

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

Answer 1

35 years

Step-by-step 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