A common stock pays a constant dividend at the end of each year into perpetuity.

Using an annual effective interest rate of 10%, calculate the Macaulay duration of the stock.

• 7 years
• 9 years
• 11 years
• 19 years
• 27 years

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

The size of the dividend does not matter, so assume it is 1. Then the duration is

[[math]] \frac{\sum_{t=1}^{\infty}tv^t}{\sum_{t=1}^{\infty}v^t} = \frac{(Ia)_{\overline{\infty}|}}{a_{\overline{\infty}|}} = \frac{\ddot a_{\overline{\infty}|}/i}{1/i} = \frac{1/(di)}{1/i} = \frac{1}{d} = \frac{1.1}{0.1} =11. [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.