Question

As a financial advisor you have a high wealth client who is thinking about making some life changes. Stanley is 50 (today is his birthday), and he want to retire at 65. He wants to put away the same amount of money every birthday (starting today) up to and including his 65th birthday. He then wants to be able to withdraw $100,000 every birthday (starting with his 66th) up to and including his 85th birthday.   He believes he can earn an average annual return of 9.5% by investing in higher risk investments over the next ten years, but will put it in a lower risk portfolio on retirement – which he thinks will earn 8%

A. Ignoring taxes, how much does Stanley need to save each year to achieve this objective?

B. As Stanley’s advisor you note that Japan has amongst the highest life expectancy in the world, and the average expectancy for males is 80.5 years?  You suggest to Stanley that he will spend less as he gets older is unlikely to need $100,000 a year for living from the age of 75 on – and advise that it would be more like $60,000. In this case what would Stanley’s revised annual saving need to be.

Answer 1

a) Let's calculate the amount he needs at age 65 using PV function

N = 20, I/Y = 8%, PMT = 100,000, FV = 0 => Compute PV = $981,814.74

Now, annual savings can be calculated using PMT function with BEGIN mode

N = 16, I/Y = 9.5%, PV = 0, FV = 981,814.74 => Compute PMT = $28,506.69 is the amount Stanley needs to save each year.

b) If PMT = 60,000 in the above case, then PV = $589,088.84

and PMT = $17,104.02 is the revised annual saving, keeping other things constant in part a.