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.

Step 1: Calculate the value (at his 65th birthday, i.e.15 years from today ) of yearly payments to be withdrawn by him upon retirement:

PV = P*PVAF(r,n), where:

• P= payment per period =$100,000
• r=rate of interest =8% = 0.08
• n=number of payment periods = 66th birthday to 85th birthday = 20 annual payments

Therefore, PV = 100,000*9.8181 = $981,810

Step 2: Calculate the monthly payments required to be made for 15 years starting from today, such that its cumulative future value is $981,810 after earning an interest rate of 9.5% per annum.

Using the TVM function of a financial calculator in BGN mode:

N=15, i/y=9.5, PV=0, FV=-981810, CPT->PMT = 29,359

$29,359 is the amount Stanley needs to save each year.

B.

Assuming Stanley's Life expentancy is still 85 years and not 80.5 years, since it is not clearly mentioned in the question that Stanley;s ;ife expentancy is equal to the average expentancy for males:

Step 1: Calulate the value (at his 65th birthday, i.e.15 years from today ) of yearly payments to be withdrawn by him upon retirement:

Age	Periods (t)	Payments ($)	PVAF(8%,t)	Cumulative payment
66 to 74	9	100,000	5.7466	574,660
75 to 85	11	60,000	7.139	428,340

Using the above data, we futher need to calculate the PV of cumulative payments received from age 75 to 85 by 9 years PVF @8% = 0.5002*428340 = 214,277

Therefore, amount required at the beginning of his retirement = 574,660+214,277 = $788,937

Step 2: Calculate annual payments required to be made beginning from today:

Using the TVM function of a financial calculator in BGN mode:

N=15, i/y=9.5, PV=0, FV=-788937, CPT->PMT = 23,592

$23,592 is the amount Stanley needs to save each year.