Question

Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $400 and has an existing customer base of 700. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of 3 percent for the next five years. The overall expenses of running the health club are $125,000 a year and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy a luxury boat for $500,000, close the health club, and travel the world in his boat for the rest of his life. What is the annual amount that Paul can spend while on his world tour if he will have no money left in the bank when he dies? Assume Paul has a remaining life of 25 years after he retires and earns 9 percent on his savings.

Answer 1

We will first calculate Paul's saving at the end of five year as under:-

Year 0 Annual fee = $400 (to be increased @6% per annum)

Year 0 Members = 700 (to be increased @ 3% per annum)

Expenses are to be increased @ 2% per annum

Year	Annual Fee	Members	Revenue	Expense	Savings
a	b	c	d = b*c	e	f = d-e
1	$424.00	721	$305,704.00	125000	$180,704.00
2	$449.44	743	$333,767.63	127500	$206,267.63
3	$476.41	765	$364,407.50	130050	$234,357.50
4	$504.99	788	$397,860.10	132651	$265,209.10
5	$535.29	811	$434,383.66	135304.02	$299,079.64
Total savings for 5 years			$1,185,617.87
Less: Cost of Boat				$500,000.00
Balance at the end of five years			$685,617.87

Thus, based on above table, Mr paul has savings of $685617.87 at the end of five years.

Annual amount that Mr paul can spend if he has remaining life of 25 years and earns interest @ 9% per annum will be = Balance at the end of year 5 / PVAF(9%,25years)

   = $685,617.87 / 9.8226

   = $69,800 (approx)