Question

Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $860 and has an existing customer base of 950. Paul plans to raise the annual fee by 7 percent every year and expects the club membership to grow at a constant rate of 6 percent for the next five years. The overall expenses of running the health club are $440,000 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 $900,000, close the health club, and travel the world in his boat for the rest of his life. Assume Paul has a remaining life of 25 years after he retires and earns 8 percent on his savings.

  

a.	How much will Paul have in his savings on the day he starts his world tour assuming he has already paid for his boat? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Part (a)

Please see the table below. All financials are in $. Please see the second column to understand the mathematics. The last row in yellow contains your answer.

Year, n	Linkage	0	1	2	3	4	5
Annual Fees	A = 860 @ 7%	860	920	985	1,054	1,127	1,206
[x] Customer base	B = 950 @ 6%	950	1,007	1,067	1,131	1,199	1,271
Revenue	C = A x B		926,641	1,050,997	1,192,040	1,352,012	1,533,452
[-] Expenses	D = 440,000 @ 2%	440,000	448,800	457,776	466,932	476,270	485,796
Savings	E = C - D		477,841	593,221	725,109	875,742	1,047,657
Years to retirement	F = 5 - n		4	3	2	1	0
Interest rate	G	8%
FV factor	H = (1 + G)^F		1.3605	1.2597	1.1664	1.0800	1.0000
FV of savings	I = H x E		650,097.95	747,287.20	845,767.03	945,801.47	1,047,656.75
Accumulated savings	J = Sum of all I		4,236,610.41
[-] Payment for boat	K		900,000.00
Hence, savings on the day he starts his world	J - K		3,336,610.41

Part (b)

Annual amount he can spend = PMT (Rate, Nper, PV, FV) = PMT (8%, 25, - 3336610.41, 0) = $  312,569.59