Question

Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $940 and has an existing customer base of 490. Paul plans to raise the annual fee by 7 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 $114,000 a year and are expected to grow at the inflation rate of 4 percent annually. After five years, Paul plans to buy a luxury boat for $400,000, 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 and earns 10 percent on his savings.

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.)

Account value at retirement

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.)

Annual withdrawal

Answer 1

Year	Annual Fee (growth @7%)	Number of customer (growth @3%)	Revenue	Cost (growth @4%)	Cash Flow	Value after 5 year @10%
1	940.00	490	460,600.00	114,000.00	346,600.00	507,457.06
2	1,005.80	505	507,627.26	118,560.00	389,067.26	517,848.52
3	1,076.21	520	559,456.00	123,302.40	436,153.60	527,745.86
4	1,151.54	535	616,576.46	128,234.50	488,341.97	537,176.16
5	1,232.15	551	679,528.92	133,363.88	546,165.04	546,165.04
					Total	2,636,392.65

If he pays $400000, then he will have (2636392.65-400000)=$2,236,393.65, the day when he will start journey on boat.

Now, he will live for another =25-5=20 year

Nper=20, rate=10%, PV=$2,236,393.65

Hence, he can spend $262685.84 per year up to 20 year till the end of his life.