Paul Adams owns a health club in downtown Los Angeles. He charges his customers
ID: 2782096 • Letter: P
Question
Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $890 and has an existing customer base of 500. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a constant rate of 5 percent for the next five years. The overall expenses of running the health club are $115,000 a year and are expected to grow at the inflation rate of 3 percent annually. After five years, Paul plans to buy a luxury boat for $410,000, 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 8 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 $
Explanation / Answer
Year Annual fee per customer Customer base Tota revenue Annual cost Profit FV @ 8% FV 1 890 500 445,000 (115,000) 330,000 1.360489 448,961.36 2 943.40 525 495,285 (118,450) 376,835 1.259712 474,703.57 3 1,000.00 551 551,252 (122,004) 429,249 1.1664 500,675.69 4 1,060.00 579 613,544 (125,664) 487,880 1.08 526,910.51 5 1,123.60 608 682,874 (129,434) 553,441 1 553,440.63 2,504,691.75 Annual fee increasing 6% every year Annual membership increasing 5% every year annual cost increasing by 3% every year Future value in his account after 5 years 2,504,692 Solution 2 P = PMT x (((1-(1 + r) ^- n)) / i) Where: P = the present value of an annuity stream PMT = the dollar amount of each annuity payment r = the effective interest rate (also known as the discount rate) i=nominal Interest rate n = the number of periods in which payments will be made 2,504,692 =Annual equal withdrawl*(((1-(1 + 8%) ^-25)) / 8%) 2,504,692 =Annual equal withdrawl *10.674 Annual equal withdrawl =2504692/10.674 Annual equal payments 234,654