Question

Problem 5-34 Real Cash Flows

Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $700 and has an existing customer base of 640. 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 $129,000 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 $540,000, 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.

Q1 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.)

Account value at retirement $______

Q1 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.)

Annual withdrawal $______

Answer 1

Current Charges = $700 (expected to increase by 7% every year)   

Current Customer base = 640  (expected to increase by 3% every year)   

Current Revenue = $448,000 , expected to increase by 10.21% (1.07*1.03 - 1) every year

Current costs = $ 129,000 expected to increase by 3 % every year.

Savings = $ 319000 (Savings for 5 years)

This amount shall be saved for 5 years and shall amount to 319000*1.08⁵ = 468715.66

Similarly savings for other years can be calculated and shall be earning interest in the bank @ 8% for corresponding time periods. Asssuming that the charges are paid by Paul and the customers in advance for the year

the total amount accumulated can be calculated from the table below :

Year	1	2	3	4	5
Revenue	448000.00	493740.80	544151.74	599709.63	660939.98
Costs	129000.00	132870.00	136856.10	140961.78	145190.64
Savings	319000.00	360870.80	407295.64	458747.84	515749.34
Accumulated savings after 5 years	468715.66	490960.74	513075.20	535083.49	557009.29
Total	2564844.37

So, Paul will have ($2564,844.37- $540,000) = $2,024,844.37 in bank account after paying for the boat at the start of world tour.

b) Suppose Paul spends $X each year (assuming at the beginning of the year) for 25 years till he retires.

The present value of this amount should be equal to his account balance at retirement

2024844.37 = X + X/1.08+ ... +X/1.08²⁴

=X *( 1- (1/1.08)²⁵) / (1-1/1.08)

= X*1.08/0.08 * (1-0.146018)

=> X = 202844.37 * 0.08 /0.922301

= $175634.21 (Annual Withdrawal amount)   

Please note that assumptions about timing of collection of healthclub charges, timing of payment of running expenses and timing of annual withdrawal will change the calculations accordingly