Question

The city of Evergreen, NC gave the McEnroe Tennis Club a 25-year lease to use a 10-acre arroyo park for its facilities. The club will pay $100,000 now and $12,000 per year to the city; additionally, the club will make significant improvements to the park facilities. The club is planning to open its tennis courts to the public from 7:00 AM to 2:00 PM Tuesday through Friday, and from 6:00 AM to 1:00 PM Saturday and Sunday (Monday will be closed). If the club spends $150,000 worth of improvements now and then $75,000 worth each year for the next 4 years, what is the equivalent annual cost of the lease to the McEnroe Tennis Club at an interest rate of 12% per yea

Answer 1

Tennis club will pay $100,000 initially while $12,000 per year for next 25 years

In terms of improvement,club will spend $150,000 now and $75,000 for next four years.

So initial cost of club will be $100,000 + $150,000 = $250,000

Cost for next four year will be $12,000 + $75000 = $87,000 per year

Cost for Remaining 21 years will be $12,000   per year

EAC = NPV/ (present value of annuity factor)

At interest rate of 12%, NPV will be

250,000 + 75,000(1/(1.12)^1 + 1/(1.12)^2 + 1/(1.12)^3+ 1/(1.12)^4 ) + 12,000(/(1.12)^1 + 1/(1.12)^2 + 1/(1.12)^3+ 1/(1.12)^4...... 1/(1.12)^25) = $571,918.87

Present value of annuity factor = ((1- 1/(1+r)^t))/r = (1 - 1/(1+.12)^25)/0.12 = 7.843139

So Equivalent Annual Cost will be 571,918.87/7.843139 = $72,919.64

Thanks