In: Finance
You own a cab company and are evaluating two options to replace your fleet. Either you can take out a five-year lease on the replacement cabs for $ 495$495 per month per cab, or you can purchase the cabs outright for $ 31 comma 600$31,600, in which case the cabs will last eight years. You must return the cabs to the leasing company at the end of the lease. The leasing company is responsible for all maintenance costs, but if you purchase the cabs, you will buy a maintenance contract that will cost $ 108$108 per month for the life of each cab. Each cab will generate revenues of $ 1 comma 000$1,000 per month. Assume the cost of capital is fixed at 12.7 %12.7%. (Hint: Make sure to round all intermediate calculations to at least four decimal places.) a. Calculate the NPV per cab of both possibilities: purchasing the cabs or leasing them. b. Calculate the equivalent monthly benefit of both opportunities. c. If you are leasing a cab, you have the opportunity to buy the used cab after five years. Assume that in five years a five-year-old cab will cost either $ 11 comma 000$11,000 or $ 15 comma 500$15,500, with equal likelihood; will have maintenance costs of $ 498$498 per month; and will last three more years. Which option should you take?
FIVE YEAR LEASE | |||||||||||
Lease payment per month | ($495) | ||||||||||
Revenue per month | $1,000 | ||||||||||
Pmt | Net monthly cash inflow | $505 | |||||||||
Rate | Discount rate=Cost of capital per month=(12.7/12)% | 1.0583% | |||||||||
Nper | Number of months=5*12 | 60 | |||||||||
NPV | Present Value of cash flows | $22,345.54 | (Using PV function of excel with Rate=1.0583%,Nper=60, Pmt=-505) | ||||||||
ExcelCommand: PV(1.0583%,60,-505) | |||||||||||
NPV per Cab | $22,345.54 | ||||||||||
Equivalent Monthly benefit | $505 | ||||||||||
PURCHASE | |||||||||||
Revenue per month | $1,000 | ||||||||||
Monthly maintenance cost | ($108) | ||||||||||
Pmt | Net monthly cash inflow | $892 | |||||||||
Rate | Discount rate=Cost of capital per month=(12.7/12)% | 1.0583% | |||||||||
Nper | Number of months=8*12 | 96 | |||||||||
PV | Present Value of cash flows | $53,606.84 | (Using PV function of excel with Rate=1.0583%,Nper=96, Pmt=-892) | ||||||||
I | Initial investment | ($31,600) | |||||||||
NPV=PV+I | Net Present value (NPV) per cab | $22,006.84 | |||||||||
Equivalent Monthly Benefit | $366.19 | (Using PVMTfunction of excel with Rate=1.0583%,Nper=96, Pv=-22006.84) | |||||||||
excel Command :PMT(1.0583%,96,-22006.84) | |||||||||||
c | PURCHASE OF LEASED CAB | ||||||||||
Expected Cost of cab =0.5*11000+0.5*15500= | $13,250 | ||||||||||
I | Expected Initialcashflow at end of 5 years | ($13,250) | |||||||||
Monthly Revenue | $1,000 | ||||||||||
Monthly maintenance cost | ($498) | ||||||||||
Pmt | Net Monthly cash flow | $502 | |||||||||
Rate | Discount rate=Cost of capital per month=(12.7/12)% | 1.0583% | |||||||||
Nper | Number of months=3*12 | 36 | |||||||||
PV | Present Value of cash flows | $14,962.99 | (Using PV function of excel with Rate=1.0583%,Nper=36, Pmt=-502) | ||||||||
Excel Command:PV(1.0583%,36,-502) | |||||||||||
NPV=PV+I | Net Present value (NPV) per cab | $1,712.99 | |||||||||
NPV is positive | |||||||||||
You should LEASE and take the purchase of old cab at end of 5 years | |||||||||||