Question

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?

Answer 1

		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