Question

Many individuals prefer to lease their vehicles rather than buy them. A new Cadillac CTSV can be leased for a down payment of $6,000 and 36 end-of-the -month payments of $599. Alternately, the car can be purchased for cash for $42,000 and a CTSV with about 60,000 miles is estimated to have resale value of $20,000 in three years from now. Should one lease or buy if opportunity cost is 6.36%APR?

Answer 1

One should buy this car.

Working;

Step-1:Calculation of present value of lease payments
Down payment		$   6,000.00
Add: present value of monthly payments		$ 19,584.56
Present value of lease options		$ 25,584.56
Working;
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0053)^-36)/0.0053		i	6.36%/12	=	0.0053
	=	32.6954229		n		=	36
Present value of lease payments	=	Monthly lease payments	*	Present value of annuity of 1
	=	$             599	*	32.6954229
	=	$ 19,584.56
Step-2:Calculation of present value of buying option
Cost of Car			$ 42,000.00
Less present value of salvge value			$ 16,534.29
Present value of buying option			$ 25,465.71
Working;
Present value of salvage value		=	$ 20,000.00	x	1.0053^-36
		=	$ 20,000.00	x	0.82671426
		=	$ 16,534.29
Conclusion:
On financial basis, present value of cash flow under buying option is lesser.
So, it should be beneficial to buy the car.