Question

Now assume that you are the manager of a corporation and your firm is trying to decide whether to lease a machine for five year sand pay the residual purchase costto buy the machine in the last year of the lease or buy the machine now.The annual lease payment would be $8,700 with payments made at the beginning of each year. The residual purchase cost would be $25,200 to be paid at the beginning of the fifth year. The lease payments are standard business expenses that reduce the corporation’s tax liability accordingly. Your firm can borrow $89,300 from the bank to buy the machine now. Annual loan payments would be made for 5 years at a 5% interest rate. The machine can be fully depreciated in a straight line manner over 5years. Both the loan interest payment and the depreciation provide tax shields against a corporate tax rate of 40%. The appropriate discount rate for both alternatives is the after-tax cost of debt,where the corporation’s cost of debt is assumed to be the same as the loan rate. Should your corporation lease or buy?

Answer 1

Option 1: Lease the Machine for 5 years
Payment made at the beginning of the year	Amount Paid as lease	Residual Purchase Cost	Tax @40%	After-Tax Cost of Lease(i-iii)	Discount @ 3%	P.V of Lease payment (iv*v)	P.V of Residual Purchase Price (ii*v)
	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)
Year 1	$        8,700		$             3,480	$        5,220	1	$         5,220
Year 2	$        8,700		$             3,480	$        5,220	0.97087	$         5,068
Year 3	$        8,700		$             3,480	$        5,220	0.94260	$         4,920
Year 4	$        8,700		$             3,480	$        5,220	0.91514	$         4,777
Year 5	$        8,700	$              25,200	$             3,480	$        5,220	0.88849	$         4,638	$        22,390
						$      24,623	$        22,390
Lease and Purchase Costs are paid at the beginning of the year.
Cost of Loan = Cost of debt=Discounting factor
Lease payments are allowed for a tax deduction.Hence post-tax discounting factor=5*60%=3%
Hence Total Cost of Lease	P.V of Lease Payment(After tax)+ P.V of Purchase price
		24623+22390
		$              47,013
Option 2: Buy Machine and avail Loan for 5 years @5%
Payment made at the end of of the year	Interest @ 5%	Depreciation	Total Amount of expenses	Tax @40%	After-Tax Cost	Discount @ 3%	P.V
Year 1	$        4,465	$              17,860	$           22,325	$        8,930	$        13,395	0.97087379	$        13,005
Year 2	$        4,465	$              17,860	$           22,325	$        8,930	$        13,395	0.94259591	$        12,626
Year 3	$        4,465	$              17,860	$           22,325	$        8,930	$        13,395	0.91514166	$        12,258
Year 4	$        4,465	$              17,860	$           22,325	$        8,930	$        13,395	0.88848705	$        11,901
Year 5	$        4,465	$              17,860	$           22,325	$        8,930	$        13,395	0.86260878	$        11,555
							$        61,345
Amount of Loan	$     89,300
Term of Loan=5years
Interest Payment	89300*5%	$                 4,465
Straight Line Depreciation	(89300/5)	$           17,860
Both Interest and Depreciation of $4465 & $ 17860=$22325 qualify for a tax deduction.
Hence Present Value of Cost of Buying	$           61,345

Hence Option 1: Lease the Machine should be exercised as there is a lower cost involved as compared to the cost of buying by ($61345-$47013)

$14,332.