Question

Your firm is considering leasing a new computer. The lease lasts for 9 years. The lease calls for 9 payments of $1,000 per year. The computer would cost $7,650 to buy and would be straight-line depreciated to a zero salvage value over 9 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 8%. The corporate tax rate is 30%. What is the NPV of the lease relative to the purchase (NAL)?

A) $1,039.78

B) $360.22

C) $339.78

D) $6,610.22

Answer 1

A) $1,039.78

Step-1:Calculation of present value of cash flow under leasing option
Year	After tax lease rental	Lost depreciation tax shield	Cash flow	Discount factor	Present Value
a	b	c	d=b+c	e=1.056^-a	f=d*e
1	$            700.00	$              255.00	$           955.00	0.946969697	$            904.36
2	$            700.00	$              255.00	$           955.00	0.896751607	$            856.40
3	$            700.00	$              255.00	$           955.00	0.849196598	$            810.98
4	$            700.00	$              255.00	$           955.00	0.804163445	$            767.98
5	$            700.00	$              255.00	$           955.00	0.761518413	$            727.25
6	$            700.00	$              255.00	$           955.00	0.721134861	$            688.68
7	$            700.00	$              255.00	$           955.00	0.682892861	$            652.16
8	$            700.00	$              255.00	$           955.00	0.646678846	$            617.58
9	$            700.00	$              255.00	$           955.00	0.612385271	$            584.83
	Total				$         6,610.22
Working:
Depreciation expense	=	(Costs - Salvage Value)/Useful Life
		=	(7650-0)/9
		=	$           850.00
Lost depreciation tax shield	=	Depreciation Expense	*	Tax rate
		=	$           850.00	*	30%
		=	$           255.00
After tax lease rental	=	Before tax lease rental	*	(1- Tax rate)
		=	$       1,000.00	*	(1-0.30)
		=	$           700.00
After tax cost of debt	=	Before tax cost of debt*(1- Tax rate)
		=	8%*(1-0.30)
		=	5.60%
Step-2:Calculation of net advantage of leasing
Cost of Asset	$           7,650.00
Present value of lease option	$         -6,610.22
Net advantage of leasing	$           1,039.78