Question

Your firm is considering leasing a new computer. The lease lasts for 4 years. The lease calls for 5 payments of $450 per year with the first payment occurring immediately. The computer would cost $5,900 to buy and would be depreciated using the straight-line method to zero salvage over 4 years. The firm can borrow at a rate of 5%. The corporate tax rate is 20%. What is the NPV of the lease?

Answer 1

NPV of the lease = Net cost of Computer - Present value (PV) of net lease payments

Net cost of Computer = cost of computer - after-tax first lease payment = $5,900 - [$450*(1-0.20)] = $5,900 - ($450*0.80) = $5,900 - $360 = $5,540‬

net lease payments = [(lease payment - depreciation)*(1-tax rate)] + depreciation

Depreciation = cost of computer/life of lease = $5,900/4 = $1,475‬

net lease payments = [($450 - $1,475)*(1-0.20)] + $1,475 = (-$1,025‬*0.80) + $1,475 = -$820‬ + $1,475 = $655‬

Depreciation is a non-cash expense, but it reduces tax or creates a tax-shield. so, depreciation is first subtracted from lease payments for calculation of taxes and then added back to after-tax lease payments to get the cash flow.

present value of net lease payments = year 1 net lease payment/(1+after-tax cost of borrowing) + year 2 net lease payment/(1+after-tax cost of borrowing)2 .... + year 4 net lease payment/(1+after-tax cost of borrowing)4

After-tax cost of borrowing = cost of borrowing*(1-tax rate) = 5%*(1-0.20) = 5%*0.80 = 4%

after-tax cost of borrowing is used to discount net lease payments because of interest tax shield.

Years	Net Lease payment	Present value
1	$655	$629.81
2	$655	$605.58
3	$655	$582.29
4	$655	$559.90
Total		$2,377.58

Calculation

NPV of the lease = $5,540‬ - $2,377.58 = $3,162.42‬

the NPV of the lease is $3,162.42‬.