Question

Your firm is considering leasing a new robotic milling control system. The lease lasts for 5 years. The lease calls for 6 payments of $300,000 per year with the first payment occurring at lease inception. The system would cost $1,050,000 to buy and would be straight-line depreciated to a zero salvage value. The actual salvage value is zero. The firm can borrow at 8%, and the corporate tax rate is 34%. what is the npv of the lease (NAL)?

Answer 1

npv of the lease = net cost of system - present value of net lease payments

net cost of system = cost of system - after-tax first lease payment = $1,050,000 - [$300,000*(1-0.34)] = $1,050,000 - ($300,000*0.66) = $1,050,000 - $198,000‬ = $852,000

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

Depreciation = cost of system/life of lease = $1,050,000/5 = $210,000‬

net lease payments = [($300,000 - $210,000)*(1-0.34)] + $210,000 = ($90,000*0.66) + $210,000 = $59,400‬ + $210,000 = $269,400‬

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 5 net lease payment/(1+after-tax cost of borrowing)5

After-tax cost of borrowing = cost of borrowing*(1-tax rate) = 8%*(1-0.34) = 8%*0.66 = 5.28‬%

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

npv of the lease = $852,000 - $1,157,388 = -$305,388‬

Years	Net Lease payment	Present value
1	$269,400	$255,889
2	$269,400	$243,056
3	$269,400	$230,866
4	$269,400	$219,288
5	$269,400	$208,290
Total		$1,157,388

Calculations