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?
A) -$111,690
B) -$295,040
C) -$305,388
D) -$309,690
E) None of these.

Question

Quizplus · Accepted Answer

Calculate the after-tax cost of leasing:
Lease payment = $300,000
Tax savings = $300,000 x 34% = $102,000
Net cost of leasing = $300,000 - $102,000 = $198,000
Present value of lease payments = $198,000 x [(1 - 1/(1 + 8%)^5)/8%] = $843,380

Calculate the after-tax cost of buying:
Depreciation expense = $1,050,000/5 = $210,000
Tax savings = $210,000 x 34% = $71,400
Net cost of buying = $1,050,000 - $71,400 = $978,600
Present value of buying = $978,600/[(1 + 8%)^1] + $210,000/[(1 + 8%)^2] + $210,000/[(1 + 8%)^3] + $210,000/[(1 + 8%)^4] + ($210,000 + $1,050,000)/[(1 + 8%)^5] = $607,992

Therefore, the NPV of the lease is:
NPV = $843,380 - $607,992 = $235,388
Since the NPV is negative, the firm should not lease the robotic milling control system, but instead buy it outright. Neither A nor D are possible as they have positive values. B is not possible since the net present value is negative, and E is not possible since we have found a valid answer.

Your Firm Is Considering Leasing a New Robotic Milling Control