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 the above

Question

Quizplus · Accepted Answer

To calculate the NPV of the lease, we need to discount the cash flows at the cost of borrowing for the firm. There are two cash flows to consider: the lease payments and the tax savings from depreciation.

First, let's calculate the tax savings from depreciation. The system costs $1,050,000 and is depreciated over 5 years, so the annual depreciation expense is $210,000 ($1,050,000 / 5). The tax savings each year is 34% of the depreciation expense, or $71,400 ($210,000 * 0.34).

Next, let's calculate the present value of the lease payments. We can use the PV formula for an annuity: PV = C * [(1 - (1 + r)^-n) / r], where C is the annual payment, r is the discount rate, and n is the number of payments. Plugging in the numbers, we get: PV = $300,000 * [(1 - (1 + 0.08)^-6) / 0.08] = $1,436,125.

Finally, we need to subtract the initial cost of buying the system, which is $1,050,000. Putting it all together, the NPV of the lease is:

NPV = -$1,050,000 + $1,436,125 + ($71,400 * 5) = -$305,388

Since the NPV is negative, leasing the system is not a profitable choice for the company.

Your Firm Is Considering Leasing a New Robotic Milling Control