Your firm is considering leasing a new radiographic device. The lease lasts for 3 years. The lease calls for 4 payments of $25,000 per year with the first payment occurring immediately. The computer would cost $140,000 to buy and would be straight-line depreciated to a zero salvage value over 3 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 12%. The corporate tax rate is 40%. What is the NPV of the lease relative to the purchase?
A) -$125,000
B) $115,412
C) $75,000
D) $125,000
E) None of these.

Question

Quizplus · Accepted Answer

To compare the lease and purchase options, we need to calculate the present value of all cash flows associated with each option, taking into account the time value of money.

For the lease option:
- Immediate payment: $25,000
- Four annual payments of $25,000 at the end of each year: $25,000 x 3 PVF(12%, 3 years) = $67,787.50
Total present value of lease option cash flows: $92,787.50

For the purchase option:
- Initial investment: -$140,000
- Depreciation expense each year: $140,000 ÷ 3 years = $46,666.67
- Tax savings from depreciation each year: $46,666.67 x 40% tax rate = $18,666.67
- Salvage value: $0
Total present value of purchase option cash flows: -$87,333.33 (negative because it's an initial investment)

Now, we can calculate the NPV of the lease option relative to the purchase option:
NPV = Present value of lease option cash flows - Present value of purchase option cash flows
NPV = $92,787.50 - (-$87,333.33)
NPV = $92,787.50 + $87,333.33
NPV = $180,120.83

Since the NPV is positive, choosing the lease option is the better choice.

Your Firm Is Considering Leasing a New Radiographic Device