Your firm is considering leasing a magic box. The lease lasts for 3 years. The lease calls for 4 payments if $1,000 per year with the first payment occurring at lease inception. The magic box would cost $3,600 to buy and would be straight-line depreciated to zero salvage value over 3- years. The firm can borrow at 6%, and the corporate tax rate is 30%. What is the NPV of the lease?

Question

Quizplus · Accepted Answer

To calculate the NPV of the lease, we need to compare the lease payments to the cost of buying the magic box and depreciating it over 3 years.

Lease payments: 
Year 1: $1,000
Year 2: $1,000
Year 3: $1,000
Total: $3,000

Cost of buying and depreciating the magic box: 
Depreciation per year: $3,600 / 3 = $1,200
Year 1: $1,200 depreciation
Year 2: $1,200 depreciation
Year 3: $1,200 depreciation
Total depreciation: $3,600
Book value at end of year 3: $0
Tax shield from depreciation: $1,200 x 30% = $360 per year

To calculate the present value of the tax shield, we need to discount it back to present value using the cost of borrowing:
PV of tax shield = $360 / (1+6%) + $360 / (1+6%)^2 + $360 / (1+6%)^3
PV of tax shield = $990.92

The cost of buying the magic box is $3,600 and we can subtract the PV of the tax shield we just calculated:
Net cost of buying = $3,600 - $990.92 = $2,609.08

Comparing this to the lease payments, we can calculate the NPV:
NPV = -$3,000 + $2,609.08 / (1+6%)^1 + $2,609.08 / (1+6%)^2 + $2,609.08 / (1+6%)^3
NPV = -$30.50

Therefore, the best choice is B, as the NPV is negative and indicates that buying the magic box would be the better financial decision compared to leasing.

Your Firm Is Considering Leasing a Magic Box