Question

Problem 27-01 Lease or Buy [LO3]

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a very common practice with expensive, high-tech equipment). The scanner costs $5,200,000, and it would be depreciated straight-line to zero over five years. Because of radiation contamination, it actually will be completely valueless in five years. You can lease it for $1,220,000 per year for five years. Assume that the tax rate is 22 percent. You can borrow at 6 percent before taxes.

What is the NAL of the lease? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Should you lease or buy?

• Lease

• Buy

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

IZU А B C 1 Cost of borrowing Tax rate After tax cost of borrowing 6.00% 22.00% 4.68% Lease Annual Payments After tax Annual Cash Flow Years NPV of Lease $1,220,000 $951,600 5 $4,156,630.39 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Buy Purchase cost useful life in years Annual depeciation Tax shield of depreciation PV of Tax shield Salvage value Post-tax Salvage value PV of Post-tax Salvage value NPV of Buy $5,200,000 5 $1,040,000 $228,800 $999,408 $0.00 $0.00 $0.00 $4,200,591.60 NPV of the lease relative to purchase (NAL) $43,961.21 Should you lease or buy? Lease

Cell reference -

A B с 1 2 3 4 Cost of borrowing Tax rate After tax cost of borrowing 0.06 0.22 =C2*(1-C3) Lease Annual Payments After tax Annual Cash Flow Years NPV of Lease 1220000 =C7*(1-C3) 5 =PV(C4,C9,-C8,,0) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Buy Purchase cost useful life in years Annual depeciation Tax shield of depreciation PV of Tax shield Salvage value Post-tax Salvage value PV of Post-tax Salvage value NPV of Buy 5200000 5 =C13/C14 =C15*C3 =PV(C4,C14,-C16,,0) 0 =C18*(1-C3) =C19/(1+C4)^C14 =C13-C17-C20 NPV of the lease relative to purchase (NAL) =C21-C10 Should you lease or buy? Lease

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.