You work for a nuclear research laboratory that is contemplating leasing a diagn
ID: 2754169 • Letter: Y
Question
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 $6,900,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it will actually be completely valueless in four years.
Assume the tax rate is 35 percent. The borrowing rate is 10 percent before taxes. Your company does not expect to pay taxes for the next several years, but the leasing company will pay taxes. Over what range of lease payments will the lease be profitable for both parties? (Enter your answers from lowest to highest. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
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 $6,900,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it will actually be completely valueless in four years.
Explanation / Answer
The ìbreakevenî lease payment would be the payment that results in a zero NPV. At that lease payment, the NPV is zero for both the lessor and the lessee.
The after-tax cost of debt is:
After-tax debt cost = 0.10(1 0.35) = 0.065 or 6.5%
To find the maximum lease payment that would satisfy both the lessor and the lessee, we need to find the payment that makes the NAL equal to zero. Using the NAL equation and solving for the OCF, we find:
NAL = 0 = $6,900,000 OCF(PVIFA6.5%,4)
OCF = $2,014,128.09
The OCF for this lease is composed of the depreciation tax shield cash flow, as well as the aftertax lease payment.
The depreciation tax shield is:
Depreciation tax shield = ($6,900,000/4)(.35) = $603,750
Subtracting out the depreciation tax shield cash flow, we find:
After-tax lease payment = $2,014,128.09 – 603,750 = $1,383,378.09
Since this is the after-tax lease payment, we can now calculate the break-even pretax lease payment as:
Break-even lease payment = $1,383,378.09/(1 0.35) = $2,128,273.98
The after-tax cost of debt is:
After-tax debt cost = 0.10(1 0.35) = 0.065 or 6.5%
To find the maximum lease payment that would satisfy both the lessor and the lessee, we need to find the payment that makes the NAL equal to zero. Using the NAL equation and solving for the OCF, we find:
NAL = 0 = $6,900,000 OCF(PVIFA6.5%,4)
OCF = $2,014,128.09
The OCF for this lease is composed of the depreciation tax shield cash flow, as well as the aftertax lease payment.
The depreciation tax shield is:
Depreciation tax shield = ($6,900,000/4)(.35) = $603,750
Subtracting out the depreciation tax shield cash flow, we find:
After-tax lease payment = $2,014,128.09 – 603,750 = $1,383,378.09
Since this is the after-tax lease payment, we can now calculate the break-even pretax lease payment as:
Break-even lease payment = $1,383,378.09/(1 0.35) = $2,128,273.98
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