You work for a nuclear research laboratory that is contemplating leasing a diagn

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 $2 million and it would be depreciated straight-line to zero over 4 years. Because of radiation contamination, it will actually be completely valueless in 4 years. Assume the tax rate is 33 percent. You can borrow at 6 percent before taxes. How much would the lease payment have to be in order for both the lessor and the lessee to be indifferent about the lease?

a. $500,000

b. $521,909

c. $552,200

d. $563,333

e. $576,477

Explanation / Answer

The break even lease payment can be calculated with the use of following formula:

Break Even Lease Payment = After-Tax Lease Payment/(1-Tax Rate)

After-Tax Lease Payment = OCF - Depreciation Tax Shield

OCF can be calculated with the use of PMT function/formula of EXCEL/Financial Calculator. The function/formula of PMT is PMT(Rate,Nper,-PV,FV) where Rate = After-Tax Cost of Debt, Nper = Period, PV = Cost of Scanner and FV = Future Value (if any).

___________

After-Tax Cost of Debt = 6*(1-33%) = 4.02%

________

Solving for OCF, we use Rate = 4.02%, Nper = 4, PV = -$2,000,000 and FV = 0

Using these values provided in the function/formula for PMT, we get,

OCF = PMT(4.02%,4,-2000000,0) = $551,239.82

Depreciation Tax Shield = Cost/Estimated Life*(Tax Rate) = 2,000,000/4*(33%) = $165,000

________

After-Tax Lease Payments = 551,239.82 - 165,000 = $386,239.82

Break Even Lease Payment = 386,239.82/(1-33%) = $576,477 (which is Option E)

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