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 $5,000,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it actually will be completely valueless in four years. The tax rate is 25 percent and you can borrow at 7 percent before taxes.

What would the lease payment have to be for both lessor and lessee to be indifferent about the lease? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Step 1: Calculate After-Tax Cost of Debt

The after-tax cost of debt is determined as below:

After-Tax Cost of Debt = Cost of Borrowing*(1-Tax Rate) = 7%*(1-25%) = 5.25%

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Step 2: Calculate Payment that Equates NAL to Zero

The payment that equates NAL to zero is arrived as follows:

NAL = 0 = Cost of Scanner - Operating Cash Flow*PVIFA(After-Tax Cost of Debt,Years) [where PVIFA is Present Value Interest Factor for an Annuity]

Substituting values in the above formula, we get,

NAL = 0 = 5,000,000 - Operating Cash Flow*PVIFA(5.25%,4)

Operating Cash Flow = 5,000,000/3.5255 = $1,418,256.79

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Step 3: Calculate Depreciation Tax Shield and After-Tax Lease Payment

The value of depreciation tax shield and after-tax lease payment is calculated as below:

Depreciation Tax Shield = Annual Depreciation*Tax Rate = (5,000,000/4)*25% = $312,500

After-Tax Lease Payment = Operating Cash Flow - Depreciation Tax Shield = 1,418,256.79 - 312,500 = $1,105,756.79

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Step 4: Calculate Break-Even Lease Payment

The value of break-even lease payment is determined as follows:

Break-Even Lease Payment = After-Tax Lease Payment/(1-Tax Rate) = 1,105,756.79/(1-25%) = $1,474,342.38 (answer)

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Notes:

There can be a slight difference in final answer on account of rounding off values.