Question

The Wildcat Oil Company is trying to decide whether to lease or buy a new computer-assisted drilling system for its oil exploration business. Management has decided that it must use the system to stay competitive; it will provide $4.7 million in annual pretax cost savings. The system costs $9.7 million and will be depreciated straight-line to zero over five years. Wildcat’s tax rate is 22 percent and the firm can borrow at 6 percent. Lambert’s policy is to require its lessees to make payments at the start of the year. Suppose it is estimated that the equipment will have an aftertax residual value of $1,040,000 at the end of the lease. What is the maximum lease payment acceptable to Wildcat?

Answer 1

Step 1: Calculate Depreciation Tax Shield

The value of depreciation tax shield is determined as below:

Depreciation Tax Shield = Annual Depreciation*Tax Rate = (9,700,000/5)*22% = $426,800

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Step 2: Calculate After-Tax Cost of Debt

The after-tax cost of debt is arrived as follows:

After-Tax Cost of Debt = Cost of Borrowing*(1-Tax Rate) = 6%*(1-22%) = 4.68%

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Step 3: Calculate After-Tax Lease Payment

The value of after-tax lease payment can be arrived with the use of equation given below:

NAL = 0 = Cost of System - After-Tax Lease Payment*(1+After-Tax Cost of Debt)*PVIFA(After-Tax Cost of Debt,Years) - Depreciation Tax Shield*PVIFA(After-Tax Cost of Debt,Years) - After-Tax Residual Value/(1+After-Tax Cost of Debt)^Years

Substituting values in the above formula, we get,

NAL = 0 = 9,700,000 - After-Tax Lease Payment*(1+4.68%)*PVIFA(4.68%,5) - 426,800*PVIFA(4.68%,5) - 1,040,000/(1+4.68%)^5

Solving further, we get,

NAL = 0 = 9,700,000 - After-Tax Lease Payment*(1.0468)*4.3680 - 426,800*4.3680 - 827,398.58

NAL = 0 = 9,700,000 - 4.5725*After-Tax Lease Payment - 1,864,281.05 - 827,398.58

After-Tax Lease Payment = 7,008,320.36/4.5725 = 1,532,721.53

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Step 4: Calculate Maximum Lease Payment Acceptable to Wildcat

The maximum lease payment acceptable to Wildcat is calculated as follows:

Maximum Lease Payment Acceptable to Wildcat = After-Tax Lease Payment/(1-Tax Rate) = 1,532,721.53/(1-22%) = $1,965,027.60

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Notes:

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