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Purchaing or leasing problem

Crawford Corporation is planning to lease a machine for the next 4 years for an annual lease payment of $3,000 paid in advance, plus a non-refundable initial fee of $3,000. There is a 1-year delay for the tax benefits of leasing. Crawford may buy the machine, depreciate it fully over the next 4 years, and then sell it for 10% of the purchase price. Crawford can borrow the money at 9% interest rate to finance the purchase, and its tax rate is 30%. Compute the price of the machine, which will make purchasing or leasing to be equally costly.

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If the company has to be indifferent to leasing or buying, the net present value has to be set at zero. Let I be the price of machine. The after-tax cost of borrowing is 9% (1 – 0.3) = 6.3%.

Depreciation tax shield lost = (I/4)*0.3 = 0.075I
Payment shield = 3000*0.3 = $900
NPV = 0
I – 3000 – 3000 – (3000)(2.658)  + (900 - 0.075I)*3.44 – 0.07I*0.7832 = 0
I – 6000 – 5582.31 – 0.258I – 0.0548I = 0
0.687I = 10877.44
I = $15,831.66

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