Tax credit for lease payments problem

Question

ABC Inc. is planning to lease a computer for $3000 per annum, payable in advance, for a period of 4 years. The lease will cover maintenance costs. ABC CFO feels that if he buys the same computer he should be able to sell it at 15% of the purchase price after 4 years. Though, in case of purchase, the company must pay annual maintenance expenses of $500 at the end of each year. The pretax cost of debt of ABC is 10% and its income tax rate is 35%. If ABC buys the computer, it will depreciate it fully in four years. What is the maximum price that ABC should pay for this computer? Assume that ABC can take the tax credit for lease payments a year later.

Answer 1

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 10% (1 – 0.3) = 7%.

Depreciation tax shield lost = (I/4)*0.35 = 0.0875I
Payment shield = 3000*0.35 = $1050
NPV = 0
I – 3000 + (1550 – 0.0875I)*3.426 – (3000*2.648) – 0.0758I = 0

On solving, we get I = $9,024.59

Since it can be sold at 15% of the purchase price after 4 years, the maximum price that ABC should pay for this computer is 15% more of this purchase price, which is $10,378.3