Answers to Chapter Review and Self Test Problems

26.1 If you buy the machine, the depreciation will be $25,000 per year. This generates a tax shield of $25,000 X .34 = $8,500 per year, which is lost if the machine is leased. The aftertax lease payment would be $27,000 X (1 - .34) = $17,820. Looking back at Table 26.2, you can lay out the cash flows from leasing as follows:

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VIII. Topics in Corporate Finance

26. Leasing

© The McGraw-Hill Companies, 2002

PART EIGHT Topics in Corporate Finance

Lease versus Buy

Year 0

Year 1

Year 2

Year 3

Aftertax lease payment Lost depreciation tax shield Cost of machine

+$75,000

-$17,820 - 8,500

-$17,820 - 8,500

-$17,820 - 8,500

Total cash flow

+$75,000

-$26,320

-$26,320

-$26,320

The appropriate discount rate is the aftertax borrowing rate of .10 X (1 - .34) = 6.6 percent. The NPV of leasing instead of borrowing and buying is:

NPV = $75,000 - 26,320 X (1 - 1/1.0663)/.066 = $5,420.09

so leasing is cheaper.

26.2 Assuming that the lessor is in the same tax situation as the lessee, the NPV to the lessor is -$5,420.09. In other words, the lessor loses precisely what the lessee makes.

For both parties to break even, the NPV of the lease must be zero. With a 6.6 percent rate for three years, a cash flow of -$28,370.26 per year has a present value of - $75,000. The lost depreciation tax shield is still - $8,500, so the aftertax lease payment must be $19,870.26. The lease payment that produces a zero NPV is therefore $19,870.26/.66 = $30,106.45 per year.

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