Question

An asset costs $640,000 and will be depreciated in a straight-line manner over its three-year life. It will have no salvage value. The lessor can borrow at 5.5 percent and the lessee can borrow at 7 percent. The corporate tax rate is 23 percent for both companies.

a.	What lease payment will make the lessee and the lessor equally well off? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.

Assume that the lessee pays no taxes and the lessor is in the 23 percent tax bracket. For what range of lease payments does the lease have a positive NPV for both parties? (Enter your answers from lowest to highest. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

    

Answer 1

a)

The different borrowing rates are irrelevant. A basic tenant of capital budgeting is that the return of a project depends on the risk of the project. Since the lease payments are affected by the riskiness of the lessee, the lessee’s cost of debt is the appropriate interest rate for the analysis by both companies.

Since both companies have the same tax rate, there is only one lease payment that will result in a zero NAL for each company. We will calculate cash flows from the depreciation tax shield first. The depreciation tax shield is:

Depreciation tax shield = ($640,000 / 3)(0.23)

Depreciation tax shield = $49067

The aftertax cost of debt is the lessee’s cost of debt, which is

Aftertax debt cost = 0.7(1 –0.23)

Aftertax debt cost = .0539, or 5.39%

Using all of this information, we can calculate the lease payment as:

NAL = 0 = $640,000 – PMT(1 – 0.23)(PVIFA 5.39%,3) - $49067(PVIFA 5.39%,3)

0 = $640,000 – PMT(1 – 0.23)(2.7035) - $49067(2.7035)

0 = $640,000 – PMT(2.081695‬) - 1,32,652.6

PMT = $2,43,718.41

b)

Since the lessor’s tax bracket is unchanged, the zero NAL lease payment is the same as we found in part a. The lessee will not realize the depreciation tax shield, and the after tax cost of debt will be the same as the pretax cost of debt. So, the lessee’s maximum lease payment will be:

NAL = 0 = –$640,000 + PMT (PVIFA 7%,3)

0 = –$640,000 + PMT (2.6243)

PMT = $2,43,874.55

Both parties have positive NAL for lease payments between $2,43,718.41 and $2,43,874.55

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