ANB Leasing is planning to lease an asset costing $210,000. The lease period will be 6 years. At the end of 6 years, the salvage value is estimated to be $30,000. The asset will be depreciated on a straight-line basis of $30,000 per year over the 6-year period. ANB's marginal income tax rate is 40%, but its average tax rate is only 31.5%. Assuming ANB Leasing requires a 12% after-tax rate of return on the lease, determine the required annual beginning of the year lease payments.

Question

Quizplus · Accepted Answer

First, calculate the annual depreciation:
Depreciation = (Cost - Salvage Value) / Lease Period = ($210,000 - $30,000) / 6 = $30,000

Next, calculate the after-tax salvage value:
After-tax Salvage Value = Salvage Value - (Salvage Value - Book Value) x Marginal Tax Rate
= $30,000 - ($30,000 - $0) x 40% = $18,000

The after-tax lease cost per year is the sum of three components: (1) after-tax depreciation, (2) after-tax interest expense, and (3) after-tax decrease in the value of the salvage. The formula is:

After-tax lease cost per year = (Depreciation - After-tax salvage value) / Present value of an annuity due of $1 per year for 6 years at a 12% discount rate.

Using a financial calculator, the present value of an annuity due of $1 per year for 6 years at a 12% discount rate is 4.9676.

After-tax lease cost per year = ($30,000 - $18,000) / 4.9676 = $2,411

Finally, adding back depreciation, the pre-tax lease payment is $32,411 ($30,000 depreciation + $2,411 after-tax lease cost per year). The pre-tax lease payment is equivalent to $22,303 after-tax lease payment ($32,411 x (1 - 31.5%)). Using a financial calculator, the present value of an annuity due of $1 per year for 6 years at a 12% discount rate is 4.9676. The required annual beginning of the year lease payment is the present value of the after-tax lease payment:

Required annual beginning of the year lease payment = $22,303 / 4.9676 = $4,486

Therefore, the required annual beginning of the year lease payment is $52,653. The answer is (C).

ANB Leasing Is Planning to Lease an Asset Costing $210,000