Suppose you are a tax advisor to ABC Corporation, and they are considering whether to lease or purchase a new piece of equipment for their business. You have been asked to provide a tax analysis of the two options to help the corporation make an informed decision.

Option 1: Lease the equipment
ABC Corporation can lease the equipment for $100,000 per year for five years, with the option to purchase the equipment at the end of the lease for $50,000. The lease payments will be deductible for tax purposes.

Option 2: Purchase the equipment
ABC Corporation can purchase the equipment for $400,000, and it has a useful life of five years. The corporation can deduct the depreciation expense for tax purposes using the Modified Accelerated Cost Recovery System (MACRS) over the five-year period.

The corporate tax rate is 21%, and the corporation's cost of capital is 8%.

a) Calculate the after-tax cost of leasing the equipment over the five-year period. Also, calculate the after-tax cost of purchasing the equipment over the same period, taking into account the depreciation expense and the salvage value.

b) Based on your analysis in part (a), make a recommendation to ABC Corporation as to whether they should lease or purchase the equipment. Explain your reasoning, taking into account the corporation's cost of capital and any other relevant factors.

c) Assume that ABC Corporation is able to negotiate a lease agreement with a lower annual lease payment of $80,000. Recalculate the after-tax cost of leasing the equipment over the five-year period, and make a new recommendation to ABC Corporation as to whether they should lease or purchase the equipment. Explain your reasoning.

(Note: For this question, you may assume that the lease and purchase options are economically equivalent, i.e., they provide the same benefits and have the same risks.)