Assume that Reynolds’s tax rate is 40% and the equipment’s depreciation would be

Question

Assume that Reynolds’s tax rate is 40% and the equipment’s depreciation would be $100 per year. If the company leased the asset on a 2-year lease, the payment would be $110 at the beginning of each year. If Reynolds borrowed and bought, the bank would charge 10% interest on the loan. In either case, the equipment is worth nothing after 2 years and will be discarded. Should Reynolds lease or buy the equipment?

The answers in the book are as follows:
Cost of owning = $127
Cost of leasing = $128

I really need to understand how they are coming up with these calculations.
Thanks

Explanation / Answer

Cost of Leasing - The payments are $110 per year payable at the beginning. The cash flow is the after tax cost. The after tax cost is 110X(1-0.4) = $66. Since the payments are beginning of the year, 1st payment is now and second is at the beginning of year 2 or end of year 1. The PV is $66 for payment now + 66/1.06 for payment end of year 1 = 66+62 = $128 The total cost is -$128 since it is an outflow. Cost of Owning - Since the depreciation is 100 per year, the cost of the asset is $200. Depreciation will give depreciation tax shield, which is 100X40%=$40 per year at the end of each year. The PV of depreciation tax shield is 40/1.06 + 40/1.06^2 = $73 The outflow is -$200 for purchase and inflow is depreciation benefit is $73 The cost of owning = -200+73 = -$127

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