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# Assume that Reynolds tax rate is 40% and the equipments depreciation

Assume that Reynold'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 cost of owning or leasing is the present value of cash flows. The discounting rate is the after tax cost of debt. The discounting rate is 10%X(1-0.4) = 6%
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

Reynolds should buy the equipment as the cost is lower