Big Sky Mining Company must install $1.5 million of new machinery in its Nevada mine. It can obtain a bak loan for 100% of the purchase price, or it can lease the machinery. Assume the following facts apply:
a) The machinery fall s into the MACRS-3year class
b)Under either the lease or the purchase, Big Sky must pay for the insurance, property taxes and maintenance
c) The firm's tax rate is 40%
d) The loan would have an interest rate of 15%
e) The lease terms call for $400,00 payments at the end of each the next 4 years
f) Assume that Big Sky Mining has no use for the machine beyond expiration of the lease. The machine has an estimated residual value of $250,000 at the end of the year.
Determine:
a. Should the equipment be leased or purchased?
Before proceeding with our NPV analysis we must determine the schedule of depreciation charges for this new equipment.
MACRS 3-year Depreciation Schedule
Year 1 2 3 4
Depr. Rate
Depr. Exp.
Tax Shield
We can now construct our table of incremental cash flows from these two alternatives. Remember, that the appropriate discount rate in this scenario is the after tax cost of borrowing, or: 15%*(1-40%) = 9%.
NPV LEASE ANALYSIS OF INCREMENTAL CASH FLOWS
Cost of ownership Year = 0 1 2 3 4
Loan proceeds
Purchase cost
Interest payments
Tax Shield
After-tax interest payment
Principal payment
Tax savings from depreciation
Annual Cost Savings
Tax on Savings
After-tax Cost Savings
Salvage value
Taxes on salvage value
Net cash flow from ownership
PV cost of ownership
Cost of leasing
Annual lease payments
Tax Shield
After-tax Lease Payments
Annual Cost Savings
Tax on Savings
After-tax Cost Savings
Net cash flow from leasing
PV cost of leasing
Cost Comparison
PV ownership cost @ 9%
PV of leasing @ 9%
Net Advantage to Leasing
To determine whether the equipment should be leased or purchased, we need to compare the net present value (NPV) of the costs associated with each option.
First, let's calculate the MACRS depreciation schedule for the equipment. Based on the information given, the machinery falls into the MACRS 3-year class. The depreciation expense for each year can be calculated using the MACRS depreciation rates.
Year | Depreciation Rate | Depreciation Expense
-------------------------------------------------------
1 | 33% | $0.33 million
2 | 45% | $0.45 million
3 | 15% | $0.15 million
4 | 7% | $0.07 million
Next, we can calculate the tax shield, which represents the tax savings from the depreciation expense. The tax shield is equal to the depreciation expense multiplied by the tax rate.
Year | Tax Shield
---------------------
1 | $0.33 million * 40% = $0.132 million
2 | $0.45 million * 40% = $0.18 million
3 | $0.15 million * 40% = $0.06 million
4 | $0.07 million * 40% = $0.028 million
Now let's calculate the annual cost savings, which include the tax savings from depreciation and the after-tax cost savings from insurance, property taxes, and maintenance. Since we need to calculate the net present value, we will discount the annual cost savings using the appropriate discount rate of 9%.
For the purchase option:
- Principal payment: This is the loan amount, which is $1.5 million. We need to calculate the interest payments separately.
- Interest payments: The annual interest payment is calculated based on the loan amount and the interest rate of 15%.
- After-tax interest payment: This is calculated by multiplying the interest payment by (1 - tax rate).
- Tax savings from depreciation: This is the tax shield calculated earlier.
- After-tax cost savings: This is the sum of the after-tax interest payment and the tax savings from depreciation.
- Net cash flow from ownership: This is the sum of the after-tax cost savings and the salvage value at the end of the year ($0.25 million).
- PV cost of ownership: This is the present value of the net cash flow from ownership, discounted at the appropriate discount rate of 9%.
For the lease option:
- Annual lease payments: This is given as $0.4 million for each of the next 4 years.
- Tax savings from depreciation: Same as calculated for the purchase option.
- After-tax cost savings: This is the sum of the after-tax lease payments and the tax savings from depreciation.
- Net cash flow from leasing: This is the sum of the after-tax cost savings and the salvage value at the end of the year ($0.25 million).
- PV cost of leasing: This is the present value of the net cash flow from leasing, discounted at the appropriate discount rate of 9%.
Finally, we can compare the PV cost of ownership with the PV cost of leasing to determine the net advantage to leasing. If the net advantage to leasing is positive, then leasing is more favorable. If it is negative, then purchasing is more favorable.
By comparing the net advantage to leasing, we can determine whether the equipment should be leased or purchased.