Net advantage to leasing) Arkansas Instruments (AI) can purchase a sonic cleaner for
$1,000,000.
The machine has a five-year life and would be depreciated straight line to a
$100,000 salvage value.
Hibernia Leasing will lease the same machine to AI for five annual
$300,000 lease payments paid in arrears (at the end of each year). AI is in the 40% tax
bracket. The before-tax cost of borrowing is 10%, and the after-tax cost of capital for the
project would be 12%.
a. What cash flows does AI realize if it leases the machine instead of buying it?
b. What is the net advantage to leasing (NAL)?
$106,000
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To calculate the cash flows and net advantage to leasing, we need to consider the cash flows related to purchasing the machine and the cash flows related to leasing the machine.
a. Cash flows if AI leases the machine instead of buying it:
- Lease payments: $300,000 per year for 5 years.
- Tax shield from lease payments: Tax savings on lease payments due to tax-deductible expense.
- Tax savings = Lease payments * Tax rate = $300,000 * 0.40 = $120,000 per year.
- After-tax cost of lease payments: Lease payments - Tax savings.
- After-tax cost = Lease payments - Tax savings = $300,000 - $120,000 = $180,000 per year.
b. Net advantage to leasing (NAL):
To calculate the NAL, we compare the present value of the cash flows from leasing with the present value of the cash flows from buying.
Step 1: Calculate the present value of the lease payments:
We will discount the after-tax cost of lease payments using the after-tax cost of capital (12%).
- PV of lease payments = $180,000 * (1 - (1 + 0.12)^-5) / 0.12 = $667,203.85
Step 2: Calculate the present value of the tax shield:
We will discount the tax savings on lease payments using the after-tax cost of borrowing (10%).
- PV of tax shield = $120,000 * (1 - (1 + 0.10)^-5) / 0.10 = $481,498.53
Step 3: Calculate the present value of the salvage value (at the end of the 5-year life):
We will discount the salvage value using the after-tax cost of capital (12%).
- PV of salvage value = $100,000 / (1 + 0.12)^5 = $56,197.92
Step 4: Calculate the net advantage to leasing (NAL):
- NAL = PV of lease payments + PV of tax shield - PV of salvage value - Cost of buying
- Cost of buying = $1,000,000
- NAL = $667,203.85 + $481,498.53 - $56,197.92 - $1,000,000
- NAL = $92,504.46
Therefore, the net advantage to leasing (NAL) is $92,504.46.
To determine the cash flows if AI leases the machine instead of buying it, we need to consider the lease payments, tax implications, depreciation, and salvage value.
a. Cash flows if AI leases the machine:
- AI will make five annual lease payments of $300,000 each, paid at the end of each year.
- The lease payments are tax deductible, so we need to calculate the tax savings based on AI's tax bracket of 40%. The tax savings can be calculated as: Lease Payments * Tax Rate.
- Since AI is leasing the machine, there is no salvage value or depreciation to consider.
b. To calculate the net advantage to leasing (NAL), we need to compare the cash flows if AI buys the machine versus leasing it. The formula for NAL is as follows:
NAL = Cost of Leasing - Cost of Buying + Tax Savings on Leasing
Now let's calculate the cash flows and NAL step by step.
1. Cash flows if AI buys the machine:
- Initial cost: $1,000,000
- Salvage value: $100,000
- Depreciation expense per year = (Initial Cost - Salvage Value) / Life of the machine = ($1,000,000 - $100,000) / 5 = $180,000 per year (rounded to the nearest thousand).
- After-tax cost of capital: 12%
- Tax savings on depreciation = Depreciation Expense * Tax Rate = $180,000 * 40% = $72,000 per year.
For each year, the cash flows would be:
Year 1:
- Cash outflow: Initial cost
- Tax savings: Depreciation expense
Years 2-5:
- Tax savings: Depreciation expense
Year 5:
- Tax savings: Depreciation expense
- Cash inflow: Salvage value
2. Cash flows if AI leases the machine:
- Lease payments: $300,000 per year
- Tax savings on lease payments = Lease Payments * Tax Rate = $300,000 * 40% = $120,000 per year.
NAL calculation:
NAL = (Lease Payments - Tax Savings on Lease Payments) - (Cost of Buying - Tax Savings on Depreciation)
Substituting the values, we have:
NAL = ($300,000 * 5 - $120,000 * 5) - ($1,000,000 - $72,000 * 5)
Now you can plug in the numbers and calculate the net advantage to leasing (NAL).