Your firm is considering leasing a new radiographic device. The lease lasts for three years. The lease calls for four payments of $25,000 per year with the first payment occurring immediately. The computer would cost $140,000 to buy and would be straight-line depreciated to a zero salvage value over three years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 12%. The corporate tax rate is 40%.
15000
To determine whether it is more financially advantageous to lease or buy the radiographic device, we need to compare the costs of both options and consider the time value of money.
Let's first calculate the cost of buying the device:
1. Calculate the depreciation expense per year:
Depreciation expense = (Cost of the device - Salvage value) / Useful life
Depreciation expense = ($140,000 - $0) / 3 = $46,666.67 per year
2. Calculate the after-tax cash flow per year for depreciation expense:
After-tax cash flow = Depreciation expense * (1 - Tax rate)
After-tax cash flow = $46,666.67 * (1 - 0.40) = $28,000 per year
3. Calculate the after-tax cash flow for the initial purchase cost:
After-tax cash flow initial = Cost of the device * (1 - Tax rate)
After-tax cash flow initial = $140,000 * (1 - 0.40) = $84,000
4. Determine the present value of the cash flows using the borrowing rate of 12%:
PV = Cash flow / (1 + r)^n
PV = ($28,000 / (1 + 0.12)^1) + ($28,000 / (1 + 0.12)^2) + ($28,000 / (1 + 0.12)^3) + ($84,000 / (1 + 0.12)^3)
PV = $106,118.11
Now let's calculate the cost of leasing the device:
1. Calculate the present value of the lease payments:
PV = Payment / (1 + r)^n
PV = ($25,000 / (1 + 0.12)^1) + ($25,000 / (1 + 0.12)^2) + ($25,000 / (1 + 0.12)^3) + ($25,000 / (1 + 0.12)^3)
PV = $77,503.55
2. Calculate the tax shield of the lease payments:
Tax shield = Lease payment * Tax rate
Tax shield = $25,000 * 0.40 = $10,000 per year
3. Determine the present value of the tax shield using the borrowing rate of 12%:
PV = Tax shield / (1 + r)^n
PV = ($10,000 / (1 + 0.12)^1) + ($10,000 / (1 + 0.12)^2) + ($10,000 / (1 + 0.12)^3) + ($10,000 / (1 + 0.12)^3)
PV = $30,834.75
4. Calculate the net present value (NPV) by subtracting the present value of the lease payments from the present value of the tax shield:
NPV = PV of tax shield - PV of lease payments
NPV = $30,834.75 - $77,503.55
NPV = -$46,668.80
The NPV for leasing the device is negative, indicating that it is more cost-effective to buy the device rather than leasing it. Buying the radiographic device results in a lower net cost compared to leasing it.