Kohers Inc is considering a leasing arrangement to finance some manufacturing tools that it needs for the next 3 years. The tools will be obsolete and worthless after 3 years. The firm will depreciate the cost of the tools on a straight-line basis over their 3 year life. It can borrow $4,800,000, the purchase price, at 10% and buy the tools, or it can make 3 equal end-of-year lease payments of $2,100,000 each and lease them. The loan obtained from the bank is a 3-year simple interest loan, with interest paid at the end of the year. The firm's tax rate is 40%. Annual maintenance costs associated with ownership are estimated at $240,000 but this cost would be borne by the lessor if it leases. What is the net advantage to leasing(NAL), in thousands?
(Suggestion:Delete 3 zeros from dollars and work in thousands)
To calculate the Net Advantage to Leasing (NAL), we need to compare the present value of the after-tax cash outflows under each option (leasing vs. buying).
Option 1: Leasing
- Annual lease payment (after-tax) = $2,100,000 * (1-0.4) = $1,260,000
- Since there are no maintenance costs for leasing, the total after-tax cash outflows during the 3-year period will be only the lease payments.
Present value of leasing (PV of leasing) = $1,260,000 + $1,260,000 / (1.1)^1 + $1,260,000 / (1.1)^2 = $1,260,000 + $1,140,909 + $1,036,281 = $3,437,190
Option 2: Buying
- The loan amount is $4,800,000
- The loan interest (end of each year) = 10% * $4,800,000 = $480,000
- After-tax loan interest payment = $480,000 * (1-0.4) = $288,000
- The annual depreciation expense for the tools (Straight-line method) = $4,800,000 / 3 = $1,600,000
- The tax shield on depreciation = $1,600,000 * 0.4 = $640,000
- Annual maintenance costs (after tax) = $240,000 * (1-0.4) = $144,000
Let's calculate the present value for buying, which is the sum of after-tax loan payments, maintenance costs, and tax savings on depreciation, all adjusted for the time value of money.
PV of Loan interest payments = $288,000 + $288,000 / (1.1)^1 +$288,000 / (1.1)^2 = $288,000 + $261,818 + $238,017 = $787,835
PV of Maintenance costs = $144,000 + $144,000 / (1.1)^1 + $144,000 / (1.1)^2 = $144,000 + $130,909 + $119,008 = $393,917
PV of Tax shield on depreciation = $640,000 + $640,000 / (1.1)^1 + $640,000 / (1.1)^2 = $640,000 + $581,818 + $529,108 = $1,750,926
Now, we will calculate the present value of buying (PV of buying) by adding up the PV of Loan interest payments, PV of Maintenance costs, and deducting the PV of Tax shield on depreciation.
PV of buying = $787,835 + $393,917 - $1,750,926 = $430,826
Now, let's calculate the net advantage to leasing (NAL) by subtracting the present value of buying from the present value of leasing.
NAL = PV of leasing - PV of buying = $3,437,190 - $430,826 = $3,006,364
So, the net advantage to leasing (NAL) is $3,006,364 in thousands.
To calculate the Net Advantage to Leasing (NAL), we need to compare the costs of leasing with the costs of borrowing and purchasing.
1. Calculate the present value of lease payments:
PV = Lease Payment * (1 - (1 + Interest Rate)^-n) / Interest Rate
PV = 2,100 * (1 - (1 + 0.10)^-3) / 0.10
PV = 2,100 * (1 - 0.7513) / 0.10
PV = 2,100 * 0.2487 / 0.10
PV = 5,215.70 (in thousands)
2. Calculate the present value of the maintenance costs:
PV of Maintenance Costs = Maintenance Costs * (1 - (1 + Interest Rate)^-n) / Interest Rate
PV of Maintenance Costs = 240 * (1 - (1 + 0.10)^-3) / 0.10
PV of Maintenance Costs = 240 * (1 - 0.7513) / 0.10
PV of Maintenance Costs = 240 * 0.2487 / 0.10
PV of Maintenance Costs = 597.69 (in thousands)
3. Calculate the present value of the tax shield:
PV of Tax Shield = (Maintenance Costs * Tax Rate) * (1 - (1 + Interest Rate)^-n) / Interest Rate
PV of Tax Shield = (240 * 0.40) * (1 - (1 + 0.10)^-3) / 0.10
PV of Tax Shield = 96 * (1 - 0.7513) / 0.10
PV of Tax Shield = 96 * 0.2487 / 0.10
PV of Tax Shield = 238.87 (in thousands)
4. Calculate the Net Advantage to Leasing:
NAL = PV of Lease Payments + PV of Maintenance Costs + PV of Tax Shield - Purchase Price
NAL = 5,215.70 + 597.69 + 238.87 - 4,800
NAL = 251.26 (in thousands)
Therefore, the Net Advantage to Leasing (NAL) is $251,260.
To calculate the net advantage to leasing (NAL), we need to compare the costs of leasing to the costs of buying the tools and financing them with the bank loan.
Let's calculate the costs for each option:
1. Buying the tools and financing them with a bank loan:
- The loan amount is $4,800,000.
- The interest rate is 10%.
- The loan term is 3 years.
- The interest is paid at the end of the year.
To calculate the interest expense, we multiply the loan amount by the interest rate:
Interest expense = $4,800,000 * 10% = $480,000 per year.
The depreciation expense is the cost of the tools divided by their useful life:
Depreciation expense = $4,800,000 / 3 = $1,600,000 per year.
The annual maintenance cost is $240,000.
The net cost of ownership for each year is the sum of the interest expense, depreciation expense, and maintenance cost:
Net cost of ownership = $480,000 + $1,600,000 + $240,000 = $2,320,000 per year.
2. Leasing the tools:
- The lease payments are $2,100,000 each year.
- The annual maintenance cost is borne by the lessor and not accounted for in our calculations.
The net cost of leasing for each year is the lease payment:
Net cost of leasing = $2,100,000 per year.
To calculate the Net Advantage to Leasing (NAL), we need to subtract the cost of leasing from the cost of ownership for each year, and also consider the tax savings due to depreciation:
Year 1:
Cost of ownership = $2,320,000
Cost of leasing = $2,100,000
Tax savings due to depreciation = $1,600,000 * 40% = $640,000
Net Advantage to Leasing (NAL) for Year 1 = (Cost of ownership - Cost of leasing) + Tax savings = ($2,320,000 - $2,100,000) + $640,000 = $860,000
Years 2 and 3:
The cost of ownership and cost of leasing remain the same as in Year 1.
Net Advantage to Leasing (NAL) for Years 2 and 3 = (Cost of ownership - Cost of leasing) = ($2,320,000 - $2,100,000) = $220,000 per year.
Finally, we sum up the Net Advantage to Leasing (NAL) for each year to get the total NAL over the 3-year period:
Total NAL = NAL for Year 1 + NAL for Year 2 + NAL for Year 3 = $860,000 + $220,000 + $220,000 = $1,300,000
Therefore, the Net Advantage to Leasing (NAL) is $1,300,000 in thousands.