What the lease-versus-buy decision is really asking
You are not deciding whether to acquire the asset. That decision is separate, and it is made with an ordinary net present value analysis of what the asset earns. The lease-versus-buy question assumes you have already decided you want the machine, and asks only how to pay for it: rent it from a lessor, or buy it with borrowed money.
Because the operating cash flows are identical under both routes, they cancel. What is left is a pure financing comparison, and every remaining cash flow is either contractual or set by the tax code: a fixed rental, a depreciation schedule, a tax rate, a residual you either keep or do not. Nothing in that list carries business risk, so nothing in it justifies a business discount rate.
That is the single idea that makes the analysis work. A lease is a substitute for a secured loan, so it is priced against a secured loan. You discount at your after-tax cost of debt — the rate on the borrowing the lease displaces, reduced by the tax deduction on that interest. Using the firm's weighted average cost of capital here is the classic error: it applies an equity risk premium to a stream of contractual payments, and it systematically flatters whichever option has the flows furthest out in time.
Building each side of the comparison
Take the two costs in turn, both expressed as present-value outflows over the lease term.
The cost of owning
You pay the purchase price today, in full, at time zero. Against that you receive two things. First, a stream of depreciation tax shields: each year's tax depreciation multiplied by your marginal rate, since that deduction reduces the tax you write a cheque for. Second, the asset itself at the end of the term, which you sell for its residual value. The sale is taxable on the gain over tax book value, so what you keep is S − T(S − BV). When the asset is fully depreciated, book value is zero and you keep only S(1 − T).
Net it: PV(own) = P − PV(shields) − PV(after-tax residual).
The cost of leasing
You pay the rental each period and deduct it, so the cash cost is L(1 − T) each time. Discount that stream over the term. If the rentals are billed in advance — which most equipment leases are — the first one falls at time zero and is not discounted at all, which raises the present value relative to arrears billing by roughly one period's interest.
You get no depreciation, because you do not own the asset for tax purposes, and you get no residual, because you hand the equipment back. Both of those absences are already priced: they sit in the owning column as deductions, so the comparison charges the lease for giving them up.
And the difference
NAL is PV(own) − PV(lease). Positive means leasing is cheaper. Since NAL is linear in the rental, you can invert it directly for the rental that makes the two identical: L* = PV(own) ÷ [(1 − T) × annuity factor]. That break-even rental is the most useful single number the model produces, because it is the ceiling you can quote back to the lessor.
Worked example: a $500,000 machine on a five-year lease
A manufacturer can buy a machine for $500,000 or lease it for $105,000 a year for five years, payable at the start of each year. The firm's marginal tax rate is 21%, it borrows secured at 7.5%, the machine is five-year MACRS property, and it expects to sell the machine for $100,000 after five years. Every figure below is rounded to the cent for display while the calculator carries full precision, so adding the printed components can leave you a cent adrift of the printed total.
- Set the discount rate. 7.5% × (1 − 0.21) = 5.925%. Discount factors for years one to five are 0.9440642, 0.8912572, 0.8414040, 0.7943394 and 0.7499074.
- Value the depreciation shields. MACRS five-year percentages are 20%, 32%, 19.2%, 11.52% and 11.52%, so deductions of $100,000, $160,000, $96,000, $57,600 and $57,600. At 21% those are shields of $21,000, $33,600, $20,160, $12,096 and $12,096. Multiplying each by its discount factor gives $19,825.35, $29,946.24, $16,962.71, $9,608.33 and $9,070.88, for a total of $85,413.50.
- Value the residual. Accumulated MACRS over five years is 94.24%, so book value is 500,000 × 0.0576 = $28,800. Selling at $100,000 creates a gain of 100,000 − 28,800 = $71,200, taxed at 21% for $14,952, leaving $85,048. Discounted five years: 85,048 × 0.7499074 = $63,778.12.
- Total the cost of owning. 500,000 − 85,413.50 − 63,778.12 = $350,808.37.
- Total the cost of leasing. The annuity-due factor is 1 + 0.9440642 + 0.8912572 + 0.8414040 + 0.7943394 = 4.4710648. The after-tax rental is 105,000 × 0.79 = $82,950. So 82,950 × 4.4710648 = $370,874.83.
- Subtract. NAL = 350,808.37 − 370,874.83 = −$20,066.46. Buying is cheaper by about $20,066 in today's money, which is 20,066 ÷ 500,000 = 4.0% of the purchase price.
- Find the break-even rental. 350,808.37 ÷ (0.79 × 4.4710648) = 350,808.37 ÷ 3.5321412 = $99,318.90 a year.
So the quote is 105,000 − 99,318.90 = $5,681 a year too expensive. That is the number to negotiate with, and it is far more actionable than the NAL itself: a lessor who cannot reach $99,319 has told you to buy.
How to read the result, and what moves it
The sign is the decision and the magnitude is the margin of safety. An NAL of −$20,066 on a $500,000 asset is about 4% of the purchase price, which is a real but not overwhelming preference: a modest change in the residual assumption or the borrowing rate can flip it. An NAL inside 1% of the purchase price should be treated as a tie and settled on the qualitative grounds below.
Four inputs move the answer most, and it is worth knowing which way each pushes at your own numbers rather than in general:
The tax rate. Depreciation shields belong to the owner, so a tax-paying buyer captures them and a loss-making one does not. Set the rate to zero and watch the owning column lose its shields entirely; that is precisely why lessors, who are usually full taxpayers, can profitably lease to companies with net operating losses. It is the oldest genuine economic rationale for leasing.
The residual. The buyer keeps it; the lessee does not. A high residual therefore favours buying, and residual assumptions are where lease-versus-buy analyses go wrong most often, because the number is a forecast dressed as an input. Re-run the model at half your residual before committing.
The discount rate. A higher rate discounts distant flows harder. Since the residual is the single most distant flow in the owning column, raising the rate weakens the buy case, while the rentals — spread evenly across the term — are less affected. Use the override field to test this rather than guessing the direction.
Payment timing. Switching from arrears to advance billing raises the present value of the rentals by a factor of (1 + r), which at 5.925% is about 5.9% of the lease cost. Lessors quote in advance by default. Comparing an in-advance quote against an in-arrears model understates the lease by that much.
Then set the model aside for the things it does not price: flexibility to walk away from an asset with obsolescence risk, service and maintenance bundled into the rental, covenant capacity, and whether you actually have $500,000 today. Those are real and they belong in the decision — but state them as judgements next to a number, not instead of one.
MACRS depreciation percentages, GDS half-year convention
| Recovery year | 3-year property | 5-year property | 7-year property |
|---|---|---|---|
| 1 | 33.33% | 20.00% | 14.29% |
| 2 | 44.45% | 32.00% | 24.49% |
| 3 | 14.81% | 19.20% | 17.49% |
| 4 | 7.41% | 11.52% | 12.49% |
| 5 | — | 11.52% | 8.93% |
| 6 | — | 5.76% | 8.92% |
| 7 | — | — | 8.93% |
| 8 | — | — | 4.46% |
| Total | 100.00% | 100.00% | 100.00% |
Each class runs one year longer than its name because the half-year convention treats the asset as placed in service at mid-year, splitting the first year's deduction across the first and last recovery years. Typical assignments: 5-year covers computers, office machinery, light trucks and much production equipment; 7-year covers office furniture and many manufacturing assets. Check the asset class in Publication 946 rather than assuming.
ASC 842 changed the accounting, not the economics
Under FASB ASC 842 almost every lease longer than twelve months puts a right-of-use asset and a lease liability on the balance sheet, so the old motive of keeping equipment finance off the balance sheet is gone for US GAAP filers. The classification into operating and finance leases survives, and it still changes how the expense is presented in the income statement, but it does not change the cash flows this calculator discounts. Treat the accounting outcome as a separate question you answer after the economics.
The tax treatment is a different matter and it does change the cash flows. A lease that the IRS treats as a conditional sale rather than a true lease gives the lessee the depreciation and denies the rental deduction, which reverses two of the terms in this model. If your lease has a bargain purchase option or a term covering most of the asset's life, get the characterisation confirmed before relying on the result.
Assumptions and limits you should know about
- Annual periods. The model discounts once a year. A monthly lease discounted monthly gives a slightly different present value; entering twelve monthly payments as one annual figure is accurate to within roughly half a year's interest on one payment.
- The rental deduction is taken with the payment. For an in-advance lease the deduction actually accrues over the following year, so the model slightly overstates the timing benefit of the tax saving on the first rental.
- No half-year disposal convention. The full table percentage is taken in each year through the end of the term. Selling a MACRS asset part-way through a recovery year normally allows only half that year's deduction, so shields are marginally overstated when the term ends inside the schedule.
- Constant tax rate, always usable. Shields are worth their full face value in the year they arise. A firm with losses, credits or a rate change should model the year the deduction is actually used, not the year it is generated.
- Bonus depreciation and section 179 are not modelled. Where they apply, they pull shields forward and strengthen the buy case. Use the straight-line option with a one-year life to approximate a full first-year write-off.
- No maintenance, insurance or end-of-term charges. If the rental bundles service that you would otherwise buy, add that cost to the owning side before comparing. Return conditions, excess-use charges and restoration obligations belong there too.
- No default or credit differences. Both routes are assumed to be honoured. A lease with a tighter security package than your bank debt is not the same instrument, whatever the arithmetic says.
When to use a different tool
If the question is whether the asset is worth acquiring at all, the answer is an NPV or IRR on its operating cash flows, and the financing question only arises afterwards. If you want to know how quickly the investment repays itself, the discounted payback period answers that on the same discounted basis.
If you want the discount rate itself, the after-tax cost of debt calculator builds it properly from a coupon or a yield rather than from a headline rate. If the depreciation side is what you actually need — a book schedule rather than a tax schedule — the straight-line depreciation schedule calculator produces the year-by-year expense and carrying value.
There is also a second, equivalent way to present this analysis: compute the internal rate of return of the incremental lease-minus-buy cash flow stream and compare it against the after-tax borrowing rate. It gives the same decision as NAL whenever the incremental stream changes sign only once, and it is the form some credit committees prefer. NAL is the more robust presentation because it is stated in dollars and does not misbehave on unconventional cash flow patterns.
Key terms
- Net advantage to leasing (NAL)
- The present value cost of owning minus the present value cost of leasing, both after tax and both discounted at the after-tax cost of debt. Positive favours the lease.
- Depreciation tax shield
- The cash tax saved by a depreciation deduction: the deduction multiplied by the marginal tax rate. It belongs to whoever owns the asset for tax purposes.
- Annuity due
- A stream of equal payments made at the start of each period rather than the end. Its present value is (1 + r) times that of the equivalent ordinary annuity.
- Residual value
- What the asset is expected to be worth at the end of the term. The buyer captures it net of tax on any gain over book value; the lessee does not.
- True lease
- A lease the IRS respects as a rental, so the lessor takes depreciation and the lessee deducts the rent. A conditional sale disguised as a lease reverses both.