What is the difference between the residual and the resale value?

The residual is written into the contract and prices the lease — it decides how much depreciation you are charged for, and therefore the monthly payment. The resale value is what the car actually fetches at the end. The first sets the payment, the second decides whether leasing beat buying, and they are frequently far apart.

What is a money factor?

It is the lease's interest rate expressed in a form that is applied to the balance without dividing by months. Divide the annual rate by 2400 to get it: 7% becomes 0.0029167. Multiply that by the sum of the capitalized cost and the residual to get the monthly rent charge, which is why the number looks small and is not.

How is the monthly lease payment built?

Two parts. Depreciation is the capitalized cost minus the residual, divided by the term: (36,000 − 20,000) ÷ 36 = 444.44. The rent charge is the average of the same two figures, times the money factor: 163.33. Add them for the payment, 607.77.

Can leasing actually be cheaper?

Yes, and the case that shows it is a contract residual above the market value. At a 65% residual over 60 months with the car reselling for 20,000, the lessee pays depreciation on only 10,000 and the lease comes out 1,920.63 ahead. The catch is that buying the car out at the end means paying 26,000 for something worth 20,000, so the advantage only holds if you walk away.

Does a bigger down payment make leasing better?

It lowers the payment and slightly worsens the comparison, which is the opposite of what most people expect. In the table, going from nothing down to 16,000 down takes the payment from 730.56 to 239.44 while the gap in favour of buying widens from 7,837.11 to 7,942.04. A down payment on a lease is prepaid depreciation — it reduces the monthly figure without reducing the total.

What is left out of this comparison?

All fees on both sides, mileage caps, wear and disposition charges, tax, and the possibility that the two sides carry different rates. It also assumes both paths end without the car. Read it as a comparison of the two structures rather than of two specific offers. And no currency is attached to any figure.

Lease Calculator

Result

7,863.00

Cost difference (lease minus buy)

Monthly payment: 607.77
Total cost of the lease: 25,879.72
Net cost of buying: 18,016.72
Monthly payment to buy: 1,111.58
Residual value: 20,000.00
Depreciation per month: 444.44
Finance charge per month: 163.33
Total finance charge: 5,879.88
Total cost of buying: 44,016.72
Money factor: 0.0029167

A lease is priced by a number that does not have to be true. That number is the residual: the value the contract says the car will still be worth at the end, which sets how much depreciation you are charged for and therefore what the monthly payment is. The market's opinion of that same car at the end of the term is a different number, and this calculator keeps them apart because they answer different questions. The residual prices the lease. The resale value decides whether leasing beat buying. On a 40,000 car with 4,000 down over 36 months, a 50% residual means the contract assumes the car is worth 20,000 at the end, so the depreciation you pay for is 16,000, or 444.44 a month. Add the rent charge — 163.33 a month, computed on the average of the 36,000 financed and the 20,000 residual — and the payment is 607.77. If the car is actually worth 26,000 at the end, buying it outright and selling it then costs 18,016.72 net, against 25,879.72 for the lease, so leasing costs 7,863.00 more. Change only the resale figure to 20,000, equal to the contract residual, and the gap narrows to 1,863.00 without the lease payment moving at all. Change the residual instead, which does move the payment, and the gap can cross zero: at a 65% residual over 60 months with the car reselling for 20,000, leasing comes out 1,920.63 ahead. That is not a contradiction. An optimistic residual is a transfer from the lessor to the lessee, and it is the reason the table below shows the gap widening as the down payment rises rather than falling.

40,000 car, 36 months, 50% residual, reselling at 26,000

Down payment	Monthly payment	Total lease cost	Net cost of buying	Difference
0	730.56	26300.16	18463.05	7837.11
4000	607.77	25879.72	18016.72	7863
10000	423.61	25249.96	17347.28	7902.68
16000	239.44	24619.84	16677.8	7942.04

The first column moves and the last one barely does, which is the finding: going from nothing down to 16,000 down cuts the monthly payment by two thirds, from 730.56 to 239.44, and moves the comparison by 104.93 — in the direction of buying. The reason is that a down payment on a lease is not equity, it is depreciation paid in advance; the total falls by only 1,680.32, from 26,300.16 to 24,619.84, because the money simply changes hands earlier. The gap itself comes from the other two columns: the lease costs a little over 24,600 to a little over 26,300 whichever row you read, while the net cost of buying and selling runs from 18,463.05 down to 16,677.80. That distance is what the resale value is doing, and it is why the resale estimate matters more than anything on this row.

Formula

Capitalised cost = price − down payment. Residual = price × residual percentage. Depreciation per month = (capitalized cost − residual) ÷ term. Money factor = annual rate ÷ 2400. Rent charge per month = (capitalized cost + residual) × money factor. Lease payment = depreciation + rent charge. Net buy cost = the purchase loan's total payments + down payment − resale value.

P: Asset price
d: Down payment, which reduces the capitalized cost
s: Residual percentage written into the contract
R: Residual value: the contract's estimate of what the asset is worth at the end
V: Resale value: what the asset actually fetches at the end
a: Annual rate, as a percentage
n: Term in months

Use it when you are choosing between leasing and buying, which is not the question the monthly payment answers. Put in the price and the down payment, then set the resale value to what the car will really be worth at the end — that number is the one you have to estimate, and it is the one the dealer's quote does not contain. Read the last column first: it is the whole comparison in a single figure, and a positive number means buying and selling wins. Then check whether the contract residual is above or below your resale estimate, because that tells you what the lease is really doing. Above it means the lessor is charging you for less depreciation than will actually occur, which makes the monthly payment look good and makes the buy-out option bad; below it means the opposite. Finally, note that the table holds the resale value fixed and moves the down payment, which is the one lever people expect to help and which barely does.

Worked examples

40,000 car, 4,000 down, 36 months, 50% residual
1. Capitalised cost: 40,000 − 4,000 = 36,000
2. Residual: 40,000 × 50% = 20,000
3. Depreciation per month: (36,000 − 20,000) ÷ 36 = 444.44
4. Money factor: 7 ÷ 2400 = 0.0029167
5. Rent charge per month: (36,000 + 20,000) × 0.0029167 = 163.33
6. Lease payment: 444.44 + 163.33 = 607.77, so the lease costs 4,000 + 36 × 607.77 = 25,879.72
7. Buying: a 36,000 loan at 7% over 36 months is 1,111.58 a month, 44,016.72 in total with the down payment
8. Selling at 26,000 leaves a net buy cost of 18,016.72, so leasing costs 7,863.00 more
The default case. The rent charge is the part that surprises people: 163.33 a month on a balance that falls from 36,000 to 20,000, which works out to 5,879.88 over the term. Compare that with the interest on the equivalent purchase loan, which is 4,016.72 — the lease is the more expensive way to borrow, before any consideration of what the car is worth.
The same lease when the car resells for 20,000
1. Everything on the lease side is unchanged: the payment is still 607.77 and the total is still 25,879.72
2. Buying and selling: 44,016.72 out, 20,000 back in, so the net is 24,016.72
3. Gap: 25,879.72 − 24,016.72 = 1,863.00 in favour of buying
4. That 1,863.00 is very close to the difference between the lease's total rent charge of 5,879.88 and the purchase loan's interest of 4,016.72
The residual and the resale value are now the same number, and the lease still loses by 1,863.00. Nothing about the lease changed — the payment, the total and the rent charge are all identical to the default case. What changed is how much the buy side recovers at the end, and that is enough to move the comparison by 6,000. The leftover gap is the lease's finance charge being more expensive than the loan's, which survives even when the two sides agree about depreciation.
A 65% residual over 60 months, with the car reselling for 20,000
1. Residual: 40,000 × 65% = 26,000, so the depreciation charged is only 36,000 − 26,000 = 10,000
2. Depreciation per month: 10,000 ÷ 60 = 166.67
3. Rent charge per month: (36,000 + 26,000) × 0.0029167 = 180.83
4. Lease payment: 347.50, and the total lease cost is 24,850.00
5. Buying: a 36,000 loan at 7% over 60 months is 712.84 a month, 46,770.63 in total
6. Selling at 20,000 leaves a net buy cost of 26,770.63
7. Gap: 24,850.00 − 26,770.63 = −1,920.63, so leasing wins
The case that shows why the two residuals have to be kept apart. The contract assumes the car keeps 65% of its value for five years; the market says 20,000, which is 50%. The lessee is charged depreciation on only 10,000, so the payment is 347.50 — cheap. The catch is at the end: buying the car out of the lease would mean paying 26,000 for something worth 20,000. The comparison here assumes both paths end without the car, which is why leasing comes out ahead; the advantage is real but it is the lessor's optimism being handed to you, and it disappears the moment you exercise the buy-out.

Limitations

Every fee has been stripped out of both sides, deliberately, because a lease quote and a purchase quote almost never itemise the same things: acquisition fees, disposition fees, excess mileage and wear charges, sales tax on the monthly payment in some places and on the whole price in others, registration and documentation. Adding them back would move the gap by hundreds, and in some cases by more than the gap itself, so this page should be read as a comparison of the two structures rather than of two offers. The purchase side assumes the car is sold at the end for the resale value entered, and that the loan runs the full term with no early repayment; a buyer who keeps the car for ten years instead has a completely different answer, because the resale value stops being the relevant number and the remaining life of the car starts being one. The lease side assumes the monthly payment has no mileage cap attached, which every real lease does, and that the car is returned in a condition that incurs no charges. Interest rates are held equal on both sides, whereas a lease and a purchase loan are frequently priced differently. Depreciation is modelled as a straight line, which it is not. And no currency is attached to any figure.

Frequently asked questions

What is the difference between the residual and the resale value?: The residual is written into the contract and prices the lease — it decides how much depreciation you are charged for, and therefore the monthly payment. The resale value is what the car actually fetches at the end. The first sets the payment, the second decides whether leasing beat buying, and they are frequently far apart.
What is a money factor?: It is the lease's interest rate expressed in a form that is applied to the balance without dividing by months. Divide the annual rate by 2400 to get it: 7% becomes 0.0029167. Multiply that by the sum of the capitalized cost and the residual to get the monthly rent charge, which is why the number looks small and is not.
How is the monthly lease payment built?: Two parts. Depreciation is the capitalized cost minus the residual, divided by the term: (36,000 − 20,000) ÷ 36 = 444.44. The rent charge is the average of the same two figures, times the money factor: 163.33. Add them for the payment, 607.77.
Can leasing actually be cheaper?: Yes, and the case that shows it is a contract residual above the market value. At a 65% residual over 60 months with the car reselling for 20,000, the lessee pays depreciation on only 10,000 and the lease comes out 1,920.63 ahead. The catch is that buying the car out at the end means paying 26,000 for something worth 20,000, so the advantage only holds if you walk away.
Does a bigger down payment make leasing better?: It lowers the payment and slightly worsens the comparison, which is the opposite of what most people expect. In the table, going from nothing down to 16,000 down takes the payment from 730.56 to 239.44 while the gap in favour of buying widens from 7,837.11 to 7,942.04. A down payment on a lease is prepaid depreciation — it reduces the monthly figure without reducing the total.
What is left out of this comparison?: All fees on both sides, mileage caps, wear and disposition charges, tax, and the possibility that the two sides carry different rates. It also assumes both paths end without the car. Read it as a comparison of the two structures rather than of two specific offers. And no currency is attached to any figure.

References

12 CFR 1013.4 — Content of disclosures (Regulation M, Consumer Leasing): paragraph (f)(5) defines the depreciation charge as the difference between the adjusted capitalized cost and the residual value, (f)(4) describes the residual value as the figure used in calculating the base periodic payment, and (k) covers the lessee's liability for the difference between the residual and the realised value — Electronic Code of Federal Regulations, United States
15 U.S.C. § 1667 — Definitions (Consumer Leasing Act): the statutory definitions of a consumer lease, the residual value and the realised value, which is where the two-number structure on this page comes from — Legal Information Institute, Cornell Law School (United States)

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