# Zero Drive Off Formula [California]

Looking for community’s help on the formula for zero drive off in California.

Based on the zero drive off quote from dealer (shown below), we believe the current zero drive off formula for California on the LH Calculator is wrong, as it does not take into consideration of the tax levied on the monthly payment when capitalizing the first month payment.

I would love to pick the brain of our math whizzes for the zero drive off formula in California! @delta737h @Rsantoro12

Here are some past discussions on how to calculate zero drive off payments in NY for reference:
NY tax worksheet
Zero drive off formula in NY
NY taxes tax in zero drive off

Thank you!

I think I’m approaching this wrong.

When I tried the calculator, I’m looking and it does not factor the tax levied on the monthly payment that does get capitalized. I experimented and added a theoretical -\$24 untaxed incentive (representing sales tax that wasn’t capitalized), and it lines up dollar to dollar.

But when I try to look at it with contracts that used the entirety of a taxed rebates to cover the DAS amount, the calculator is penny accurate - could it have something to do with the fact that these situations are treated differently? Here’s a signed example from cjsen’s camaro.

But when I looked at another signed contract with first month covered by untaxed rebates (direct to dealer cash), you have to add the tax back in to get an accurate #.

These are all California examples of \$0 DAS with different methods, one direct capitalized payment, another with taxed rebates covering the whole amount, and another with untaxed covering it. I think a larger sample size will give a more definitive answer.

Edit: Another sample size like the first Mazda, with a part of the taxed rebate covering the DAS - an adjustment is needed for the sales tax of the first payment. I’d like to see others’ math as well.

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I am getting a slightly different base payment that they are (351.73). When reverse calculating, I get a MF of 0.000008591. I know the payment/tax is rounded and therefore there is manufactured specificity here but this is not an insignificant difference, and I’m not sure what they’re doing there.

When adjusting for this new MF, I can get within two cents of the sheet, though I cant vouch for its accuracy since I just built the formula now.

When looking at the tax as an addition to both the interest and depreciation base, you can see how you pay 23.77 in added depreciation (66 cents per month) and about a cent to capitalize that tax (extremely nominal, but would be more significant given a greater MF)

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I think you’re correct in that this is not the same Zero Drive Off. In this instance, many fees are “paid upfront” (and hence taxed as such). However, the 2750 rebate is used as cash to pay down those fees and the first months payment, leaving the buyer with no drive offs to be paid with their “actual” cash.

Same here. As long as rebates are covering that DAS amount, they aren’t "Zero Drive Off " in the spirit that I think @littleviolette is referring to, as we would want to capitalize every fee and the first month payment, effectively eliminating upfront taxes (in the state of CA)

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Hmm makes sense to me. I’d still want to tinker with it a little bit more with other contracts to be 100% sure.

C’est la vie

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Zero drive off scenario given that payment streams are taxed.

In this scenario, we capitalize all fees including both taxable and non-taxable fees. In other words, the goal is zero drive off fees given that each payment is taxed. Arizona, California, and Florida are just a few of the states that compute sales tax on the payment streams. When all fees are capitalized, including the first monthly contractual payment, the calculation of the contractual payment is a bit more complicated if payment streams are taxed as opposed to tax levied on the selling price or tax levied on the total payments as is done in New York and Ohio. We’ll consider the OP’s consumer retail lease transaction originating in California. See California pub 34 below regarding treatment of sales tax in retail leasing.

Let

Below are the relevant formulas…

Po is an intermediate calculation whose only purpose is to determine payment sales tax.

Using the OP’s Data, find the required contractual monthly lease payment, sales tax, as well as the monthly taxable payment and monthly base payment given the following OP data.

C = 27,125; F = 0.00001; R = 16,353.30; N = 36; A = 1,000.75; G = 26.10,  = 7.25%
D = 360; N = 36

NOTE: I erroneously and deliberately included the 288 title/registration fee in the variable A because that is what occurred in the OP’s “Lease Alternatives.” Title registration fees are NOT taxable according to California’s pub 24 and should NOT be included in A. I assume the title/registration fees charged are not excessive.

Plugging the above values into the first equation and evaluating, we arrive at Po = 326.53. The second Equation gives T = 23.67 and third Equation yields Pb = 327.95. Sales tax levied on the taxable payment (326.53) gives a contractual payment of 327.95 + 23.67 = 351.62. These results are summarized below.

Agreed Upon Value (Selling Price)………………… 27,125.00

Amounts Financed (Capitalized)
Doc Fee……………………………………………………………… 80.00
License/Title Fee………………………………………………. 288.00
Tire/Battery Fee………………………………………………. 8.75
Other Fee………………………………………………………… 29.00
Cap Reduction Tax…………………………………………. 26.10
1st Month’s Payment…………………….…………………… 351.62
Acquisition Fee………………………………….……………… 595.00
Total Capitalized Amount………………………………… 1,378.47

Capitalized Costs
*Gross Capitalized Cost…………………………………… 28,503.47
Capitalized Cost Reduction……….…….…………………. 360.00
Adjusted Capitalized Cost………………….……………… 28,143.47

Residual Value…………………………………………………… 16,353.30

Money Factor……………………………….…………………… 0.00001
Term (months)………………….…………….…………….…… 36

Monthly Base Payment excluding Sales Tax…… 327.95
Sales Tax………………………………….………… 23.67
Monthly Lease Payment including Sales Tax…… 351.62
DAS…………………………………………………… 0.00

Observe that the above procedure avoids computing tax on tax and emphasizes the need to separate taxable items from non-taxable items.

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Just to confuse matters further, with at least some banks, there is a distinct difference between a \$0 due at signing lease and a “sign and drive” lease, despite both situations having \$0 due at signing.

They are not interchangeable terms.

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The difference being capping the first payment and waiving it?

With ccap, for example, a sign and drive brings an additional incentive equal to one month’s payment, along with a mf mark up.

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Thank you for everyone’s inputs!

Given the above, I got a different result:
Po = 317.45
Pb = 291.01
Pt = 341.83

I didn’t quite get the logic behind your formulas. A would include non-taxable fees (e.g. government fees) because it is capitalized – meaning it is getting taxed monthly.

The G you applied above (26.10) is the tax on cap cost reduction (\$360) instead of what you defined – Capitalized Non-Taxable Fees.

I am also getting 351.73 too. I think it’s due to rounding. What I didn’t understand is how the worksheet applies 351.66 to the net cap cost (28,143.51), as 351.66 is the output of the monthly payment based on the said net cap cost (so it’s circular reference). I recall from my math class years ago that you would have to go through trial and error to solve the variable (the monthly payment) in this case .

@HersheySweet Thank you for posting the contracts and the calculator links! After reviewing different zero drive-off contracts, I don’t think there is a uniform way to calculate monthly payments for zero drive-off. For now, I will calculate the zero drive-off payment using the following assumption:
Net Cap Cost = selling price + all fees + tax on cap cost reduction - cap cost reduction + monthly payment after tax assuming all fees are capped and \$0 down

I suppose that’s the rebates they apply on the contract. Not sure if they are taxed.

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I guess I can use code to approximate the monthly payment in the case of zero drive-off. ChatGPT is suggesting the Newton-Raphson method or the bisection method. Any pointers?

Here are the proposed formulas:
C = Net Cap Cost
A = All capitalized fees (taxable and non-taxable)
T = All capitalized taxes
D = Cap cost reduction
R = Residual value
N = Number of months
F = Money factor
p = monthly payment before tax
t = tax rate

Let:
C = S + A + T + p(1+t) - D
p = (C + R) * F + (C - R) / N

Solve for p.

This sounds more like cattle breeding than sales tax calculation.

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You are right. I went down the rabbit hole. Now I need help getting out.

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Algebra/Calculus Hackr?

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Not sure if it will help but OmegaAutoGroups calc supports Zero drive off for CA, maybe you can go their site and compare?

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My results are close to those of the dealer. The dealer’s Pb = 327.89 while mine equals 327.95. I have no idea why the dealer is off by \$.06. Likewise for the sales tax where the dealer’s (23.77) is \$.10 more than mine (23.67). Pb includes both A & G or taxable and non-taxables, respectively and therefore, not subject to tax as you would be levying tax on non-taxable items. I added the payment tax to Pb …… 327.95 + 23.67 = 351.62 = Pt. The dealer’s Pt = 351.66 . So, the dealer is \$.04 off.

Apparently, the dealer erroneously included the 288 title/registration fee as a taxable item. That’s a red flag. However, I did the same thing for the sake of apples-to-apples comparison and, per the above, the difference is only pennies. However, it is a significant difference which is troublesome. I’ve used my formulas for zero drive off leases originating in PA and in Fl and was spot on with those of the dealer.

Variable A captures only taxable capitalized fees, not non-taxable capitalized fees. Non-taxables are not subject to tax by definition. Taxable fees include such items as acquisition and doc fees. Variable G captures only non-taxable items such as government fees, title/registrations fee, taxes (I consider taxes a fee) including capital reduction tax (26.10). The 26.10 is a tax and is not taxable which is why it is included in G. The formula for Po includes A but excludes G. Therefore, Po captures all capitalized taxable fees and excludes G -all non-taxable fees. As such, it reflects the taxable base payment. This means that sales tax @7.25% is levied against this payment… 7.25% x 326.53 = 23.67 so that all taxable fees get taxed and non-taxable fees don’t get taxed.

Hope this helps.

EDIT: added apples-to-apples

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The Newton-Raphson method of successive approximations is an iterative procedure wherein you need to seed the equation with an initial value to find the next value. This is repeated until you achieve convergence where the next value equals the previous value. There are a lot of other details and caveats that I won’t get into unless you really want to know. While you can use this procedure, why use it when it can be solved algebraically.

So, once you solve for p, are you going to calculate the sales tax based on p? It looks like it according to your first formula. This is invalid because p includes all taxable and all non-taxable fees as they are included in C as reflected in your second equation. You would be levying tax on the non-taxables including capitalized taxes, T. As such, your equations are not valid. However, solving for p, I get…

P = [FN(S+A+T-D+R) + S+A+T-D-R] / [N – (1+t)(FN+1)]

I substituted the expression on the right in the first equation for C in the second equation and then, solved for p. Kind of looks somewhat similar to my first and third equations, huh?

One way around this dilemma is to do this in stages (steps) by first deriving the taxable payment, Po that includes only taxable capitalized fees. Next, calculate the sales tax t x Po. Then, compute Pb which includes ALL capitalized fees, both taxable and non-taxable. Finally, compute the contractual payment Pt = Pb + t x Po. The programming effort would likely require a well-defined step function as well as some nested conditional statements. I’d have to get into it to know for sure.

EDIT: Rearranged equation slightly.

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@delta737h Thank you for the detailed explanations!

Yes you are absolutely right – I should have solved the equation algebraically!

I applied the above equation to the calculator and was able to get to the same monthly payment as the ones I have seen on zero drive-off offers. Below is the calculator link to the Mazda deal in the OP:

@delta737h I understand your philosophical argument, but what I have observed from dealer’s deal sheets in states that levy taxes on monthly payments are:

1. In the zero drive-off scenario, both taxable fees and and non-taxable fees (government fees) are capitalized and taxed on a monthly basis.
2. Tax on cap cost reduction is capitalized and taxed again on a monthly basis.

So yes you have to pay tax on taxes and on government fees when you elect to capitalize them.

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