Car finance, depreciation, negative equity

Financing a car sets two numbers running side by side, and different things decide them.

What you owe is contractual. The amount borrowed, the rate, the term and the schedule that grinds the balance to zero are all fixed at signing, which is what the loan payment calculator above works out. A car loan is a secured loan and the car is the collateral, so the lender's claim is written down in advance and does not shrink just because the car does.

Everything below assumes that shape: a fixed rate, and a schedule that repays the whole balance to zero. Balloon loans, personal contract purchase agreements and leases behave differently, because a large slice of the value is deferred to a single payment at the end instead of being repaid along the way, and the contract rather than the used market usually fixes what that slice is assumed to be worth. Where that happens some of the residual risk sits with the lender, and the arithmetic here does not carry across unchanged.

What the car is worth is not contractual. It is whatever the used market pays on the day you ask, and nobody promised you a number.

Your equity in the car is the distance between the two:

$$\text{equity} = \text{market value} - \text{balance outstanding}$$

When that is negative you are in negative equity, also described as being upside down or underwater on the loan. Nothing unusual has to happen for it to arrive. Market value falls fastest in the first year or two. A loan balance falls slowest in the first year or two, because interest is charged on what is still owed and the early payments are mostly interest, which is the subject of amortisation. Fast down against slow down, and the gap opens by itself.

On a $35,000 car financed over 72 months at 9 percent with nothing down, a year in the balance is $30,392.28 and a car that has shed 18 percent of its value is worth $28,700. The loan is about 106 percent of the asset standing behind it, and no payment was missed to get there.

Depreciation is the fall in a car's market value over time. For most owners of a new car it is the largest single cost of the whole exercise, larger than fuel and larger than interest, and it is the only one that never appears as a payment.

Two things push the losses towards the front.

The first is arithmetic, and it applies even to a perfectly steady decline. A percentage taken off a falling value takes a smaller cash amount every time. At a constant 18 percent a year the first year of a $35,000 car costs more than two and a half times what the sixth year costs, with the rate never moving.

The second is the used market, and for a new car it is usually the larger of the two. A car crosses from new to used the moment it is registered, and the buyer of a used car does not pay for what the first owner paid for: the new-car premium, delivery and registration costs, and the earliest stretch of the warranty. That step down lands on the first owner alone.

A constant 18 percent a year, as a share of the purchase price:

Every figure on this page uses that model, which is deliberately simple and mildly flattering. Real curves are steeper in the first year than a constant rate, so the early gap between value and balance tends to be wider than shown here. Real rates also move with model, mileage, condition, fuel type and market, and used values can rise for a while when supply is short, as they did in the early 2020s.

Put the debt line and the value line on the same scale by writing both as a share of the purchase price. On the $35,000 example at 9 percent over 72 months with nothing down:

The lines cross early in the fourth year, a little past month 39. For the first 39 months of a 72 month loan, selling the car at full market price would not clear the debt: more than half the term with no way out at par. Read the table rather than the headline year: the hole is deepest in the second year, not the first, because the value line goes on falling faster than the balance for a while after signing.

Term is what drives that. Interest is charged on the balance, so a longer schedule puts less of every payment against principal and the debt line flattens. The value line does not know the term exists. Stretch the term and the debt line slides right while the value line stays put, which widens the gap and holds it open longer. It is the same arithmetic a leverage ratio measures on a balance sheet: a thin equity cushion under a large debt disappears on a modest fall in the asset.

Four things move the debt line down at the start, and none of them touches the value line:

• Money down. A deposit, or equity carried from the last car, starts the balance below the price.
• A shorter term. More principal in every payment from the first one.
• A lower rate. Less of each payment lost to interest.
• Nothing rolled in. Financing tax, fees, an extended warranty or an old shortfall starts the balance above the price of the car. In the United States, sales tax and registration fees are commonly financed this way.

While you keep the car and keep paying, negative equity costs nothing. It is a number on a page. It bites at three moments, and none of the three is reliably yours to choose.

A sale or a trade-in. The car does not cover the loan, so the shortfall is settled in cash or carried into the next agreement. Carrying it costs twice: the old shortfall is financed again at the new loan's rate, and it starts the new loan above the price of the new car, where the next round of negative equity begins. On the numbers here, $1,692.28 rolled into a fresh 72 month loan at 9 percent adds $30.50 a month and $2,196.31 in total, of which $504.03 is interest on a car you no longer own.

A write-off or a theft. A motor insurer normally settles a total loss at what the car was worth, not at what is owed on it, unless the policy happens to carry a new-car replacement or agreed-value term. The balance does not move to meet the settlement, so the borrower pays the difference and has no car. Cover for exactly this gap is sold in many markets, inside the finance agreement or separately, and whether any is in force is a question about the policy documents rather than about arithmetic.

A repossession. If a secured loan is not paid, the lender takes the collateral and sells it, usually into the wholesale market rather than at the retail price a private seller would ask. The proceeds often fall short of the balance, and the remainder, called a deficiency balance in the United States, is generally still owed. How far a lender may pursue it depends on local law, and some jurisdictions give a borrower a statutory right to end the agreement early that others do not.

There is a quieter cost too. Negative equity removes options, because changing car or moving to something cheaper to run is hard while the asset cannot repay its own debt.

A straight loan has four numbers in it: the price, what you put down, the rate and the term. The payment is not a fifth number. It is the output of the other four, which is what makes it useless as a comparison. A balloon or lease deal does add a real fifth, the value assumed at the end, and the payment is then the output of five.

Term is the easiest of the four to move, and it pushes the payment one way and the cost the other. The same $35,000 at 9 percent:

In cash, 36 months costs $1,112.99 a month and $5,067.66 of interest; 72 months costs $630.89 a month and $10,424.35. The payment falls by 43 percent and the interest roughly doubles, on the identical car at the identical rate.

The table holds the rate still so that only the term moves. Lenders commonly price longer terms higher, so the real spread between a short deal and a long one is usually wider than the table shows, not narrower.

A question about what payment you are looking for is therefore a question about the term, not about the car: a wide range of cars fits the same payment once the term is free to move, so the payment on its own cannot rank two offers.

Three numbers survive that problem: the price of the car including everything added to it, the APR, and the total amount payable. Consumer credit rules in the United States, the United Kingdom and the European Union all require an APR on the agreement, so the comparable figure exists to be asked for.

A longer term is not automatically a mistake: a lower payment is worth something real to a household with a tight month. What it never does is make the car cheaper. Paying cash changes the comparison rather than settling it, since it removes the interest and none of the depreciation, and the money spent gives up whatever it would otherwise have earned, its opportunity cost.

The finance payment is the most visible cost of a car and rarely the majority of what the car actually costs. Under it sit fuel or charging, insurance, maintenance and tyres, registration and road tax, and whatever parking and tolls the driving involves. Over all of them sits depreciation, the largest line for most new-car owners and the only one that never leaves a bank account.

One plausible monthly stack of payments for the $35,000 car above, financed over 72 months. Depreciation is not a row in it, because nothing is ever paid out for depreciation:

The payment is 59 percent of that total, so a car chosen on the payment alone has been chosen on just under three fifths of the monthly cash and on none of the depreciation.

Cash out and cost are not the same thing, and the table is the first of the two. Most of the $630.89 is principal, which buys an asset rather than spends it, so the only cost inside the payment is the interest. Depreciation runs the other way: it is cost with nothing paid out. The two do not cancel. Across this six year loan the cash handed over runs ahead of the economic cost by exactly what the car is still worth at the end. The bottom row is a budgeting figure, in other words, not a measure of what the car costs.

On a gross income of $6,000 a month the cash stack takes 17.7 percent, against a rule of thumb, common in United States personal finance writing, that keeps all transport costs under 10 percent of gross income, which here would be $600 a month. That 10 percent is a convention rather than a finding. It takes no account of whether the rent is high or low, or of whether the car is the thing that makes the earning possible.

Two things follow. A debt-to-income test of the kind United States lenders run counts the $630.89 payment and none of the four lines beneath it, so a car can pass an affordability check while taking far more from the household than the check ever saw. Practice differs elsewhere: United Kingdom affordability rules, for one, expect a lender to allow for household running costs and not only for credit commitments. And these line items are the most jurisdictional part of the subject: insurance pricing rules, registration and road tax and fuel duty differ by country and, in the United States, by state. They also move with fuel prices and insurance cycles, so read them as a shape rather than as current amounts. An electric car shifts weight away from fuel, and in several markets recently towards insurance and depreciation, though electric residual values have swung hard in both directions and are not a settled quantity.

Depreciation still dwarfs the rest. Over the same six years the car in this example falls from $35,000 to $10,640.23, and the value lost is more than twice the $10,424.35 of interest. Neither figure is discounted; both are six years of nominal money, which is the arithmetic a reader expects here but is not a present value.