Models of Car Depreciation

In general, I prefer not to include car equity in my net worth. Let’s spend a few minutes rationalizing why and how I do it anyway.

Car Expenses

Car purchases (ideally) don’t happen very often. You can maintain very low monthly or annual expenses and completely hide how expensive your vehicle is. My personal budget tracker has evolved over the years to include a “car account” against which I expense an average car cost every month.

Today’s topic is car depreciation, but maintenance is the other major amortizable car expense. If you know oil changes and other maintenance items happen every 10k miles, then you can begin to amortize those expenses over the months. This gives you a smoother and more accurate picture of the true cost your vehicle is extracting from you every month.

If you can begin to split out depreciation due to time from depreciation due to distance, then you can attribute some of the car expense toward the activities that require driving. If your daily commute costs you $2.00 per mile instead of the assumed $0.70, then that’s really good information.

Vehicle Depreciation

According to exponential decay

Without being overly precise, car depreciation seems to follow roughly a 1% per month decrease. Buy it for P_0 now, then after n months of average use, it’ll be worth somewhere in the neighborhood of the following.

This isn’t terribly useful or convenient for your personal accounting system, but maybe it helps you plan ahead for the next trade-in.

Probably its most valuable use is to showcase just how much value a vehicle loses in the first 3 years. When financially conscious people talk about buying 3 year old cars, it’s because they’re perfectly happy to let some other sucker take that initial depreciation hit.

Finally, when you drive a “new” car off the lot toward the end of its model year, then this dynamic explains why it immediately “loses” 10% of its value.

Straight line

If you simply need a vehicle to drive back and forth to work every day (and whatever else is necessary to live in modern society), then maybe a straight line depreciation is more appropriate. The car is just as necessary on the 1^\textrm{st} month as it is on the n^\textrm{th}. Assuming the car will last N total months, the following gives your straight line depreciation schedule.

In particular, the depreciation due to time is constant each month. This is (probably) the most convenient for every accounting or budgeting system in existence. You can overthink it by adding depreciation due to distance if you choose.

Inflation adjusted straight line

Before 2021, we had a long period of subdued inflation. Didn’t we? Everything we could import remained consistently inexpensive as the rest of the world fell all over themselves to trade real goods for green paper (sometimes electronically without the paper even). Everything we couldn’t endlessly import (e.g. housing, education, medical care, skilled labor) did see much higher levels of inflation. While vehicles are certainly in the import camp, it seems the rest of the world realized in early 2022 that their paperless green paper could be confiscated whenever it suits us.

We probably want to assume inflation is here for a while. Our end goal is to build in an inflation-adjusted but level monthly (or annual) expense, aiming to be representative of replacement cost. Inflation adjusting the straight line depreciation model over N total months with annual inflation rate r (compounding monthly) gives the following.

With one month depreciation at month 0\leq n\leq N given by \frac{P_0}{N}\left(1+\frac{r}{12}\right)^n.

This is probably the most realistic for any accounting system. It loses the constant depreciation but properly measures the most relevant expense. Therefore, it’s reasonable to take a hybrid approach where you inflation-adjust on an annual basis but use a constant depreciation within the year.

Inflation adjusted Exponential Decay

So, this is the easiest of the four, since we’ve already done it! The exponential decay model already contains this when the rate r is the combination of inflation and depreciation.

The r=-0.01 utilized above seems to approximately model what I see in practice (at least prior to 2021).

Other Models

Electric vehicles are currently depreciating much faster than traditional gas powered vehicles, probably for the same reason laptop computers depreciate so fast.

• The battery degrades quickly
• The technology becomes quickly outdated

Iconic cars depreciate much more slowly, presumably because they’re valued as more than a functional means of transportation.

Why I Value My Car

Accounting 101 requires it; the accounting equation needs to balance.

I want my monthly expenses to include an honest-to-goodness indication of how much my vehicle (and it’s operation) is costing me. I’ll need to replace it some day, so I want that future expense to be accurately amortized over time.

My monthly expenses on the right should contain vehicle expenses. Therefore, the value of the vehicle on the left should decrease. Ideally, those deltas will match.

Which model do I use? None of them, actually. I’ve overthought this one to death, and today’s article set us up to overthink the FIRE version together.