# New car vs used: how to compare value?

When buying a car, I care only about what I'd call "pure utility": maximum usefulness for minimum dollars and trouble.

I'd always heard that a new car is nearly always a worse deal than one that's about 3 years old, because although it depreciates a lot in those first few years (in terms of market value), the utility of the car doesn't decrease much.

I'm now reconsidering that idea, and I want to see if my new calculation makes financial sense.

Suppose that I expect a Model X car to last for 200k miles. A new one costs \$16k.

Now suppose I find a used Model X with 50k miles on it, and I reason that it's "25% used up". If that's true, it must cost 25% less than the new car to be an equally good deal. I should not pay more than \$12k for this car.

Furthermore:

• The used car comes with some risk; if it's been driven aggressively or maintained poorly, it may be more than "25% used up", but I don't know that.
• In any case, the first 50k miles are the "best" ones, with the fewest repairs needed. So even with ideal care, we might say that 50k is more than "25% used up".

Both of these should decrease the price I'm willing to pay for a used car (though it's hard to say by how much).

Obviously, I'm estimating and guessing a lot of things here. But does this basic idea make sense?

In comparing the value of a used car to a new one, does it make sense to discount the value of the used car based on how "used up" it is? (And if so, is there a better name for this idea?)

• Oh, now I want a Tesla Model X that lasts for 200k miles and costs \$16k! – Rocky Apr 15 '15 at 20:23
• The model is flawed because the lifetime expectancy goes up. If the car is sold at 50k miles, it wasn't totaled, and its remaining life expectancy is perhaps 170k miles. The 200k expected for new cars is averaged over all cars, including those that will be wrecked within 50k miles. – MSalters Apr 16 '15 at 12:07
• @MSalters: Even discounting wrecks, there are two basic causes of failure: bad design/manufacture and wear. The bad stuff is likely to show up fairly soon, while wear takes a long time - think Yugo vs Honda/Toyota. And FWIW my car is currently at about 190K (miles), the truck at 225K when the odometer broke a few years ago. – jamesqf Apr 16 '15 at 17:40
• @jamesqf: Of course. It's popularly known as the bathtub model. The point is that life expectancy is a statistical measure, not a single hard number. – MSalters Apr 16 '15 at 17:59
• @MSalters I see your point about a statistical average, but I'm really going on something less scientific: "I think Model X is a good car, I've had friends get about 200k miles out of similar cars", etc. It's definitely a guess, but it's not based on an average that includes early wrecks. – Nathan Long Apr 16 '15 at 19:15

Generally speaking, you are correct. People usually discount vehicles by the mileage. The first 50k or so miles are the best to drive the car in terms of repairs etc., however many makes and models remain relatively trouble-free even after they've driven twice as that.

There are plenty of websites or on-line communities of certain makes that discuss common issues of specific models. You can find loads of information to draw your attention on exact areas when you are out to view the car.

Also, you may be interested in a paper by George Akerlof "The Market for 'Lemons'" (got a Nobel prize in Economics for that). While the paper is about asymmetric information and this theory can be applied to a whole range of markets, it uses new and used cars as an example.

Generally speaking, when a person is shopping around for used cars he assumes that there are some good cars and some 'lemons', thus he intuitively sets his price somewhere in-between. As a result such price attracts more of the 'lemons' sellers but those who have a car in a really good condition are not prepared to sell it that cheap. As a result, the majority of cars on the used car market are lemons. But that's just a theory to keep in mind.

Also, it is a good idea prior to purchase, to send the car you like to a garage for technical inspection. This may reveal some weak-spots and may help you negotiate lower price or, at least, you would know what to expect from your purchase.

Good luck with making a correct choice.

This depends heavily on the car model and its demand. I have a 2010 Forester, and was amazed to find a 2011 Forester (essentially the same car, no major changes 2010-2011) at an auto show at a "discounted price" of \$18,800, 53k miles, with a supposed sticker of over \$20k. The most expensive model you could buy that year (when we looked) was around \$30k, and I doubt the on display model was that - I think it had the base engine, for example, so it was probably \$24k.

Recent Foresters, like Civics and Accords of recent years, have a good reliability and safety rating, and as such have less of a discount than, say, a Dodge; and they're not luxury cars with a more substantial instant drop off (as you lose some of the "rich tax"); but still, somewhere between 60% and 75% of its original price 4 years later with over 50k miles is mildly crazy. Cars like this are better frankly to buy new - if you don't get much of a discount to buy them used, and they have high resale value (and you have no reason to believe that value won't exist on a new model, of course), then you're unlikely to get a good enough discount.

To figure this out, which is what I think you're asking, you should look at the price curve over time of a particular model, make, or category. There are some sites you can do this on, like Car Gurus for example. Look at how the models age over time; obviously in a Forester there's a big dropoff in 2008 because the 2009+ models had much higher build values, but you can still see in the chart about what the car will probably be worth in a year or two's time.

You have a good rule of thumb in place above. The mileage is a good measure of use, though it is good to also consider age (a car will develop problems even if it is not driven) as well as make and model of the car. Consumer Reports has some nice examples and advice on their site.

Trouble is always a tough thing to measure. Some people would be severely personally or professionally inconvenienced if their car was out for a couple days but most would adapt without issue. It is worth thinking about which camp you are in.

Don't be scared off used cars by Andy's comments above. The paper he cites is a wonderful piece of work, but Andy draws exaggerated conclusions from the paper. While it is correct that a used car, especially a lightly used car, when sold is more likely to be a lemon than a car not currently being sold. It is not even close to true that a majority of used cars on the market are lemons. People sell cars for all sorts of reasons not just because they are failing. Also, now that cars are so much more reliable the percentage of lemons is small even among cars currently being sold.

However, the other consequence of asymmetric information is fairly interesting and useful. Because people are risk-adverse (scared of buying lemons) the price of a car 25% through its useful life is often far below 75% of the original price. So, if you are willing to put some effort checking into a car (checking its history, bringing it to a garage) you can often get much more "pure utility" from a used car.

Finally, because the cars tend to drop so much of their initial value so quickly (Kelly Blue Book) by the time you buy even a lightly used car the value of the car will tend to depreciate more slowly for you. This helps even more with the utility/cost as you will get (relatively) more money back when you sell compared to the price you bought at.

• Actually that Kelly Blue Book calculator is pretty awesome and can help get a good feel for the cost of ownership over your expected lifetime. – rhaskett Apr 23 '15 at 19:08

What you are looking for is a function that presents the age (in months or odometer reading) of the car along the X-axis, and the price of the car along the Y-axis. This function is not going to be the simple linear relationship that you might desire and would be easiest to express and understand. The function will be one that starts high, drops swiftly for the first couple of months (depreciation, why buy a car with 500 miles on it for nearly the same price as a new car?). Then the price drops more gradually, until the car is about 3 years old/50K miles, where it has reached about 50-60% of the original price. That price point varies by make and model of car (some cars hold more value, others less, depending upon their desirability and utility).

Were you able to (accurately) graph this function over the useful life of the car, you would find that it would have discontinuities (jumps of \$1000's of dollars) as events happened to the car (accidents, breakdowns), as well as smoother periods. As a car approaches major event points (replace the tires, replace the timing belt, replace the alternator, brakes, rotors, catalytic converter, hybrid battery), the price will drop more, and (may) jump back above the price trend line (function graph) after each repair or replacement occurs.

Each make and model of car has a similar graph, although the price changes at different rates -- so that were you able to scale all vehicles to the same price, and superimpose each age/price graph, you would observe that they would differ by make, model, type, options, even color. But you may note (as I have) that every vehicle follows a similar shaped curve.

There is also a value function (subjective to you) that you would place on the car. Since you seek to use the car, the value you place on the car is a simpler function, where you judge the value to be the cost to acquire the car, costs to make expected repairs on the car, less residual sale price. And this value function would depend upon the expected remaining life of the car. You may sketch this function as a straight line from the original purchase price to the expected residual sale price (when you finally dispose of the vehicle).

And every other person seeking to buy a similar car in the used car market also has a value function for the car, some starting at decided points (want to buy a car less than price P) different than yours, and some ending at decided points (keep for specified duration), at differing ages or values. Their functions differ from yours, and are part of the reason why the price fluctuates so much. Some people want to buy newer used cars (fewer expected problems), others want to buy older used cars (lower purchase price).

The challenge and the problem you are trying to solve, is one of two approaches to saving money. One is that you want to find the inflection point, where the slope of the price curve levels out (becomes less negative). At that point in the price curve, you would pay less money for the usage of the car. Or you may superimpose your value function and the price function for a car onto the same graph, and as a rational person you would seek to buy the car at the age when the difference (gap) between the price of the car, and (your) value of the car is large (thus saving the most money). But everyone in the used car market is also trying to do the same, but with different factors which they value, and that is where the variations in the price function of the car occur.

Factors people who choose to buy used cars, and the priority they place on those factors vary,

• Some people seek to save the most money
• Some choose to minimize the cost to own the car
• Some want to own newer cars
• Some need to buy cheaper cars
• Some try to avoid paying repair bills
• Some desire certain makes, models, styles, options, or colors

My approach on the past several car purchases has been to find a car with low odometer and a price around 50% of the original price.

Good luck!

In theory what you are proposing would work however there are too many variables that are not logical or quantifiable. Your idea would be a good starting point.

Some makes/models are considered to be more sought after than others, this can artificially increase the price and the opposite is true of models that are not sought after. There are dozens of other factors that can similarly affect price, color is a good example, some people may like a yellow car, others not so much!

The best way to identify value for money is to compare vehicles that are for sale on a variety of websites and you can then filter these based on all your criteria until you settle on what the market rate is. Then you can try to find a car that is good value for money.

Bear in mind that the price a car is advertised at may be higher than what the seller is willing to accept for a sale!