Saturday, September 26, 2009

Should You Buy An American Car?

There are many factors to consider when purchasing a car (budget, value, safety, reliability, etc.); to properly address the proposed question, I'd have to consider all of those factors. This post will consider the very specific question of which cars have the best resale value. If you'd like to see more posts with elite writing on this site or, perhaps, your own, check the examples at

For the purposes of this post, I'll define the Fractional Resale Value (F) as the 2009 Kelley Blue Book (KBB) used car value divided by the U.S. CPI inflation-adjusted original manufacturer's suggested retail price (MSRP):
For example, a 1996 Honda Accord had a base MSRP of $14565. In 1996, the CPI index for urban consumers was 156.9 (in July 2009 it was 215.351). The CPI adjusted MSRP is $14565 x 215.351/156.9 = $19991. The KBB value is calculated assuming the car is in good condition with 130,000 miles (10K a year) for a 3rd party sale in Charlottesville, VA. In this case, the KBB value is $3010. The fractional resale value, F is 3010/19991 = 0.151

I collected data for the base option (cheapest possible version of a given car, when possible) of 12 different cars over the past 20 years. I then took each data set and fit it to a decaying exponential:
In the above equation t is the model year of the car under consideration; Tau is the decay rate of the cars value; F_infinity is the fractional value of the car after a really long time (should be close to zero); and F_0 is the initial fractional value immediately after the car is purchased.

In a perfect world, F_0 would equal 1 -- if it did, a car wouldn't lose any value the moment its purchased. In many cases F_0 is less than one. There are two possible reasons for this:
  1. Once purchased, a car becomes used and immediately loses value -- why would you pay the same price for a used car when you could purchase a new one?
  2. Cars are often purchased for less than the MSRP through rebates and haggling (all data collected used the MSRP)
Tau is the decay time constant of the car -- it is the time it takes for the car to lose half of its value (at any point in time). If a car is worth $10,000, after a half life it will be worth $5000 -- after two half lives it will be worth $2500.

The above graph plots the fractional resale value (F) for a Ford F150 truck. The fit is surprisingly good (it has a small Root Mean Squared Error (RMSE) and it looks good by eye -- the model appears to describe the data well). Since F_0 is very close to 1, this truck doesn't lose too much value when purchased new. The fit parameters are summarized in the table below.

The fit parameters and country of origin of 10 different cars are listed above (and ranked by half life in years). The errors listed are for 68% confidence bounds. For example, the Hyundai Sonata has a fairly large error on its half life equal to 0.47 years. The fit on the data is 68% confident that the value of the half life is between 2.47 (2.94 - 0.47) and 3.41 (2.94 + 0.47) years.

Since the table is sorted by half life, it appears that cars made in the USA don't last as long as their foreign counterparts; however, the errors on the half lives are fairly large. The half life and its associated errors from the above table are plotted below:
Unfortunately, with very few exceptions (BMW 3 Series, Ford Taurus, Volvo 240 Series), most of these cars hold onto their value equally well (within error). The only real standout is the Ford Taurus (which we all knew was a crappy car, anyway). The F-150, however, holds its value as well as some of the best imports.

A Direct Comparison
I've completely ignored the cost of maintenance (which is one of the reasons (some) imported cars have such a good reputation). Since I don't have any easy way of acquiring maintenance data, I'll have to settle for direct comparison between badge engineered cars.

Between 1989 and 2002, Toyota and Geo/Chevy collaborated and built the Prizm, which was very similar to the Toyota Corolla (actually, according to Wikipedia, the Prizm was based on the Toyota Sprinter, an "upmarket version" of the Corolla). For the USA market, both cars were manufactured in Fremont, CA in the NUMMI plant. Since these cars are nearly identical (in fact, my import-only mechanic will work on my wife's Prizm), their Fractional Resale Value should be comparable.

After 2002, the Prizm was discontinued. To make a fair comparison, I ignored data after 2002 on the Corolla. However, since there's no fit data for the last 7 years, neither fit is great.
Once again, the half lives are well within error of each other; however, the Corolla clearly maintains its value better (the Corolla curve & data points are higher than the Prizm's) in spite of the fact that they're essentially the same car & were built at the same plant! Clearly, in this specific case, American cars get a bad rap.

Once again, I don't have too many & I've already mentioned them.

It would be interesting to have a look at DMV automobile registries -- perhaps from that data it would be possible to extract a true car lifetime (one that accounts for when a car is no longer worth keeping). This could be accomplished by analyzing current and previous varieties of automobiles from a given model year. However, that data isn't conveniently available.

Copyright © 2009 Peter Dolph

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