A formula to find a cheap car

Simon BrownLatest, Wealthy Maths

Finding a cheap car to buy

Finding a cheap car to buy

IMPORTANT: This article is based on the assumption that you’re buying a second-hand car.

Buying a car is not fun. I have to trust the sales agent, which I dislike, because they have way more expertise and information than I do. And while it’s good advice to ‘buy the newest model with the lowest mileage’, how do you decide the balance between age and mileage?

Find your answer in the math

I used the method below to determine the numbers I should look for when I bought my last car some seven years ago, and it worked an absolute charm. I eventually found a car in Pretoria that was probably some 35% below what I would have expected for the same make and model. Even better.

But first – what do you want from a car?

A necessary starting point is to identify your quality/value criteria. The following two assumptions guide my method for finding a mispriced car:

Firstly, I assume that a car loses its resale value when it’s either

  • 10 years old and/or
  • has 150,000 km on the clock

Although it will most definitely have utility and will probably work just fine, selling it would get you very little. At this stage, any cash value in your car has gone so its resale value is pretty much zero.

Secondly, I estimated my yearly mileage at about 15,000 km per year. Coming out of the pandemic it’s likely to be a lot less, so I’ll revisit that estimate when I replace my current car. But you’ll need to determine your own average yearly mileage.

Considering the above, I now know how long a car will hold its resale value, so I can calculate the cost per year of available cars. 

With this knowledge, I browsed second-hand car websites looking for my preferred make and model. The purpose of this exercise is to establish the market trend of cost per year. 

The contenders

I found the first car that I like:

  • 5 years old
  • 35,000 km on the clock 
  • R200,000 price tag

The maths

Five years old meant it had another five years before it was properly old. As I said above, I wasn’t looking to sell it then, but it would have no real cash value even if it kept on working.

The 35,000 km on the clock meant it had 115,000 km before it was old. At my rate of 15,000 km a year, that meant seven years.

So which of the two metrics should one consider in this scenario? The age of the car said five years until it’s old, and the mileage said seven years. I used the five years as it’s the shorter time period. Yes, the mileage would still have been below my 150,000 age limit, but that’s fine. Means more bang for my buck here.

I then divided that five years into the price (R200,000 / 5 years), which gave me a cost of R40,000 a year. 

Basically I am looking for the cost per year until it’s old and has no value.

But then I found another one, the same model but

  • Priced at R220,000
  • 3 years old and
  • 60,000 km on the clock

This car had seven more years until my assumption rendered it old. The 90,000 km until old meant around six years of use. The cost per year here was around ±R37,000 (R220k / 6). Again, I used the shorter period – six years for the mileage test. It’s a little cheaper than the first car I saw.

And then, I saw the third one

  • R180,000,
  • 4 years old and
  • 60,000 km on the clock

Both mileage and age will last me six years. Dividing that into the R180,000 price I got ±R30,000 a year. Now we’re talking cheap, with its position nicely below the first two options.

No madness here, just good ol’ method

If you do this often enough across a few different websites, using the same make and model, you’ll soon see the trend of cost per year. In my experience, this does settle around a certain level. 

And then, when one stands out as much cheaper – BUY IT.

When I bought my current car the cost per year was around R30,000. And then I found one priced at R24,000 per year, which was a significant saving.

How do you decide which car to buy? Let us know on social media – we’re always looking for great tips and tricks.

Simon Brown

Many of us avoid making financial decisions because we worry that we can’t do the maths. Luckily, there are only a few formulas you need to understand to make good financial choices. This series of articles is dedicated to helping you understand how to do the calculations for yourself. Once you grasp these simple formulas, you can make better financial choices on the fly.