Cars: Repair or Replace?

(This follows on from the previous post)

All this got me thinking about the economics of new vs major repair.

(Context: this discussion is not for people who buy new and trade in after three years, or who do a lot of longer-distance driving and so need a comfortable car with a bit of power under the bonnet. This discussion is about second-hand cars and owners who don't drive tens of thousands of miles a year.)

The purchase price of a car is the first of many payments we are signing up for. We are also taking on a stream of future servicing and maintenance payments, including a stream of "average" repairs over the life of the vehicle, caused by "average stuff happening". Those future payments are what we should be expecting because we are using a piece of heavy equipment some of whose parts run at 5,000 rpm and more, and are jolted by that pot-hole we just drove over, as well as left out in the cold, wet, heat and dry.

So when the car comes up for that timing belt replacement (around 7 years or 70,000km), it's not time to wonder if you should trade it in. It's part of the cost of the car that, well, nobody was over-keen to mention. The odd shock-absorber and front suspension bracket should also be taken in one's stride.

However, if in addition to the usual niggles, the dealer starts quoting thousands to repair gearboxes or other core components, that is the time to consider replacing it. Cars having mid-life crises can be expensive.

At this point I need to make clear that the “cost of repairs” is not what the Main Dealer Service Report says, but what The Guys In Your Local Garage That You Trust say. Which is usually about half what the Main Dealer says. So we get that clear. Main Dealers have, um, conflicting incentives.

Okay. Now for the theory.

The numbers we need to make the decision concern the costs of the repairs that will be needed in the future, for both the current vehicle, and our replacement of choice. That is the great unknown. Sure, a mechanic can look it over and warn you about visible rust on the body panels, and chassis, and the condition of the suspension and exhaust. They can't look into the gearbox, engine case and other such places where the real nasty surprises can be.

That doesn't mean we can't invent other criteria based on numbers we do know, and many people have done, but it does mean those criteria don't address the essential issue: the (unknown) future costs of both vehicles.

However, there is a way round this, which is to use averages to deal with all those might-be's and could-happen's that so many people rightly mention in the car forums when discussing this question.

Let's assume the car has been used "normally". Any other vehicle of the same same age, model and mileage also used "normally" will be in roughly the same condition, with roughly the same expected future expenses. Anything you are trying to dodge spending money on, any one else will surely have dodged as well. There no savings in buying a like-for-like replacement, unless it costs less than the repairs. Which is unlikely.

We have two decisions (note: not cars) available now: repair the current vehicle, or buy a replacement. Our "average" replacement will be running well after our "average current car" has reached the end of its life. So if we decide to repair, we will need to buy another car when the current one finally expires. Assume it is a comparable model to the one we would have bought if we had replaced it, the cost of replacing it later will be greater than or equal to the cost of replacing it now - because inflation.

Now repeat that with the replacement car when it gets its first painful repair bill. The same argument means we replace it, short of its possible full life-span. If it was bought new-ish second-hand (as opposed to middle-aged second hand), we may get ten years out of it. So over the course of our driving lives (say fifty years) we will be buying five cars on average.

If we repair-and-replace, we are effectively adding the cost of the repair onto the purchase price of the current vehicle, and buying a replacement after a longer period of time. Let's say the repair(s) cost £R and the purchase price is £P, and ignore inflation for the moment. Let's say that with repairs, we get an extra five years out the car. Then we will buy four cars over the fifty years (and still have some time left over) at a cost of £4*(P+R).

That compares with 5*P for the "replace" option. The two are equal if 4*(P+R) = 5P, or 4R = P. So if the average "exceptional" repairs cost less than a quarter of the purchase price of the replacement, it's better to repair-and-replace, rather than simply-replace. This proportion will vary with the life we get out of the cars, but isn't too far from what happens now. I'll leave writing the general formula and including inflation to the reader.

The more expensive the purchase price of the car, the more expensive the repairs need to be before replacing it. This does make sense: the repairs are deferring the high cost of a replacement of the same standard.

The shorter the life of the car, the more cars we are buying, and the lower the acceptable repair costs become.

This one-quarter rule is for all the future exceptional repairs to the car, not just the first one. There is no way of avoiding a prediction about the future behaviour of the car. While we may know the cost of the exceptional repairs now we do not know if there will be any more next year. Neither does the mechanic, unless the rust is staring both of you in the face. Those are our dice to roll.

Finally, we have been using averages. With averages come standard deviations, which will mean the costs may vary noticeably between two people running the same cars on this plan.