My usual policy is to keep cars until they just become too unreliable or expensive to service (or, as it turns out, get unexpectedly destroyed), rather than trading in early so as to always have a relatively new one.
I sat down and did the maths once to work out the optimal policy for buying and replacing cars. Based on the assumptions that
a car's buying price decays exponentially with age
its selling price is a constant factor of its buying price at any given time
running costs are independent of the car so can be neglected
the sole optimisation goal is to minimise cost of ownership per unit time (i.e. (B-S)/T, if you buy for price B and sell after time T at price S)
my conclusion was that the optimal strategy was to decide how old a car you could possibly put up with, and always buy cars a fixed amount newer than that, where the length of time is given by a formula involving the time constant of the depreciation, the buying-to-selling price ratio, and the Lambert W function, and (after fitting some figures from Parkers to my simplistic pricing model) it worked out to about 3.5 years for the sorts of cars I was interested in. Of course you can't choose the age of the car you buy that precisely, so the second question is what to do with a car you've bought which is newer than that – and the answer is to still keep it until it's as old as you can put up with.
Of course every assumption in that list is shaky. I occasionally wonder about trying to come up with a better model which is still simple enough to analyse. I'd particularly like to be able to factor in the increase of maintenance cost as the car gets more decrepit, which I suspect would give rise to an objective minimum that didn't have that irritating dependency on personal preference; but I'm not sure where to get good figures for that.
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I sat down and did the maths once to work out the optimal policy for buying and replacing cars. Based on the assumptions that
- a car's buying price decays exponentially with age
- its selling price is a constant factor of its buying price at any given time
- running costs are independent of the car so can be neglected
- the sole optimisation goal is to minimise cost of ownership per unit time (i.e. (B-S)/T, if you buy for price B and sell after time T at price S)
my conclusion was that the optimal strategy was to decide how old a car you could possibly put up with, and always buy cars a fixed amount newer than that, where the length of time is given by a formula involving the time constant of the depreciation, the buying-to-selling price ratio, and the Lambert W function, and (after fitting some figures from Parkers to my simplistic pricing model) it worked out to about 3.5 years for the sorts of cars I was interested in. Of course you can't choose the age of the car you buy that precisely, so the second question is what to do with a car you've bought which is newer than that – and the answer is to still keep it until it's as old as you can put up with.Of course every assumption in that list is shaky. I occasionally wonder about trying to come up with a better model which is still simple enough to analyse. I'd particularly like to be able to factor in the increase of maintenance cost as the car gets more decrepit, which I suspect would give rise to an objective minimum that didn't have that irritating dependency on personal preference; but I'm not sure where to get good figures for that.