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So you are frugal, and understand that driving to work is not an exercise in style. Therefore you hope for your car to get to 250,000 miles. However, parts start to break down at 150,000 miles and you are hit with a couple of repairs within the last two years of $2,000 and $5,000 respectively for a car you bought for $25,000 in 2010.

Now there is a new repair bill coming in, and if you make the calculus of investing the difference between $25,000 you would be spending in a new car minus the cost of the expected repairs in a 5-year period you expect to keep the current car if you repair it (for example $8,000, and assuming it is paid upfront today) at a 6 percent yield (say, stock market): the present value of the investment will be -$17,000 and the future value of that investment will be ~$23,000 in 5 years, for a gain of $6,000.

If this way of thinking is sound, there is no question that keeping the car, and repairing is the right choice. Further, if you buy a new car now, as opposed to in 5 years, that new car will start siphoning savings in repairs 5 years earlier also.

The counterargument is that I should already be factoring in the $7,000 spent in recent repairs, and although this is money already spent, I could make the same argument every day, even if I was hit with a similar repair every day in the next few months. So there has to be a different way to calculate the difference.

I could just calculate the future value of $25,000 invested in stocks at an expected return of 6 percent (conservative or not - I don't know - but there is no bank interest anymore, so just humor me) for 5 years as $33,000, and say that the break-even figure is $8,000, but of course, this is future money - not present.

So what is the right way to calculate whether to dump the car or repair it?

Antoni Parellada
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    Your question is a bit confusing, but are you basically asking "at what point is it better financially to buy a new car versus repairing an old car"? And does "new" mean "new from GM" or "new to you, but can be used"? – Joe Nov 13 '19 at 20:56
  • Yes, you understood the question properly. New in this context maybe used - just "new" to me at a cost of $25,00. – Antoni Parellada Nov 13 '19 at 20:59
  • @Joe I think that answer is very qualitative, and focused on specifics. I'm interested in the time value of money and comparison of strategies from a purely mathematical viewpoint. – Antoni Parellada Nov 13 '19 at 21:01
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    I don't think I see how the question can really be answered quantitatively, because the numbers differ for each case, no? Ultimately isn't it just a matter of comparing the cost of a new car to the cost of future repairs (ignoring sunk costs)? You can amortize the cost of the new car of course if you're not taking out a loan, and create an effective interest rate vis a vis the time value of money as you say, but isn't that it? – Joe Nov 13 '19 at 21:08
  • @Joe. Can you write up the reasoning with an example? BTW without financing the new car. – Antoni Parellada Nov 13 '19 at 21:11
  • Have you read the fourth answer on the suggested duplicate? That does that, more or less... – Joe Nov 13 '19 at 21:15
  • @Joe what is the meaning of "amortize the cost"? – Antoni Parellada Nov 13 '19 at 21:17
  • Besides the case by case variation, the difficulty in answering the quantitatively is that any answer is going to be based on predicting the future, so there's a degree of risk. Generally speaking, for most people, the risk largely accounts for the differences in outcome (i.e. the "cheapest" route is likely to be riskier). So, rather than thinking of this as a problem with a solid answer, it's just as much a problem where you have to determine your risk tolerance before answering. – dwizum Nov 13 '19 at 21:19
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    @Toni Amortize means spread it out over time - i.e., $25k for a car that you think will last 10 years means you allocate $2500 cost per year for those 10 years. – Joe Nov 13 '19 at 22:05
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    "…that I should already be factoring in the $7,000 spent in recent repairs" No. These costs are sunk costs, you cannot do anything about them. – glglgl Nov 14 '19 at 10:29

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