[edit] Thank you all so much for your responses!
Given your information, I'm not sure that a replacement car would be better than your car with a new transmission.
What is the value of the car without repairing the transmission? Probably a lot less than $3,100. Let's say $1200. So $1200 + $2300 maximum saved from repairs is $3500. Can you get a better car than the Malibu (with a brand new transmission) for $3500?
You'd probably be looking at 2000-2006 Toyota Corollas and Honda Civics, and they'd have 140-180k miles on them in that price range. Possibly "better" than your Malibu, though going through the trouble rather than just getting the repair seems like a stretch.
We're getting our car appraised right now to see how much it's actually worth in its current state. It seems like the usual advice (at least around here, and correct me if I'm wrong) is to only replace your car when the cost of the repairs exceeds the value of the car.
When faced with a problem like mine, could it also make sense to pay more for a car in nicer shape and use that for another X years?
(thinking our loud, bear with me)
There's a break even point somewhere between fixing your existing car and paying for a new one.
If I bought a new-used car for $9000 and kept it for 10 years, the annual cost of buying that car would be $900.
If I chose to repair our current car for $2300 and kept it running for 3 years, then the annual cost of owning the car would be $766, or cheaper than buying a new-used car.
hmm, I guess it doesn't really make sense, does it? It would really only tip in favor of buying a new-used car if I kept it for significantly longer, or if the transmission repair would only keep the car going for another year or two (unlikely).
First, have you gotten a 2nd and 3rd opinion on the supposed work that needs to be done, along with estimates for said work?
Also, get a second opinion from another shop. Maybe they're wrong and you don't need to replace the transmission after all. Either way, it can't hurt to get another set on eyes on it (and don't tell them what the other shop said before they look at it, just say "symptoms are happening, what's wrong with my car?").
We haven't gotten a second opinion, partially because I trust the first diagnosis. A transmission fluid flush was initially suggested - the mechanic said that it had a decent chance of fixing the problem, and a replacement would be needed if that didn't work out. However, our car has had a history of transmission issues, including a transmission-related recall that we had maintenance for around a year and a half ago IIRC. Only after telling him this did he decide that a fluid flush probably wouldn't fix the problem and would be a waste of money.
I suppose a second opinion wouldn't hurt, though.
Second, you don't mention why you don't want to just have your current car repaired.
Is there a reason you don't want to fix it?
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Third, you don't mention what your budget is for a new vehicle.
Is it $5K, $25K, $50K? Do you have the funds saved up to pay for a new vehicle in cash?
There are other flaws the car has (gas gauge is somewhat broken, mirror buttons don't work, lock/unlock buttons are getting worn out) that don't bother me as much as they bother my wife, but that does factor into our decision as well. Also, since neither of us are very car savvy, it would be nice to have a car that requires low maintenance.
Tentatively our budget is ~$9k. We don't have a new car fund but we have emergency funds that can cover the cost of a new car.