A wrecked car understandably has less trade-in value than one kept in pristine condition, because it commands a lower price on the market. What may come as more of an unpleasant surprise is that this lowered value often extends to cars that have been extensively repaired and show no sign of damage. Once a car has been in a major wreck, the perception is that the vehicle will never be the same -- and consequently, the value won't be the same either.
As far as car dealers are concerned, major wrecks diminish the value of your trade-in, particularly if there was damage to the frame. You won't get the value noted in price guides, like Edmunds or the Kelley Blue Book. That said, even a wrecked vehicle has value. Some will take the vehicle and sell it "As-Is," passing all the risk along to the buyer, though those sales don't fetch anywhere near top dollar. Others will try and move them at auction or sell them overseas.
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Your best bet when trading-in a vehicle that's been in a wreck is to be honest. Even if the car passes the eye test, a dealer will be able to see details of the accident and the damage in the vehicle history report. A law passed in 2009 requires insurance companies to share data on totaled vehicles with the National Motor Vehicle Title Information System, a Justice Department database that dealers can access to flag damaged cars. As a result, trying to pass your vehicle off as a car only driven to and from the grocery store one night per week is unlikely to work.
Instead, let the dealer know the car has been in a severe wreck, and what you did to repair it. Bring copies of the documents from the body shop that detail the work done. If broken parts have been replaced by Original Equipment Manufacturer replacement parts, and if you can demonstrate that the car has been well-maintained since the accident and has avoided subsequent problems, you give yourself the best chance at maximizing your value. Getting an appraisal from CarMax provides a floor for negotiations -- if the dealer won't offer you more than that appraisal, you can simply sell it there and use the money to help purchase your next vehicle.
If the car is totaled and irreparable, or the damage is too severe to be worth fixing, you'll have a difficult time trading it in for anything other than a portion of what it could make by selling it to a salvage yard for the value of the metal and parts. Look for dealers that advertise their willingness to buy any car, and don't go in with the expectation of defraying much of the cost of your next vehicle.