Also, don't forget the tax benefit you get by the lower price of the care you're buying. Not sure if this is new cars only but that offset can be thousands, depending on the trade-in value and new car cost.
To explain (for anyone not familiar since the way you phrased it might be confusing):
New car price: $30,000 Your trade in: $10,000
Net price: $20,000
So Sales tax 6%20,000 vs. 6% 30,000 (example of a state with 6% st)
If you sell the car yourself you can still use it as a trade in if you can coordinate with the dealer and your buyer and do what is known as a courtesy trade.
But you have to get the buyer to show up and take your used car when the dealer delivers your new car. The dealer does the paperwork and usually charges a few hundred dollars or less for handling the sale. It is well worth the trouble if you can get the cooperation from the buyer.
The average dealership doesn't know if they're going to keep a car for their own inventory or going to sell it at auction/wholesale until they own it. Standard procedure is to purchase a car (purchase = take it on trade-in/buy it) and then have the mechanics inspect it to see what it needs done on it to get it back out to sell. If it's too expensive, they wholesale/auction it. This means, 90% of the time, they default to offering you the lowest value.