Read what gpb said above. It's all true. Especially the part about sales tax and you need to take that into consideration. The rule about paying sales tax on the difference on a trade in is true here in Ohio also. Ticks me off too. It's like screwing you for selling you car yourself and then buying another car and forcing you to use a dealer.
It really matters how much your car is actually worth.
When my youngest daughter turned 17 I was looking for a car for her. Late one night a neighbor down the road calls me and says he is trading his Honda Accord Coupe and the dealer is only offering him $2500. KBB private party at the time was around $4,000. I said heck I'll give you $3,000 for it and he took it. We both made out on the deal. And my daughter loved that car.
2006 Alpine White/Terra Cotta BMW 330xi
1995 Yellow Volvo 850 T5R - Very rare car
2000 Red Crownline 180BR - Lil Red
2003 Dark Blue Toyota 4Runner V8