I wouldn't be buying it without the trade. I've already paid those taxes when I bought the vehicle I'm trading.

The dealership doesn't pay tax on a trade in so it shouldn't be making up part of the trade value. Just like taxes aren't collected on the full value when there's a trade so they shouldn't be part of the equation either.

If I get to the same final number by excluding taxes that don't exist from the trade and from the new vehicle and then applying it to the difference. That means they are getting my trade for a lower value.

In this case they can tell me about tax savings all they want but at the end of the day they are getting my vehicle minus the taxes they added.