My $0.02. If I had been badly low-balled on the trade-in (and thankfully I was not), I would have walked out with my printed copy of the 'great purchase price' and shopped the sale to other dealerships. Most dealerships will at least match a competitors price, as long as its real. At a minimum, they will bend-over backwards to get very close to any other dealer's price.this to me seems like a dealer can give you a great purchase price only to dog you on the trade-in value. your out-of-pocket expense can end up even greater on the "better" purchase price.
So worst case: I spend some more time to get competing bids on the trade-in, all while staying at or very close to the great new car price that I negotiated from the first dealer. To be honest, I didn't want to shop the deal ... I made it clear to the dealer that I didn't want to shop the deal, as long as they made a fair offer on the trade-in ... and in my case the dealer did increase their trade-in offer in order to keep me from shopping the deal. Win-win.
A great new car price in writing is like gold: Once you've got a committed great price on the new car, you really have all the leverage as long as you don't let yourself get emotionally invested in buying on the spot.
As always, YMMV, and I'd love hear other's opinions/strategies.