You should offer lower than what they show you for invoice. Dealers have discounts from the manufacturer so the invoice they are showing you is not what they paid for the car, but rather what the manufacterer would sell the car at face value for (not including discounts+incentives to the dealer).
I just bought a 2010 370Z Touring last weekwhich listed at $38,000 and the invoice was $34,555 but I ended up walking out after offering $33,000 without them coming down from invoice. They called back later that day and said they will do it for $33,000. Just my advice, you might make up another 1-2,000 off the price of the car which will offset your trade in if they don't budge on trade in.
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