it's up to the dealer.
if your car is worth the same then they may do a straight swap (well actually it would have to be worth a little more as they will want to sell your exchange car and still make a profit)
if your car is worth significantly more than the new car then it may even end up with the dealer giving you money and you drive off in another car.
But there is no rules or requirements for part exchange, it's solely at the discretion of the dealer if they even want to take you car as part exchange and how much they value it at.