Your shipping agent should have the figures, I've dealt with the port at Izmir a couple times, it used to be so hit & miss on charges. Heard of people (Brits) kicking up hell there over the "!how did you come up with that price"? In one case their gear remained at the port for two extra weeks till they paid.
Most time I have heard it runs right & proper.........if its only furniture it shouldn't cost an arm & a leg. Obviously you will need someone with you who speaks Turkish & of course all your own relevant documents.