Interesting. Where are you coming up with $10.5k/day? Reading through GNK's quarterly reports their cash break even has been hovering around $5500/day (excluding debt servicing). GNK pre-paid their 2013 debt payments last year. i.e. no new debt payments until Q1 2014. So don't be surprised if their cash position increases from Q4. They won't have more than $100M in cash on hand because of the sweep account arrangement with their largest creditor.
It is in GNK Q3 earning presentation. In the Q4 expense estimate (free cash flow), the direct operating is $5200 per day. The General management fee is $1425 per day. The interesting cost is $3879 per day. The total free cash flow cost is $10500 per day. The $5500 you mentioned does not include interest cost and General Management cost.