9 to 12 months most likely. Rumorville says both AMD and Nvidia have just recently taped out their first 16nm GPUs. Now they need to make some "first run" chips, and start testing those out. If they find any problems, they will need to modify their design, tape out again, and start all over with the testing. Eventually, they will get some stable silicon, but at relatively poor yields, and the fabs will be trying to improve that for them, but it all takes time. Lots of testing, modifying designs and processes, and eventually they learn how to with with that node better, and yields increase.
Designing GPUs is an expensive and very time consuming process. Latest estimates on cost to design a modern GPU and bring it to market is between $250,000,000 and $450,000,000.