The BMW K1300S is only homologated to Euro 3 standards which means you can't buy a new one and get it on the road next year anymore. At least in Europe. Thus BMW has already removed it from its home page and sells off the remaining stock. Probably until the end of the year (they could license it and sell into 2017 but stock seems to be quite low).
I had the bike since 2009 as a company bike and when I returned to Germany that was the thing I found to have missed abroad the most. This is a bike from the time when the company strived to built the best motorbike technically possible. A time that has since passed in most of the automotive industry. Sad but true. Lifestyle products anyone?
So ... I've already bought mine last year.
It hasn't changed much from 2009 so there is no reason to buy a 2016 model year, buy any in good condition.
Double check that the handlebar switch units have been replaced with the improved versions (both sides). The stock ones don't like heat and stop working when it gets really hot. I got stuck at a friend's house after going for a long swim in the warm summer of 2015. BMW had a free replace-if-customer-complains (silent) recall until the end of last year. Prod your dealer to get some good will out of BMW Motorrad. Esp. before you buy. Also check the cardan drive for excess degrees of freedom. It doesn't take "binary" road racers too well. So make sure you get to know the previous owner.
As Motorrad 17/2016 put it:
In last years' sportstourer concept comparison the K 1300 S [..] still blew the competition away.
Brutal while well honed, that's the lasting impression. [..] Extra-ordinary stable, tight and still comfortable.
And still today the K 1300 [S] is the reference in breaking, because of the wide wheel base and because she stays up when breaking. [The K-BMWs of the last generation] are cold perfection, executed into each detail. Just different.
That light we see is burning in my hall. How far that little candle throws his beams! So shines a good deed in a naughty world. William Shakespeare, The Merchant of Venice