IBM is a 20-30k employee company that employs 10 times that many, even after selling off most of its lines of business.
IBM's sole sources of consistent, stable income at this point are mainframes and legacy software. Poughkeepsie, San Jose, RTP and a few other major sites are keeping the company in business. You don't need armies of overpaid executives to run all that stuff, yet IBM still has them in droves. It will all come to an end.
@sws+1snaakHH makes a great point.