In fact, the gov't makes the company pay the "going rate", In my experience, this is not true. Unless the going rate for a masters in mechanical engineering and 5 years experience is $20,000 to $25,000 per year.
Completely false. I work in compensation for an engineering firm ... the gov't rate for an engineer with a Masters is about $55,000. But, that also depends a great deal on the job and the skill set required.