i7-6700 ! Sorry , not 6200
I would say low FPS will be a problem with the graphics driver or graphics card. Something that interferes game play performance.
Have you checked with your computer manufacturer for more information about this issue?
If this is a processor problem, you need to check with your computer manufacturer for possible warranty options.
Provided that the voice tools you're using are VoIP-based (at least Teamspeak is), you have to keep in mind that they might utilize quite a bit of (network) bandwidth, depending on the codec and quality settings.
So one thing you could / should monitor to narrow down possible causes is your network traffic. If your bottleneck is network bandwidth, it might appear as if it's FPS drops.