The Vorpal Sword is a legendary magical item that allows heads to be struck from bodies, as well as doing a tonne more damage if it doesn't. A good summary has already been discussed on this site

I'm a little unsure how it would affect a creatures CR though, and would like some help.

In order to make this question specific, but I would like to understand your workings, How would giving a Bugbear a Vorpal Sword affect it's CR?