Try $100m. There's no reason it can't be done. Take TWOK and break it down in to what it physically is in terms of sets, models, number of actors etc. The TOS crew, Montalban, Judson Scott, Paul Winfield, a few cheap actors for Montalban's crew, Reliant bridge crew, Enterprise engineering extras, Enterprise, Reliant bridge sets, Celti Alpha planet set, Kirk's quarters, sickbay, Genesis tunnel, and the Genesis cave which was a matt painting.
Would it not be cheaper to go back to physical models than all this excessive CGI? Trek was always content over flashy visuals, not that there was any flashy visual technology in the 80s when the TOS films were made. I'd rather watch the slow suspense of the Mutara Nebula chase than any of the visually overbearing CGI sequences in the Abrams reboots.