Replacing Rear Derailleur on Kmart blue-light special bike

No, this thread is not about one of my bikes (my two bikes are Treks) but that of the bike of a coworker's daughter (who's like college-aged). Somehow, she broke the rear derailleur (in pieces is how it was described to me) and so my coworker, who figured I know something about bikes, asked me what to do about it. I said that it probably isn't really worth fixing (it's a $90 bike originally that's at least a couple of years old) because the repair would cost more than the current value of the bike. Am I right? How expensive would the part be roughly? He didn't seem to want to replace the bike given that his kids all barely ride, but would still like to have a bike for that daughter to ride.