More expensive to have them out of jail.
Specially if you are the one that gets robbed/beaten/murdered.
Applying your brilliant logic of simply ignoring costs v benefits, one would have to rule out all kinds of other things in life. By the way, it's "especially" that you were looking for. Most robbery victims, I can assure you, do not suffer 100K of loss. That's average cost of incarcerating a criminal each year. There's a reason why, by and large, every semi-informed commentator on all sides of the political spectrum regard prisons as a social and economic failure.
LOL - an English lesson, however correct, doesn't make your rebuttal correct. English lesson aside, your maths is flawed.
Here is some cost vs benefit analysis for you - only 6.2% of burglary's were solved in Auckland last year (LINK). Criminologist etc regularly assert that criminals are only convicted of a fraction of their actual crimes. That means that your average burglary criminal is possibly/probably responsible for up to 16 times more damage than he is being given credit for. If we take a conservative average cost of $10K in damage & loss per burglary(think property repairs, goods replacement, time off work sorting it out, the investigating cops wages, forensic analysis, cost of upgrading security/cameras/alarms/insurance etc), for a total cost of $160K pa to keep a thief at large vs $100K pa to keep them in jail, society would save a cool $60K per year, per burglar by keeping these guys in jail.
That is a return on investment of 60% which is a damn compelling cost vs benefit.
Prison is for punishment of offenders and the safety of the public. The fact that it fails at corrective training reveals lost opportunities, not a failure of the punishment, and not a failure to protect people as it is 99% effective at preventing prisoners from harming the public.
Edit: avoiding a schooling in English.