There's two ways to look at this. One is, "Is hiring an intern a net profit?" The other is, "Is the intern's work, minus the cost of mentorship, a net profit?"
When I was in college, I did a paid internship at a health insurance company, wherein I audited, documented, and updated requirements for a large SQL script that pulled data from hospitals and used it to calculate reimbursement for Medicare/Medicaid claims (RAPS). Basically, you have to map hospital billing codes to federal ones.
The script was written several years prior by my mentor, and the risk adjustment department had no visibility into how the codes were mapped -- and if it was wrong, we could be fined up to ~$10M (depending on severity), or be missing out on ~$1M in revenue. (It turned out my mentor had done a pretty good job and we only needed minor adjustments, although we also updated the architecture so the risk adjustment folks could define the mapping themselves going forward.)
So in short, I can definitively state that
1) it would have cost the company less for my mentor to do the work directly.
2) The several thousands of dollars that the company spent between my salary and my mentor's was definitely worth the millions in mitigated risk/liability.
3) My mentor enjoyed teaching me much more than he would have enjoyed doing the work himself.
And I'd like to think that I ended up doing a slightly more thorough job than my mentor might have done -- his long tenure at the company and accumulated knowledge of these sorts of scripts being job security of some sort ;)
Anyway, the point here is that internships don't have to be a zero sum game. They can cost more than paying your existing employees to do the same work, and still be valuable.