"The Adolfsens claim that theirs is 3.5 percent, but Herning calls that figure “highly unlikely. All the other refugee companies that I’ve looked at have a much higher profit margin.” She says that in handling revenue from nursery schools and nursing homes, the Adolfsens have played a shell game, shifting profits from one business within their conglomerate to another. “I wouldn’t be surprised if they were doing that for Hero as well,” she says."
Also, quick searches seem to indicate that for-profit prisons (in the US at least), an analogous industry, have profit margins significantly north of 3.5%. [1] I wouldn't be surprised if the actual profit margins for the refugee care companies, when all subsidiaries are included, are between 5-10%.
I don't know if there's a perfect solution to refugee care that optimizes spending and societal harmony, but private enterprises running the show with close government oversight (and no shell games), seems like a somewhat happy middle ground.