I know I'm going to get slated for this, but it actually made me understand this stuff better...
On my FM12 season (laughs starting already

), I was Man U (they headhunted me, I didn't start off there!) and the club was losing 12m a month, my 1st season I won the league and the season after, I won everything and actually made a profit for the year despite losing astonishing amounts a month (especially in the transfer window), next season, I get massive sponsorship deals, stadium gets extended (91.6k) and got 12m for winning CL + 6m in TV money (probably more) 15m for the league (as well as TV money), so, my point is here, these clubs can afford to lose colossal amounts a month if they are successful, they get it back, so yes, football can be profitable even for the likes of Man City.
Cue the 'hating' because I mentioned FM!