they paid for it with the aguero money. they could've put that money into their debts, and then slid down to a mid table club. or they buy falcao and chase champions league glory, sell falcao + make some money through champions league windfall. what they've done is better than the alternative, which would be slipping into nothingness, being consumed by debt and really becoming obsolete.
i'll link this again, it's a fascinating read.