They don't have to cost you nothing, just little enough that you're net ahead. And since startups that use the freemium model invariably manage to make free accounts cheap, I assumed I didn't have to mention that explicitly.
But isn't the percentage of users who pay what determines whether you're net ahead, and not the total number of paying users [1]?
If Dropbox has ten million users paying them $10 / month, but they have to support another billion free users for twenty cents per month each, they're screwed.
1. Assuming you're making enough to cover fixed expenses
profit = paying users * price per user - total users * expense per user - overhead expenses
Business on the internet seems to be much more about driving up total users while driving down expense per user, rather than driving up paying users / total users.