I'm not running a faucet myself, but just today I checked that freebitco.in transfered over 0.13 BTC, and that's for one week only, to their users. I think it's profitable if they are doing this for years already.

I think the amount of your initial investment depends mostly on how much your faucet will be giving and on how many users you will have. The more users the more you have to pay, but on the other hand you can make money on ads on your site if you have a lot of daily visitors.