If you have really cheap power and can grab a bunch of cheap cards from the panicking miners - why not?
FPGAs seem more promising, though. But that's painfully not the "cheap" part.
Here is a reason why not:
A 6x RX480 8 GB rig will earn $1.81 a day with free power. That is $0.30 per day, per GPU, of profit, again assuming you have zero electric costs.
Used RX480 8GB on eBay averaging around $120 (some cheaper some higher). That represents over a 400 day payback period just to earn your investment back before really starting to turn a profit.
Oh wait, I can already hear you say that the coin's price will recover by then making it a smart investment.
Well here is an idea, if the price is going to recover (probably well before the 400 days it would take to ROI on your used GPUs) why not just buy the coins outright, sit back and not worry about miners, electricity, heat, noise, etc., and profit?
Right now in today's market (may change in the future) it makes zero sense to invest in mining equipment even with free power. If you want to invest money, simply buy the coins.
Sure the prices may go down a bit more, but right now is the time to be thinking of buying coins. For less than the price of that used GPU ~$120 you can now buy a whole Ethereum coin, which would take you over one year to mine with the used GPU. I expect in the near future you may be able to pick up close to 2 ETH for that $120, so then would definitely be the time to jump in.
The super low coin prices will seem like everything is over but in reality they will represent the time of maximal opportunity. Opportunity that is for investing in coins directly, not in mining.