I was going to write a bunch of clever calculations but you are right. It is actually more sensible to just exchange the $15 to 0.03 btc.
But if you really wanted to make a profit with a mining device of some kind, how would you be able to gauge the performance? Like "price per ghash per watt < x"? Did anyone make an online calculator for that?
-Michael
http://mining.thegenesisblock.com/ is pretty good. It suggests an average (exponential) increase per month, but you can input your own estimates. If you are serious about trying to profit, you should probably analyze a few different scenarios to see if it makes sense to purchase a particular miner.
I have made a more detailed post in the past, which may interest you.Of course this all assumes your primary goal is profit.
Generally (at this time) you will have a hard time finding a miner at a cost low enough to be profitable.