You will be competing with *3'd GENERATION* ASIC miners trying to do that - total waste of time.
For comparison, your RX 480 *MIGHT* manage as high as 2 Megahahs/sec using 150 watts or so (my actual estimate would put it closer to 1.5 megahash).
My A2 *2'nd GENERATION* ASIC manages 110 Megahash at 1250 watts - 55 TIMES the hashrate at less than 10 times the power - and MY units are not highly profitable at this time even with my very cheap electric cost.
Current generation ASIC miners manage closer to 500 Megahash at around 800 watts.
You should be looking at something like ETH or ZEC or such to mine, you might be able to make SOME coin that way.
Trying to mine anything Scrypt on it is going to cost you quite a bit more in electric usage than the value of any coins you manage to mine - and solo-mining you'd have better odds buying a lottery ticket for Powerball.