12 USD per day and per machine ?
So 12kUSD per years ?
No. 12 USD per day * 365 days in a year = 4380 USD. This is with the current difficulty and is surely to be different (lower) as time goes on.
It's very safe to assume that you won't really make 4380 on the first year but less, unless Bitcoin's price increases to reflect the increase in mining difficulty.
You should also account for the reduced hashrate from the broken hashboards the S9 frequently exhibits. It's actually a horrible miner in terms of reliability but most likely the only profitable one.