No way it'll cost that much.
Just did a dummy booking, the cost of taxes/fees for one way LAX - SIN is US$360 in F.
Your bigger problem is finding saver awards in first. I had to go all the way to July to find one and that too was one with a ridiculously long layover in Tokyo.Saver award is 91375 miles including the online 15% discount for one way LAX-SIN. The more likely standard award is 178500 miles incl the 15% online discount.