I'm rather certain you won't have to spend anywhere near that amount to get a computer to run BF4...even on max settings. I'll be back in a few minutes with a list of parts.
With that much money, you can build pretty much whatever you want...try this...
http://pcpartpicker.com/p/1dVU8
If that isn't enough power for you, grab another GTX 780 and run them in SLI. You could also go with radeon GPUs if you wanted. I think at E3 they were using two HD 7970s in Crossfire to run BF4. If I'm not mistaken, I think BF4 is going to be optimized for AMD GPUs as well. Not sure if it's true, but it was a rumour I heard a couple weeks ago.