I think I have come up with a really cheap PC build that might be able to handle next gen. On the BF4 system requirements page on BF4 Central, it said that the low-end GPU was a GTX 550 TI Boost, but I couldn't find a TI Boost so I just got the TI. Since it has the Intel Core i5-330 3.0Ghz it meets the recommended requirements on BF4 central system requirements. And the 8gb of RAM, I think it can handle most games at 720p right?
Build: http://pcpartpicker.com/user/IAmMatt907/saved/2lKi
Build: http://pcpartpicker.com/user/IAmMatt907/saved/2lKi