Hmm 450$ is tough
I have my prices in € so I can give you a rough estimate but it should get you started (US prices are often cheaper)
Amd APU 7700k ~110
AMD R7 260 ~120
FM2+ Mainboard ~80
550-650w PSU ~70-80 (xfx, corsair)
2133mhz RAM 8GB ~80 (Gskill, corsair)
-> and we´re already over... but this is what you´ll need for BF4 @1080p medium settings and 40-50FPS