it is only possible if you can cannibalize some standart parts everyone should have.
Like casing, keyboard, mice, monitor, dvd-rom, hdd, desk, chair ...
what I could get for 500 bucks was:
530w psu: 35€
Motherboard z87: 80€
i5 4670k: 180€
amd 7870: 150€
8gb ram: 65€
the rest I already had ... dunno if it can compete with a ps4, but 1080p60fps is no problem until now.
except star citizen ... 1080p30fps only :/