Cheers in advance
The simple answer is you need HDMI to be able to play games and maximise the visual capability the PS4 offers! Seems a bit mad to spend so much money on the PS4 but not replace your TV to get the graphical / non game lag benefits!
Anyway, the ONLY way you might get this to work is by buying a converter.
search for HDMI to RCA cables.
You might want to ascertain what other types of connectivity you have from a visual capacity before you try and go this route.