for the money you use to buy a PS4 plus PS+ subscription, you could probably find a reasonably good HDTV in 2015.

Your TV surely has some sort of input connector, SCART, RCA (composite or component), S-Video, VGA, whatever, you should be able to find the right HDMI to x converter to use it:

https://www.google.it/search?q=converter+"hdmi+to"

What, there isn't an AV Multi Out on the PS4? Haven't really looked much at my console :( but there is only HDMI? Sony really pushes new technology. Not that I complain.

Your TV is probably not full HD anyway. Your TV can be 1080i but only have a 720p native resolution (does your TV even support true 1080p?).

Seriously if you buy a PS4 you need a full HD (1080p native pixels) TV!

Hard to really HDMI new :p

OT: A new mediocre tv like others have said would be the best option. They're cheap and the quality gain in playing will be easily noticable

You can run it through a cheap surround sound. You can find them for less than $100.

Then yeah just the cheap converter Pi linked to will work fine. It won't be HD, but it'll look good enough on your TV.

I wouldn't call it new. The 360 launched in 2005 and already had a HDMI port. Almost 10 years later is time to move on.

I think you need HDMI converter that converts from HDMI to component.

No. The HDMI port was added in later models in 2007.