Connect Apple TV to VGA Computer Monitor using a VGA to Component Cables?

Hey all,

I have an older CRT monitor I use for watching my iTunes content while in bed, which is connected by a 25 foot VGA cable to my iMac in my bedroom.

I will be moving into a new apartment next weekend and my places configuration is going to change. I wont have room for my desk in my bedroom anymore (smaller bedroom) so it will need to go in the living room (3 times as big as before).

So everything is shifting around but I still want to be able to watch my iTunes content in bed. So now I am curious, is it possible to use something like below, which sends out the video signal over component RGB and the cable converts it into a VGA signal for the CRT monitor?

http://microcenter.com/singleproduct_results.phtml?productid=0260535


If not, any recommendations? I know they make converter boxes, which are kind of expensive, but for that kind of money, I might look for a cheap LCD with HDMI input to use the Apple TV with or something.

Thanks in advance!
Tim