I don't know where in the world you are, but here in Canada I can buy a cheap Chinese FM radio at The Dollar Store for $1.00. It comes with earphones, a battery and has a light that is a flashlight.
It uses a Chinese copy of a Philips radio IC.
You don't tune it, it scans the dial and you can stop the scan at a station.
Its reception is for strong local stations only, it picks up a lot of interference and its sound is very distorted.
You might be able to make one for $25.00 in parts if you can buy all the parts somewhere.
My Sony Walkman FM radio cost $19.95. It is stereo, sounds very good and picks up strong and medium local stations. It gets overloaded by strong local stations so it has an attenuator on its antenna input.
There are some super-regen FM radio projects on the internet. They work poorly but are cheap. Look in Google for Radio Shack Special and click on the RSS link.
**broken link removed**