If you are about precision, then you aren't going to find cheap + accurate ammo without reloading. However, if you don't want only soft-point stuff, and are willing to potentially "settle" for 1MOA out of a .5MOA rifle, then you can find some stuff down into the ~$7/20 range, like this:
AMM-7340 - Ammo .308 Win. TulAmmo FMJ 150 Grain 20 Round Box Made in Russia 2800 fps Steel Cased Polymer coated.
However, you can load quality ammo for about $20/50 (i.e. $8/20), not including cases, if you are willing to get into it. Though, reloading takes a pretty good investment so it would take several hundred rounds to break even.