There are lots of possible itineraries using the Oneworld or Star Alliance RTW products that can touch all the continents with a base price of under US$2400. These would include checked bags and could be changed at no or minimal cost. For example, starting in Budapest you could fly
BUD-MAD-BOG-DFW-NRT-SYD-JNB-DOH-BUD (Oneworld LGLOB34) with a base price of US$2374.