Is there some tax advantage? It is such a waste to pay that amount when you can buy a copy for $25 from a street corner seller. Plus it would come with a frame.
An object is worth what someone will pay for it. The buyer clearly wanted a piece of human history, an utterly unique and famous work, and isn't merely interested in the viewing of the image itself. We all just got that for free by looking at the article. If you have an extra half-billion laying around, being the only person on earth with a daVinci painting isn't a bad bit of fame to purchase... and with almost 100% certainty, it will appreciate in value... which cannot be said for most investments.