The first thing Mark Cuban did when he became a billionaire was a "little naked billionaire dance."

Then he bought a plane, he tells the audience at OZY Fest in New York City.

Cuban became a billionaire back in 1998. That's when he and Todd Wagner took their online audio streaming company, Broadcast.com, public.

"Obviously I knew exactly what the number was to become a billionaire," Cuban says of the stock price, to the audience at OZY Fest.

"And so I am sitting there naked one morning. Naked. Bam, bam, bam, refresh, refresh," says Cuban. He was repeatedly hitting "return" on the keyboard to update the website where he was watching the stock.

"[The price] gets up there — and then I did my little naked billionaire dance."

He jokes that becoming a billionaire affected his appearance, too. "I was so much more handsome that next day. No lie," says Cuban.