To win a championship. Pagliuca didn't commit to paying the tax next year, though. Time will tell.
The team can certainly afford it in light of the massive profits they've been making.
Ownership claims they were losing money through most of the KG/PP era (I can't find a link, but I've heard Wyc say this a couple times). We always had one of the highest payrolls, and that was under a bad local TV deal and a less lucrative CBA and national TV deal. They gotta be rolling in cash now. They will pay the money if needed.
It also helps having a fanbase that continued to pump money into the franchise during talent-lean years after the KG/Pierce departures. C's fans are the best in the league, and you can bet that gives ownership a lot of confidence to spend money and keep the ball rolling.