Some billionaires and CEOs will have to choose between Trump's inauguration and day one of Davos.AP Photo/Evan VucciDecisions, decisions.Billionaires and CEOs have to choose between Donald Trump's inauguration or the first day of Davos.Attending Trump's inauguration could mean scoring face time with the new president.It's a scheduling conflict most of us will never know.Some of the world's wealthiest and most powerful people are staring down a decision as the first major events of the billionaire social calendar this year overlap.President-elect Donald Trump's inauguration on January 20 coincides with the first day of Davos, an annual gathering of the world's business and politics elite in Davos, Switzerland, held by the World Economic Forum.Those invited to both must now decide: Do they miss potential face time with the incoming president and members of his inner circle or skip a day of networking with political leaders and business titans from around the globe?Trump's swearing-in begins at noon ET on Monday.The first item on the agenda at Davos, "First Impressions: Inauguration Day," starts at 3 p.m.