Startup investor Chris Dixon posed an interesting question yesterday: we know that Facebook’s current business is selling ads on its site – what is its next business?

Facebook needs another line of income to live up to its huge value, conferred by stock buyers who, as Dixon puts it, see the company as the sum of:

“the existing display ad businesses, and a probability-weighted option on a new line of business.”

Almost a billion people have a direct interest in what that business turns out to be, since the data they’ve volunteered to Facebook will be a part of it (read our feature “What Facebook Knows” for more on how the company uses data from its users).

A recent Goldman Sachs report suggested three possible new businesses for Facebook: expanding its existing business into China, using data it holds to target ads that appear on other websites, and launching a Google-style search engine with lucrative ads.

Dixon dismisses the first two as not being profitable enough:

“The only (known) models that deliver [margins] high enough to compete with Google are search, payments, and e-commerce.”

There’s evidence that Facebook is actively considering all three of those. Facebook’s founder and CEO Mark Zuckerberg said himself last week that launching a search engine was a possibility (see “Facebook Eyes Search”). Facebook already makes a lot of money from payments used in games such as Farmville, but in May Zuckerberg’s CFO told investors that:

“In the future, we may seek to extend our payments into areas outside of games.”

That might have something to do with the “want button” the company is testing for people to signal interest in specific products, which could could provide a mechanism for Facebook users to buy goods from within the site. Whatever Facebook’s other business turns out to be - and it could be none of those three - we can be sure that it will rely heavily on the company’s most valuable asset: what it knows of the relationships, life events, music listening habits and more of its members.