Facebook's user population has more than doubled since January, from 150 million to 350 million. But investors who still hold shares of this pre-IPO social superstar may be sitting on an 18-bagger.

More on the math in a minute. First, the news: TechCrunch's Michael Arrington reports that Facebook recently repurchased shares at $25 apiece for an implied valuation of $11 billion. Yet the price may be inflated, more a consequence of contractual demands than market demand.

"This transaction was initiated by a third party and was going to be run through Second Market," Arrington writes. "When common holders indicated they wanted to sell, Facebook had to let the sale happen or exercise a right of first refusal. They exercised that right."

Maybe this isn't so bad. Microsoft (NASDAQ:MSFT) purchased an earlier stake in Facebook at a $15 billion implied value. Twitter is already worth $1 billion, and Web-based companies are gaining steam in the IPO market. Recent examples include OpenTable (NASDAQ:OPEN), LogMeIn (NASDAQ:LOGM), and Changyou.com (NASDAQ:CYOU).

What worries me is Facebook's run-up in price. In January, investor Paul Kedrosky mused that Facebook's value had topped out at $600 million. Say he was off by 100%. Say Facebook was worth $1.2 billion at the dawn of 2009. Longtime investors would still have seen a nine-fold gain in their holdings this year. And if he was right, those same investors are now sitting on -- yep, that's right -- an 18-bagger.

All of this is problematic if Facebook wishes to go public in 2010. CEO Mark Zuckerberg can't price his company at $11 billion if that's what private equity investors are paying now. They're looking for a mark-up. A big mark-up, if possible.

You know what 2009's biggest IPO to date was worth? Brazil's Banco Santander (NYSE:BSBR) came public in October at just over $4 billion. Rocket stock A123 Systems (NASDAQ:AONE), one of September's newbies, is still worth only $2 billion, and that's after a 56% run-up.

In the end, it really doesn't matter what anyone says Facebook is worth. All that matters is the pricing the IPO market will tolerate. Right now, $11 billion looks too rich.

Have a different view? Let's hear it. You can weigh in using the comments box below.

OpenTable is a Motley Fool Rule Breakers recommendation. Microsoft is a Motley Fool Inside Value pick. Motley Fool Options  has recommended a diagonal call strategy on Microsoft. Try any of our Foolish newsletter services free for 30 days.

Fool contributor Tim Beyers didn't own shares in any of the companies mentioned in this article at the time of publication. Check out Tim's portfolio holdings and Foolish writings, or connect with him on Twitter as @milehighfool. The Motley Fool is also on Twitter as @TheMotleyFool. The Fool's disclosure policy is always public about disclosure.