I've said before that I'm interested in buying shares of the Facebook IPO. I'm still interested, even though my earlier prediction -- that the social network would command a \$50 billion valuation -- now appears to have been off by about 50%.

Some see that as a problem. How could Facebook's \$4 billion in annual revenues be worth \$100 billion when Apple (Nasdaq: AAPL) nets just five times as much market value while producing 35 times as much revenue? Google's (Nasdaq: GOOG) \$40 billion in sales is worth just \$200 billion in market cap.

And don't forget Renren (NYSE: RENN), China's version of Facebook. The social-networking site is profitable and using Groupon-style tactics to milk revenue from its 147 million active user base, yet commands less than \$3 billion in U.S. market value. There's virtually no precedent for Facebook's stunning valuation, but there is a theory.

It's called Metcalfe's law, which states that the value of a telecommunications network is equal to the square of the connected nodes. Credited to Robert Metcalfe, founder of Hewlett-Packard division 3Com and one of the originators of the Ethernet networking protocol we depend on as modern Internet users, the theory describes the geometry of network effects.

There's value to the idea. Network participants create value when they interact with each other. Thus, more participants create more value, as has been the case at eBay (Nasdaq: EBAY) throughout its history. Facebook benefits from similar math. The larger the social network gets, the more valuable its data and advertising platform becomes.

Enter Metcalfe's law. According to the formula, Facebook's 900 million active users compound to create a network worth 8.1 x 10 to the 17th power, or \$8,100,000,000,000,000,000. Crazy, you say? Undoubtedly, especially since Metcalfe's law was originally intended to describe the value of fixed cost nodes rather than human participants with varying behaviors.

Yet the number produced using Metcalfe's law doesn't have to be accurate to be instructive. The point is that, going by the current math, Facebook's 900 million active users are worth \$111 each in market value. Do advertisers see that as fair? I think so, especially given the millions spent annually on scattershot broadcast campaigns that -- at least according to some executives -- are nowhere near as effective. If I'm right, Facebook is worth every penny of the premium investors will pay on opening day, although it doesn't come without its questions. In fact, one Fool, our senior technology analyst, thinks another social-media company holds even greater promise than Facebook. To find out exactly which stock he thinks can outgrow the mighty Facebook, access our free research report today.

Fool contributor Tim Beyers is a member of the Motley Fool Rule Breakers stock-picking team and the Motley Fool Supernova Odyssey I mission. He owned shares of Apple and Google at the time of publication. Check out Tim's Web home, portfolio holdings, and Foolish writings, or connect with him on Google+ or Twitter, where he goes by @milehighfool. You can also get his insights delivered directly to your RSS reader.

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