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Photographer: Jin Lee/Bloomberg

LinkedIn shares doubled in price early Thursday after making their public debut, giving the company a value of more than $8 billion. How expensive is that for such a stock? By my math, even at the subscription price of $45 a share, with a corresponding market value of $4.3 billion, LinkedIn was the costliest stock in America relative to the money it makes. More on that in a moment.

LinkedIn (LNKD) boasts more than 100 million members worldwide, up from 55 million at the end of 2009. (Facebook says it has 500 million users.) Joining is free. LinkedIn makes money in three ways. It sells companies that are looking for workers access not only to job-seekers, but also to talent employed by rivals. It also sells targeted marketing services and premium subscriptions. The latter allows users to initiate contact with anyone in the network, not just with friends of friends. It's for users with something to pitch, in other words.

The company says it adds a new member each second. More than half of users are from outside the U.S.

Some of the typical methods of valuing a company aren't much use here. LinkedIn's profits are tiny for now, and in ratios like price-to-earnings, tiny denominators give nonsensical results. Over the past four quarters, the company has earned $15.6 million, up from a negligible profit a year earlier. Assuming a $4.3 billion market value, the P-E ratio is about 275, versus a market average of around 15. Again, that's the wrong number to use, and earnings for young companies often rise rapidly from such a small base. Asset value is similarly unhelpful. As an Internet business, LinkedIn uses relatively scant assets to make money, so its price-to-book ratio is close to 100, versus less than 2 for the typical U.S. stock.

 

Markets Hub: LinkedIn Shares Top $100, Double IPO

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LinkedIn's stock topped $100 a share, more than double its $45 IPO price, as the professional networking site began trading on the New York Stock Exchange. WSJ's Dave Kansas, SmartMoney's Jack Hough & MarketWatch's Ben Pimentel discuss.

The price-to-sales ratio is more telling. LinkedIn booked $292 million in sales over the past four quarters, up from $142 million a year earlier. That gives it a P-S ratio of 14.7.

I recently hunted for a higher P-S ratio among the large, midsize and small companies that form the S&P Composite 1500 Index. I eliminated companies with less than $100 million in yearly sales (again because small denominators skew ratios). That left 1,476 companies. I then eliminated banks, investment trusts and other companies that don't produce sales in the classic sense, leaving 1,227 companies. Among these, just one company has a P-S ratio above LinkedIn's pending 14.7. Much higher, in fact. It's Vertex Pharmaceuticals (VRTX), and it recently received regulatory approval -- regulatory applause, even -- for a drug that raises the cure rate for hepatitis C to nearly 80% from its current rate of about 40% with existing drugs. Last year Vertex recorded just $143 million in sales. Wall Street analysts expect that figure to explode to $2.3 billion by next year.

 

digits: Is LinkedIn Evidence of a Bubble?

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Shira Ovide, Spencer Ante, and Rolfe Winkler join digits to talk about LinkedIn's soaring stock its first day out of the gate and discuss the sky-high valuations of social media companies.

If Vertex is a statistical freak -- an anomaly to be dropped from the results -- then LinkedIn is now America's most expensive stock. Even beloved names aren't close. Cloud computing wunderkind Salesforce.com (CRM) and Red Hat (RHT) sell for closer to 10 times sales. Old men Apple (AAPL) and Google (GOOG) are 4 and 5 times sales, respectively. Facebook would be close to LinkedIn's valuation, judging by a recent offering, but it's not publicly traded.

Obviously, investors are anticipating breathless growth for LinkedIn. Its sales doubled over the past year, after all. But other companies valued at close to $4 billion include Panera Bread (PNRA), GameStop (GME) and BE Aerospace (BEAV), which bring in between six and 38 times as much in sales. So LinkedIn's price is an ambitious one.

For Thursday's trading, excitement matters more than math. But there are three reasons for long-term investors to be cautious, not including the lofty valuation. First, most IPOs underperform in their first year of trading, long-term studies show. Second, and perhaps a related point, an IPO means current owners of the company feel it's a good time to unload part of their stake. Among reasons to sell something, the belief that its value is about to rocket higher is usually not chief among them.

Third, like family-controlled media companies, LinkedIn will have a dual share structure. Class B shares are for longtime owners. Class A shares are for newcomers. Guess which ones control voting? Shareholders are supposed to be owners. Those who buy LinkedIn shares Thursday and hold them long-term will get economic exposure to the company's decisions but will have little ability to influence them.