By Lauren Silva Laughlin
March 5, 2014

FORTUNE — Is Facebook overvalued? The social network’s shareholders have fared well since the company went public in mid-2012. Shares are up more than 80% since its IPO and have climbed steadily over the last six months. But investors have paused since Mark Zuckerberg, Facebook’s founder, announced on his page two weeks ago that his company was buying WhatsApp, a young but popular social network. The price tag: a shocking $19 billion.

It’s not just a matter of digesting the news. Investors already have lofty growth expectations built into the company’s stock price. And as the WhatsApp acquisition shows, Facebook (FB) is working hard to justify those assumptions partly with acquisitions — and it has good reason to do that. Based on at least one metric, a small blip to investors’ forecasts could skim nearly a tenth off the stock price.

In many ways, the WhatsApp acquisition makes sense. Scale is important to social networking. Bringing WhatsApp into the fold only makes Facebook that much harder to touch. “The large and rapidly growing user base attracts new advertisers and retailers,” Laura Martin of Needham recently said in a report. “We believe the scale of Facebook’s network represents a significant competitive advantage and a significant barrier to entry.”

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However, paying top dollar to grow can turn into a dangerous cycle. “It can be like a dog chasing its tail,” said Lawrence Hrebiniak, emeritus professor at The Wharton School of the University of Pennsylvania. If more interesting social networks photo-bomb this growing family portrait, Facebook will have to continue to purchase other companies to keep up.

Jim Chanos, the prominent bearish investor who runs hedge fund Kynikos, is skeptical that scale matters in general. He says he is worried “about the inability of these businesses to ‘scale’ profitability.” “Everyone points to Amazon as their valuation framework safe-harbor, not the scores of Internet road kill.” (Chanos is not currently involved with Facebook or similar companies.)

Investors don’t necessarily have to choose a side just yet. But it helps to consider how delicate Facebook’s stock price actually is, considering the outsize growth expectations for the company. Following Facebook’s acquisition of WhatsApp, analysts started to kick around a metric different than one that’s often used. Rather than value WhatsApp based on a revenue multiple, analysts showed how much Facebook was paying to acquire each individual WhatsApp user. That magic number was $42 per user ($19 billion for 450 million users).

It seems like a lot considering WhatsApp’s business: It takes in 99 cents per user one year after they have signed on. But Facebook’s users are worth $122 apiece at its current enterprise value of $167 billion, assuming the company hits Evercore’s expectations of around 1.4 billion users by the end of this year.

The hope is that Zuckerberg will add some kind of magic sauce to WhatsApp users so Facebook can jack up their value too. But it may not be that simple. First, Facebook’s users are worth more because they bring in more money for the company. Each Facebook user currently adds $6.73 to the top line. Evercore assumes this number will grow a quarter by the end of this year to $8.44, making each Facebook user worth some 14.5 times the revenue they contribute.

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Add that to the 16% more people Evercore assumes will join Facebook, and investors have to hope things continue on the up and up.

Say those estimates are a bit off: Revenue per user grows 20% to $8.08. It is still a lot, but not what investors currently assume. And say that users grow a tenth rather than 15%. Each Facebook user at the same multiple (14.5 times) is worth $117, and there are fewer to boot (1.3 billion users), valuing the company at about $151 billion. Add back Facebook’s $7 billion of cash, and the market cap of the company is about $158 billion, nearly 10% below its current price.

Small tweaks to a business model that needs to be scaled can be dangerous, especially when investors are paying top prices based on lofty growth assumptions

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