Facebook is an amazing company with a unique product and profile. Starting from scratch, its founder Mark Zuckerberg designed a new medium of social interaction that now, only seven years after its launch, interconnects over 750 million people worldwide. To be connected or not to be connected, that is the current existential question, and as such, facebook touches the heart of a significant part of the world population by providing a need that has become almost as basic as food and shelter.

From a managerial point of view, the growth of facebook reads like a text book example of creativity and entrepreneurial skill. User base, revenues and profits – all indicators have followed nothing but exponential trajectories in the past seven years. It is thus no surprise that investors, investment banks and business media are going exuberant in wild anticipation of a looming initial public offering (IPO), which is expected for the second half of 2012. Valuations are circulating in business media ranging from 50 to 100 billion USD.

These estimates raise fundamental qualms: is there a risk that a new financial bubble is in the making on the anticipation of unlimited future exponential growth? Investment sentiment is currently at a historical low and market confidence is shattered by a banking crisis that has turned into a government debt crisis. It should be carefully considered what the impact might be for the stability of financial markets and the global economy if a new bubble were built on top of these fragile bases.

In line with the roman poet Decimus Junius Juvenalis, who questioned who would be watching the watchmen themselves, we ask thus a similar question: Quis pendit ipsa pretia? Who values these actual valuations?

The predictability of S-curves
Facebook generates most of its revenues with customized advertisement. If a user puts in her profile that she lives in Zurich and loves skiing and hiking, she may receive advertisement from an outdoor shop nearby. Facebook’s core asset is its user basis. If its users grow, its revenues and profits will grow. Whereas most other companies need to pay for detailed proprietary customer information, facebook receives this raw material for free due to its unique core application.

Economic theory dictates that the value of a company is basically the present value of its future profits. To estimate facebook’s value through its future profits, we need to have a view on its user growth and how this will evolve in the next 10 to 50 years. For that purpose, we developed a growth model that was based on the historical evolution of the number of users, which is periodically published on the facebook press website.

Growth in competition, with boundary conditions and limited resources follows what is called a S-shaped logistic curve or S-curve. This pattern is characteristic of a species population growing under Darwinian competition such as a pair of rabbits on a fenced-off range. There is a population explosion in the beginning. However, the available food can feed only a limited amount of rabbits. As the population approaches its limit, the growth rate slows down. Eventually the population stabilizes as the S-curve reaches its ceiling.1

The physicist and strategic analyst Theodore Modis describes this process as follows: «Whenever there is growth in competition (survival of the fittest), a ‹population› will evolve along an S-curve, be it sales of a newly launched product, the diffusion of a new technology or idea, an athlete's performance, or the life-long achievement of an artist's creativity. And because every niche in nature – and in the marketplace – generally becomes filled to completion, S-curves possess predictability.»2

The same paradigm applies to the number of facebook users: In the beginning, there is exponential growth. However, under the constraint of competition, a limited amount of user devices (such as smart-phones or pc’s), impenetrable markets and, a fortiori a limited world population (of 7 billion) the growth rate decays, the number of users stabilizes and will reach a ceiling. As such, its idiosyncratic growth process stops and further growth is limited to systemic growth, like general growth of the world population, global GDP or of similar technological constraints.

Value of 32.9 billion USD in a scenario of extreme growth
We used such a logistic model or S-curve to do a statistical analysis of the data. From that novel methodology to determine the fundamental value of firms in the social-networking sector we observed that the user growth underwent in 2010 a change in regime. It has clearly started deviating from the exponential trajectory (which would result from unlimited growth) and is now perfectly following the natural track of the logistic function (which is the result from growth in competition). This analysis provides us with three different scenarios: a base case, a high growth and an extreme growth scenario. In each of these, the value of the company was calculated using a discount factor of 5 percent, a profit margin of 29 percent and 3.5 USD of revenues per user per year – all figures were chosen conservatively so as not to devalue the company unnecessarily. Our analysis resulted in a valuation of 15.3 billion USD in the base case scenario, 20.2 billion USD in the high growth scenario and 32.9 billion USD in the extreme growth scenario.

Our results clearly need to be put in perspective. According to facebook’s website, a capital increase was done last January valuing the company at 50 billion USD. Rumors, spread by popular business media, value the company up to 100 billion USD. According to our model, this would imply that facebook would need to increase its profit per user before the IPO by a factor of 3 to 6 in the base case scenario, 2.5 to 5 in the high growth scenario and 1.5 to 3 in the extreme growth scenario.

It appears that facebook has already moved (at least in its rhetoric) to address the issue of saturating user numbers, as founder Mark Zuckerberg has decreed recently that unique user numbers are no longer the default traffic measurement, but the volume of sharing is supposed to be a better representation of activity.3

If facebook is not able to raise its revenue per user, we are dealing with a bubble based on nonlinear demographic dynamics.

The full study can be downloaded from http://arxiv.org/abs/1110.1319


Didier Sornette is professor of Entrepreneurial Risks and director of the Financial Crisis Observatory at the ETH Zurich. He is member of the Swiss Finance Institute and one of the leading risk scientists.

Peter Cauwels is a senior researcher at the chair of Entrepreneurial Risks at the ETH Zurich. He received a PhD in physics from the Universiteit Gent and was Head of Research Global Markets at BNP Paribas Fortis.


1 Zvi Griliches: Hybrid Corn: An Exploration of the Economics of Technological Chane. Technology, Education and Productivity: Early Papers with Notes to Subsequent Literature. New York: Basil Blackwell, 1988. S. 27-52.

2 Theodore Modis: «Anticipating the Economic Turnaround with S-curves», (15 January 2009). http://www.growth-dynamics.com/articles/Seifert_REVISED.pdf (Last visited September 14. 2011).

3 PDA, the digital content blog: «Facebook's revenues are up, but what about user numbers?» The Guardian (8 September 2011), http://www.guardian.co.uk/technology/pda/2011/sep/08/facebook-revenues-ipo