Quis Pendit Ipsa Pretia: Facebook Valuation and Diagnostic of a Bubble Based on Nonlinear Demographic Dynamics

Abstract

Cauwels and Sornette present a novel methodology to determine the fundamental value of firms in the social networking sector, motivated by recent realized IPOs and by reports that suggest sky-high valuations of firms such as Facebook, Groupon, LinkedIn Corp., Pandora Media, Inc., Twitter, and Zynga. The authors’ valuation of these firms is based on two assumptions:1) revenues and profits of a social networking firm are inherently linked to its user base through a direct channel that has no equivalent in other sectors, and 2) the growth in the number of users can be calibrated with standard logistic growth models, which allows for reliable extrapolations of the size of the business at long time horizons. Cauwels and Sornette illustrate the methodology with a detailed analysis of Facebook, one of the biggest of the social media giants. A clear signature of a change of regime, occurring in 2010 in the growth of the number of users, is observed. The change of regime is a move from a pure exponential behavior (a paradigm for unlimited growth) to a logistic function with asymptotic plateau (a paradigm for growth in competition). The authors consider three different scenarios: a base case, high-growth, and extreme-growth scenario. Using a discount factor of 5%, a profit margin of 29% and $3.50 of revenues per user per year yields a value of Facebook of $15.3 billion in the base case scenario, $20.2 billion in the high-growth scenario, and $32.9 billion in the extreme-growth scenario. According to the authors’ methodology, this implies that Facebook needs 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 in order to meet the current, widespread high expectations. To prove the wider applicability of their methodology, the analysis is repeated for Groupon, the well-known deal-of-the-day website, that went public in November 2011.The results are in line with the Facebook analysis. Customer growth will plateau. By not taking this fundamental property of the growth process into consideration, estimates of the Facebook IPO are wildly overpriced.