Cauwels and Sornette then calculate a value for the company based on the prospect of each user generating $1 profit per year, the approximate average over the last five years.
It's worth pointing out some of the assumptions behind this calculation. It generously assumes that real interest rates are essentially 0% for the next 50 years, that Facebook's profit margins remain as high in future as they are now and that its revenue per user remains constant in future.
This last one is particularly generous. Cauwels and Sornette have worked out the average revenue per user over the last five years. But the truth is that Facebook's revenue per user appears to be halving every 3.5 years, a fall that is entirely masked by taking an average.
If the current valuations are to be achieved, Facebook will somehow have to improve its profit per user by between 1.5 and 6 times.
Arxiv - Quis pendit ipsa pretia: facebook valuation and diagnostic of a bubble based on nonlinear demographic dynamics (18 pages)
We 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, Zynga. Our valuation of these firms is based on two ingredients: (i) revenues and profits of a social-networking firm are inherently linked to its user basis through a direct channel that has no equivalent in other sectors; (ii) the growth of the number of users can be calibrated with standard logistic growth models and allows for reliable extrapolations of the size of the business at long time horizons. Illustrating the methodology with facebook, one of the biggest of the social-media giants, we find a clear signature of a change of regime that occurred in 2010 on the growth of the number of users, from a pure exponential behavior (a paradigm for unlimited growth) to a logistic function describing the evolution towards an asymptotic plateau (a paradigm for growth in competition). We consider three different scenarios, a base case, a high growth and an extreme growth scenario. Using a discount factor of 5%, a profit margin of 29% and 3.5 USD of revenues per user per year yields a value of facebook 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. According to our methodology, 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 in order to meet the current, widespread, high expectations.
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