When Do Users Justify Facebook's Valuation?

A recent writeup on TechnologyReview pegged the value of each Facebook FB user at $116. That is what you get when dividing the $104 billion valuation at the Initial Public Offering by 900 million users at that time. That gives us the chance to look at Facebook and its quality as an investment in a manner that is free from the technical volatility that has characterized shares since its May 18 debut on the Nasdaq NDAQ. (I preface what follows with a warning that the scenarios herein are overly simplified and are meant to make a simple point on how some may view a company's value). We take the simple formula PV = c/(k-g), which discounts a perpetual series of cash flows to the current present value. The present value, or PV was $104 billion at the IPO. Or, as TechnologyReview calculated it, $116 per user. The coupon - denoted by c in the formula - is the annual return which, in this case, an investors would look to get in order to hold on to the stock. It is the variable to solve for in our case - it denotes the annual appreciation of the company's valuation in dollars per user. K is the investor's discount rate, or the rate of return for an investor, in percent, in order to hold on to the stock. Normally, its calculation involves the risk-free rate of return, a stock's beta and an equity market risk premium. Given that we do not yet have a beta for Facebook, we are making a giant oversemplification and assuming the discount rate is an even 10%. The growth rate - g in the formula - is the growth rate for the company's business operations. In another gross oversimplification, I am estimating this at 5%. Part of this will be driven by user growth, part by potential increases in revenue per users. Solving this formula for a dollar appreciation, we have c = PV*(k-g), or c = $116*(10%-5%), which means c equals $5.80. Each of Facebook's users, then, would be responsible for $5.80 per year in Facebook's revenue in order for the IPO valuation thesis to remain intact. To further dissect revenue per user, we oversimplify yet again. We assume CPM - cost per thousand impression - is the only metric that accounts for Facebook's revenue. According to Techcrunch, CPM for facebook is $0.296 as of Q1 of 2012 - let's call it 30 cents. This means that, to realize the requisite revenue, each user would have to log in a number of thousand-impressions equal to $5.80 divided by $0.30. Thus, a Facebook user will have made good by Facebook - by justifying its IPO value - when registering 19,595 impressions per year. At 365 days per year, each of 900+ million users would need to contribute in 54 impressions per day across ads on Facebook. Given the average 14 minute per day the average user spends on Facebook, that would equate just under 4 impressions per minute. The question to ask, then, is: can each Facebook user look at 4 ads per minute each day, every day? If this is doable, Facebook is fairly valued. The limitations of this back-of-envelope calculation are many. But the point I want to make is that valuing Facebook should not be as cryptic as many are making it to be. By the way, the same TechnologyReview writeup put Instagram's per-user value at $25, which makes its acquisition by Facebook a steal. Unless, that is, those users were already on Facebook.