That’s the question investors are struggling to answer this morning as they recover from the shocking news last night that Facebook agreed to pay $16B (or $19B if you include some restricted stock) for WhatsApp. Facebook WhatsAppAnalysts like the broad appeal of the messaging service which uses the Internet, as opposed to phone networks, to easily work with different platforms at a low cost — it can take the place of Apple’s iMessage, Google Hangouts, and Blackberry BBM. An average of 450M people used WhatsApp in December, and the number is growing at a rate of 1M a day. (It’s free for the first year, and costs 99 cents a year after that.) But the service would have to generate $1B a year in cash flow to justify the price tag, and “few data-points to support such an assumption were provided by the company, as evidently few are available,” Pivotal Research Group’s Brian Wieser says. It’s not clear how much cash it can generate: Execs said last night that they won’t sell ads on WhatsApp. As a result, “it is not hard to come up with plausible assumptions that suggest the price is 50% too high…or too low,” says Bernstein Research’s Carlos Kirjner. While he says it was strategically sound for Facebook to take the gamble, the deal also suggests a potentially worrisome degree of self-doubt — that the company didn’t think it could replicate WhatsApp’s success for less than $19B. Others who feel warmer about the acquisition say that other metrics justify the high price. Facebook is paying about $42 per user while Twitter trades for $131 per user and Microsoft paid $50 per user for Skype, Nomura’s Anthony DiClemente notes. And Cowen and Co’s John Blackledge is impressed by the growth rate: WhatsApp adds 10 users every second while Facebook adds 5.4 and Twitter adds 1.8 per second. What’s more, Facebook “significantly enhances its global capabilities in mobile/messaging” especially in Europe, Latin America, India, and Asia — and prevents a rival from buying WhatsApp. Facebook shares are down 1.6% in early trading.