* Hilton Worldwide has yearly revenues of $9.7b.
* Marriott International has yearly revenues of $11.8b.
* Best Western has yearly revenues of $6b.
Now, I don't know what their current revenues are. Based on how many people from all over the US I've spoken to that use them frequently already, I'd assume they're growing at a decent clip. Furthermore, they have virality on their side, where their competitors just plain don't. It takes years to open a new hotel. If Airbnb wants to deploy to Casper, WY, they only have to make the effort insofar as basic background checks. If they want to do a stronger deployment, they find maid services and anything else they might need to support local hosts.
Furthermore, as much as there are local law issues in places like NYC against them, I don't anticipate those lasting long or having a large effect on their revenues. The same way that if you're in Uber's way you get painted as being anti-jobs, Airbnb gets to say the same thing. And that's in the few places that have them.
I think they've got a long way to grow. I look at $13b, and part of me thinks that might even be soft, especially if they look into starting their own hotels, to provide a higher 'minimum' to a given city, which allows Airbnb to maintain itself as a premium brand(as yet, I've never stayed or heard anyone else staying anywhere that wasn't a much better deal than anything else nearby), even if their prices don't reflect it.
Remember: These valuations aren't for what a company is currently worth. Otherwise, there's no point to investment. They valuations are for where they see the company going, and more probably, growing past.