In short, someone was willing to pay $16bn, therefore it's worth $16bn.

Trying to tie intrinsic value to private companies is tough, and doesn't follow a logical path. If you look at Facebook's angle, it becomes pretty clear:

When you have 1 billion users, but still want to grow, you have to pay for it. FB looked at the WhatsApp acquisition purely from a user acquisition perspective, they paid $45 per user, which is a justifiable fee on their end. What makes it crazy is there were a lot of users involved. Because Facebook has become a mobile app company, and WhatsApp adds to the company portfolio, it makes long-term sense.

Additionally, much of WhatsApps user base was international, which is a huge untapped chunk of the world for Facebook. Acquiring WhatsApp allowed FB to make a big international splash in no time.