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.
Having been at the table for a few M&A deals, I will like to add couple of reasons among many others First is the patience shown by the WhatsApp leadership in finding the right strategic buyers as they rapidly scaled by the numbers of users - and second excellent negotiation skills by the WhatsApp management team - most folks would have been ecstatic to sell a company for 1.6 B - but it is apparent that WhatsApp team knew they get much higher valuations if they found the right strategic buyer. I am sure it was not an easy decision and but turned out to be a great call !