Did FB go horribly wrong in evaluating Watsapp?

May be I am asking a wrong question in the wrong forum, but I would like to ask it anyway.

How does this deal even make sense? Facebook Purchased Watsapp for 16 billion, how does this even make sense? Watsapp has 450 million users and on an average Facebook is paying $56 per user. That would mean Facebook needs to wait for 56 years to recoup its investment just on me, considering the fact that Watsapp will remain an Ad Free service.

But if along the way there are better ways to chat why would I not switch?

Did FB go horribly wrong in their evaluation process of Watsapp, which should not have been worth more than 5 billion at max?