Facebook's worldwide ARPU is ~$6.09 (Q3 2018)
Facebook's margins are ~30-40%
And Facebook paid ~$19B for WhatsApp
So, very roughly, about two years of monetization gets $19B in revenue. And five years gets $19B in profit to recoup the purchase.
WhatsApp MAUs: techcrunch.com/2018/01/31/wha…
Worldwide ARPU: fourweekmba.com/facebook-arpu/
Margins: wired.com/story/facebook…
Acquisition: techcrunch.com/2014/02/22/cru…
Those could cancel out, but the roughly 10 year time frame from 2014 acquisition to 2024 breakeven looks right. After that? Profit.