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WhatsApp has >1.5B users (Q2 2018)
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.
Key assumption is that WhatsApp will monetize like other Facebook properties. Given that, I think the ballpark estimate holds.

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…
Also, while Facebook's margins are on a downward trend due to the human curators, their ARPU and WhatsApp MAU numbers are likely still trending up.

Those could cancel out, but the roughly 10 year time frame from 2014 acquisition to 2024 breakeven looks right. After that? Profit.
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