On the surface it seems ridiculous. Facebook (NASDAQ:FB), which paid $1 billion for the seemingly wildly popular Instagram, just announced that it's acquiring WhatsApp for $4 billion in cash and $12 billion in Facebook stock (with another $3 billion in stock incentives that pay out over time).

But while WhatsApp may not have the name recognition of Instagram -- at least among adults -- it has a dramatically larger audience than Instagram did when Facebook acquired it. So while this deal seems like Facebook CEO Mark Zuckerberg acted like a kid in a toy store with a pocket full of birthday cash, it actually has the potential to be a prudent purchase.

What did he buy?

At the time Facebook purchased Instagram, the site had 30 million users, according to The New York Times.

WhatsApp, according to the Facebook press release announcing the deal, has user numbers that dwarf those. WhatsApp currently has:

  • Over 450 million people using the service each month
  • 70% of those people active on a given day
  • Messaging volume approaching the entire global telecom SMS volume
  • Continued strong growth, currently adding more than 1 million new registered users per day.

So, while Facebook paid $16 billion to $19 billion for the WhatsApp versus $1 billion for Instagram, it actually got a bargain of sorts. At current levels, if Facebook were paying on a per-user basis, the comparable price would have been $15 billion. But Zuckerberg clearly doesn't believe WhatsApp will have only 450 million users for long.

"WhatsApp is on a path to connect 1 billion people. The services that reach that milestone are all incredibly valuable," said Zuckerberg in the press release.

With 1 billion users, Facebook would be acquiring WhatsApp at a more than 50% discount over what it paid for Instagram (which now claims 150 million active daily users on its website). And it can be argued that while growing to 30 million is impressive, getting to 450 million and staying on a rapid growth path is incredibly rare.

It might be a good deal, but what is it?

WhatsApp, according to its website, is "a cross-platform mobile messaging app, which allows you to exchange messages without having to pay for SMS." Basically, WhatsApp messenger lets users communicate through their phones over the Internet, which avoids the charges associated with using the phone part of your smartphone. This type of communication has become increasingly popular in certain parts of the world.

"Facebook is trying to get involved in the new era of communication," said Ben Bajarin, principal industry analyst at tech research firm Creative Strategies, to USA Today. "It has shifted from social networking to these messaging services, which are becoming new platforms in and of themselves."

With this deal, Zuckerberg is essentially hedging his bet. If certain parts of the world or certain age groups leave Facebook for the type of communications WhatsApp offers, Facebook won't be left behind. And Facebook has to be concerned about its appeal to younger users as is detailed in this article.

Will the Facebook, WhatsApp marriage work?

If the purchase of Instagram can be taken as a blueprint, there is every chance this acquisition will work.

As it did with Instagram, Facebook intends to keep the WhatsApp brand and maintain its seperate headquarters in Mountain View, Calif. In addition, the company said in its press release, "WhatsApp's core messaging product and Facebook's existing Messenger app will continue to operate as stand-alone applications."

Facebook bought Instagram in April 2012, and in the nearly two years since Instagram's users base has grown 500%. If Facebook can do that for WhatsApp, the company would have 2.25 billion users. That number may be preposterous, but if in under two years Facebook can build WhatsApp to one billon users -- which Facebook has -- the company will control two services with unparalleled reach.

Consider that the biggest television audience of the year is the Super Bowl, which drew 111 million viewers and you realize that with 450 million current users -- 315 million of them active on a daily basis -- WhatsApp is already a major power. The challenge for Facebook will be to continue that momentum, something the company has already proven it can do with Instagram.

While $16 billion to $19 billion might be a hefty price tag (it's the fourth-largest technology acquisition of the past decade, according to Dealogic), it's a risk grounded in simple math. If Facebook can do what it has done before, than $19 billion may end up seeming like a bargain.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.