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The frenzy to acquire fast-growing technology start-ups reached new heights on Wednesday as Facebook announced its largest acquisition ever, saying it would pay at least $16 billion for WhatsApp, a text messaging application with 450 million users around the world who pay little or no money for it.

The eye-popping price signals the lengths to which Facebook’s co-founder and chief executive, Mark Zuckerberg, will go to protect his company’s turf as the dominant social network on the web, and is sure to fuel the debate on whether consumer Internet companies are overvalued.

Facebook, based in Menlo Park, Calif., will pay $4 billion in cash and $12 billion worth of shares for WhatsApp. But the ultimate cost of the deal could rise to $19 billion, with WhatsApp employees and founders receiving an additional $3 billion in restricted stock units, which would vest over the next four years.

By any measure, Facebook is paying a steep price for a service that is widely used internationally but is less known in the United States. WhatsApp does not sell advertising and has very little revenue. It charges users a flat fee of $1 a year to use the service, and the first year is free.

The purchase price dwarfs the $1 billion Facebook paid for Instagram, the photo-sharing service. At the time of that deal in 2012, critics assailed Facebook for overpaying, and this megadeal is sure to attract similar scrutiny. And the price is also much higher than the $3 billion Facebook unsuccessfully offered to acquire Snapchat, another messaging service, late last year.

But Mr. Zuckerberg is clearly willing to spend big to acquire hot messaging technologies, which typically attract younger people than Facebook does.

“Facebook is constantly working to not lose anybody,” said Nate Elliott, an analyst with Forrester Research. “Sometimes that is them innovating on their own, sometimes that’s them mimicking competitors, and sometimes that’s them buying competitors.”

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The acquisition also reflects a new strategy at Facebook: The company intends to acquire or build a family of applications instead of simply buttressing its core social network.

Now a 10-year-old social network with 1.2 billion users globally, Facebook has become so ubiquitous in many countries that it risks losing some of the attention of users.

In buying WhatsApp, which is growing faster than its rival Twitter and other social services, Facebook gains access to customers who prefer communicating one-on-one or with very small groups rather than sharing information more widely.

Facebook also has struggled to gain traction in the message space in recent years, a big motivation for its failed offer for Snapchat. While Facebook Messenger, the company’s chat platform, is popular with users, recent attempts to create its own direct messaging service have failed.

Facebook is justifying the price of this deal by citing WhatsApp’s startling growth, which has been even faster than Facebook’s own in its early years. On a conference call with analysts, David Ebersman, Facebook’s chief financial officer, compared WhatsApp to companies with the potential to grow to 1 billion users.

“The primary thing we focused on was how healthy this network is and the pace at which it was growing,” he said. “We looked at other networks that have achieved those kinds of scale” and that helped provide a framework, Mr. Ebersman said.

In the announcement on Facebook’s website, the company said that WhatsApp’s messaging volume is now approaching the entire volume of all text messages sent globally. Based on global estimates, that number could be as high as seven trillion messages sent on WhatsApp a year.

In the conference call, Jan Koum, WhatsApp’s co-founder and chief executive, played down the idea of putting ads on WhatsApp and said he was satisfied with its current subscription model.

“Monetization is not going to be a priority for us,” Mr. Koum said.

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The two companies have held informal talks for two years, but the deal came together quickly. In the spring of 2012, Mr. Zuckerberg first reached out to Mr. Koum. The two met at a coffee shop in Los Altos, Calif., and spoke for an hour, then took a walk for another hour and a half. Later that year, they began a series of dinners, and continued to discuss messaging and communication services during meals and walks in the hills above Silicon Valley.

Mr. Zuckerberg asked Mr. Koum to dinner at his home on Feb. 9, where he formally proposed a deal and invited Mr. Koum to join the Facebook board. Mr. Koum thought about it for a few days, and the two men met again on Valentine’s Day. Mr. Koum came over to Mr. Zuckerberg’s home, crashing the dinner Mr. Zuckerberg was sharing with his wife, Priscilla Chan. They negotiated over a plate of chocolate-covered strawberries intended for Ms. Chan.

By the end of the weekend, they had struck a deal.

Corporate advisers played some role as well. Michael Grimes, the Morgan Stanley banker who orchestrated Facebook’s flawed initial public offering in 2012, was this time on the other side of the table, advising WhatsApp on its sale. A big winner is Sequoia Capital, the venture capital firm with a long track record of success that provided WhatsApp’s principal funding.

By some metrics, the cash and stock being paid for WhatsApp make it among the richest deals of all time. With 55 employees, WhatsApp is commanding a price equivalent to $344 million an employee, or about $28 a user. And it is the largest acquisition ever of a venture capital-backed start-up, according to Dow Jones VentureSource.

Facebook had $7.9 billion in revenue last year, most of it from advertising. Mr. Zuckerberg said that money would help give WhatsApp the breathing room to focus on growth without needing to come up with an immediate plan for making money.

In that sense, Mr. Zuckerberg is following the successful strategy he used for Instagram, allowing the service to grow quickly before gradually adding in revenue — in Instagram’s case, from advertising.

WhatsApp, which is based in a small office in Mountain View, Calif., was founded by Mr. Koum and Brian Acton, two former Yahoo executives, in 2009.

Mr. Acton and Mr. Koum have enjoyed portraying WhatsApp as the antithesis of Silicon Valley. Unlike many young start-ups that clamor for attention, the WhatsApp founders often turn down interviews with the press.

They have denounced the model of relying on ads for revenue. And in an interview last year, they made clear they were not quickly adding users with the goal of selling their business.

“Selling the company is easy,” Mr. Koum said last year. “It happens in Silicon Valley all the time. Anybody can build a company and sell the company the next day. That doesn’t make you special, it doesn’t make you unique, it doesn’t make you all that great.”

Contributing reporting were Brian X. Chen, Nick Bilton, Nicole Perlroth and Jenna Wortham.