NEW YORK — Facebook is spending $1 billion to buy the photo-sharing company Instagram in the social network’s largest acquisition ever.

On the surface, that’s a huge sum for a tiny startup that has a handful of employees and no way to make money.

But the lack of a business model rarely dampens excitement about hot tech upshots these days. As Facebook has shown, itself without ads or revenue in its early days, money goes where the users are.

Instagram lets people share photos they snap with their mobile devices. The app has filters that can make photos look as if they’ve been taken in the 1970s or on Polaroid cameras. Its users take photos of everything from their breakfast egg sandwiches to sunsets to the smiling faces of their girlfriends.

In a little more than a year, Instagram attracted a loyal and loving user base of more than 30 million people. Apple picked it as the iPhone App of the Year in 2011.

Instagram’s fans, brand recognition and its potential are difficult to put a price tag on. Yet Facebook has — and can afford it. The company is preparing for an initial public offering of stock that could value the company at as much as $100 billion in a few weeks. What’s $1 billion? A drop in the bucket, really.

“Facebook after this IPO is going to be in a position to be predatory. They can make sure no one steps in their way and buy anyone who gets in their way,” said Wedbush analyst Michael Pachter, who follows social media.

Buying Instagram, he added, not only eliminates a rival but gives Facebook the technology “that is gaining crazy traction.”

Facebook is paying cash and stock for San Francisco-based Instagram and hiring its dozen or so employees.