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I have a vision of how suitors decide how much to offer for a start-up they want to buy. Several executives go into a conference room. Each scribbles a number on a piece of paper and places it in a hat. Then the chief executive pulls out a number, and there it is.

It might sound like a stretch, but given the seemingly random and sometimes nonsensical amounts for which start-ups with no revenue, or no users, or even no product are bought, I might not be far off.

But let’s say there is a logical way to value a company. During Bubble 1.0 there seemed to be — at least sometimes. Tech start-ups were valued by the number of eyeballs they attracted. When Broadcast.com was acquired by Yahoo for $5.9 billion in stock in April 1999, it was estimated that the company paid $10,000 per user.

Today, when eyeballs mean much less, how do start-ups with no revenue come up with a valuation? Well, it depends on a buyer’s reason for wanting the company.

One of the growing forms of acquisitions is an acqui-hire, in which a company is bought for its talent.

“If the company has no revenue and no users, then it comes down to the price of each engineer, which on average ranges between $750,000 to $1.5 million per person,” said Sam Hamadeh, chief executive of PrivCo, a firm that follows privately held companies, who noted that such acquisitions were up 91 percent from a year ago. “Facebook certainly pioneered and popularized this phenomenon as it made acquisitions to essentially snuff out competition.”

An investor report released by PrivCo in late March found that 12 of the acquisitions by Facebook last year were of this type. Often Facebook integrated the engineers and then shut the newly purchased company. The report also found that Twitter had acquired eight companies to get their engineering talent. Yahoo, Google, Apple, LinkedIn and Airbnb have also done transactions just for engineers.

Given Mr. Hamadeh’s estimate, we can begin to guess at a start-up’s value if it’s clearly an acqui-hire. If a company has 10 employees, no revenue and no users, it could be worth about $15 million. Throw in the cost of some office equipment, shutting down the technology and paying back investors, and it’s valued at $30 million.

Chris Dixon, a general partner at the venture firm Andreessen Horowitz, said in an interview that although some of the recent start-up acquisition prices might seem high, many are amortized over four years, which makes some deals seem more rational. “If you’re paying $1 million per engineer in an acqui-hire, that’s split up over four years and ends up equaling the salary of other engineers in the Valley,” he said.

But some of these transactions have people scratching their heads — like that of Summly, a news-reading app built by a 17-year-old with two employees, which Yahoo bought for a reported $30 million last month. As Emin Gün Sirer, an associate professor at Cornell, noted, Summly didn’t use any unique technology and has only a couple of employees.

When a company has users and it is a straight-up product acquisition, the numbers can be more difficult to figure out. Amazon recently purchased Goodreads, a social media site built around sharing books, for a sum said to be $150 million. Mailbox, which had not properly begun, sold for $100 million last month to DropBox. And, of course, there is Instagram, which was bought for $1 billion.

Thomas R. Eisenmann, a professor at the Harvard Business School, said that when companies weren’t being acquired just for their talent — like Goodreads and Instagram — three possible calculations were used to determine a valuation. The first requires exploring how much time and effort it would take to build the product from scratch and attract new users. The second is potential cash flow.

The third is “in the realm of, ‘What number do we need to put on the table to convince the management and investors to part with their dream?’ ” he said. “Often, they end up somewhere in the magic middle.”

Of course, all of this math starts to fall apart when a start-up receives an exorbitant amount of press and exposure on social networks. Then suitors become irrational, making the price people are willing to pay seem as if it were plucked out of a hat.

E-mail: bilton@nytimes.com