Yahoo is one of the best-known brands on the internet, but its core internet business is in a grim situation. How grim? There's a debate over whether the company itself — what most of us think of when we think of Yahoo — is actually worth less than zero dollars.

Back in 2005, Yahoo invested $1 billion in one of China's hottest technology startups, Alibaba, getting a roughly 40 percent stake. The bet has paid off handsomely. In 2012, Yahoo sold part of its stake back to Alibaba for $7.6 billion. Since then, Alibaba has continued to grow rapidly, and Yahoo's remaining stake is now worth around $25 billion.

That number is remarkable because Yahoo as a whole isn't worth much more than that. Indeed, if you subtract the value of all of Yahoo's major assets — including a multibillion-dollar stake in Yahoo Japan (an independent subsidiary in which Yahoo is a minority shareholder) and a few billion dollars in cash — from its market value, you get a big negative number. "If you just solve for the missing number, you are forced to conclude that Yahoo's actual core business of being Yahoo (and Tumblr and whatever) is worth negative $13 billion," as Bloomberg's Matt Levine put it in December.

I don't think that's true, for reasons I'll get into shortly. But it's created a secondary crisis for the company — and a deep distraction for its CEO, Marissa Mayer.

In 2012, Yahoo's board hired Mayer, then one of Google's best-known executives, to turn the company around. Nearly four years later, it's becoming clear that her turnaround effort is failing. Mayer has invested lavishly in both engineering and media talent, but there's no sign that these investments are paying off in the form of higher revenue.

And over the past year, Mayer's management of Yahoo the business has been overshadowed by an argument over whether Yahoo can distribute its Alibaba holdings to shareholders without paying billions of dollars in taxes on them.

Things came to a head on Tuesday, when Yahoo released its quarterly financial results along with a new turnaround plan. Yahoo announced that it was laying off 1,700 workers and focusing on its most successful products — including its search engine and popular email service. But in the same press release, the chairman of Yahoo's board announced that the board is going to "engage on qualified strategic proposals" — that is, consider offers to sell the company.

It's a humiliating announcement for Mayer, because it clearly signals that the board is losing patience with her turnaround efforts. And the looming possibility of a sale is going to make it all the more difficult for her to motivate Yahoo's remaining staff to work hard on her latest turnaround plan.

Yahoo's perpetual media/tech identity crisis

The most successful companies in Silicon Valley — including Google, Facebook, and Apple — have an intensely technology-focused culture. These companies are obsessive about hiring the most talented engineers (and in Apple's case, designers) so they can build the best technology products. And this culture tends to be self-perpetuating — very skilled, highly motivated people like to work with other very skilled, highly motivated people. Once you have a critical mass of such people it becomes easy to recruit more of them.

Yahoo has never had the same kind of obsessive focus on recruiting technical talent. Paul Graham, a well-known Silicon Valley investor who sold his company to Yahoo in 1998, has written that even in the late 1990s, Yahoo was ambivalent about its status as a technology company.

"One of the weirdest things about Yahoo when I went to work there was the way they insisted on calling themselves a 'media company,'" Graham wrote. Yahoo employed a lot of programmers and produced a lot of software, of course — and still does. But it never made software as core to its identity as some of its major competitors.

That's probably because at the time Yahoo was founded, in 1994, no one had ever heard of an ad-supported software company. Back then, software companies sold their products in shrink-wrapped boxes at Best Buy. Yahoo had the same business model as CNN and the New York Times — build up a large audience and then make money by selling ads — so it was natural for Yahoo to think of itself as being in the same industry. But one consequence of this was that Yahoo didn't focus as much as it could have on recruiting the best programmers.

Marissa Mayer's roots are as an engineer at Google, and she has made an effort to beef up Yahoo's technical talent. She instituted a more rigorous hiring process, and the company has worked hard to hire more computer scientists, especially from top universities.

But there's little sign that these moves have changed the culture or improved morale among Yahoo's programmers. "I just try to ship products that I’m not ashamed of," a Yahoo executive told the New York Times in December. This is not an attitude that tends to produce excellent products.

At the same time, Mayer has doubled down on the "media company" side of Yahoo's personality. In 2013, she hired television news anchor Katie Couric for Yahoo's news site. Couric's contract was renewed last year in a deal reportedly worth $10 million. Mayer also recruited gadget reviewer David Pogue from the New York Times to anchor Yahoo's relaunched technology news section.

But despite these investments, Yahoo doesn't have nearly the prestige of a New York Times or a CBS. The company is seen as something of an also-ran both in Silicon Valley and in the media world. Yahoo creates technology products that people use and media properties that have an audience, but its attempt to be a technology company and a media company simultaneously has resulted in an organization that's less than the sum of its parts.

Yahoo's core business might be worth less than nothing

In the past few years, Yahoo's media and tech businesses have been overshadowed by a third line of business: venture capital. At the same time Yahoo's core business has been in decline, its Alibaba investment has been soaring in value. Indeed, when you subtract the value of Yahoo's major assets from the total market value of the company itself, you get a large negative number.

The uncharitable way to interpret this is that the core Yahoo business is actually destroying value. It's possible that Marissa Mayer could increase her stock price by simply announcing that she was shutting down all of Yahoo's websites and laying off all of its employees.

But there's another major factor in Yahoo's depressed share price: taxes. On paper, Yahoo's Alibaba share is worth around $25 billion. However, if Yahoo ever tried to sell its stake and pay out the proceeds to shareholders, it would owe billions of dollars in taxes to the IRS.

After adjusting for these tax liabilities, it's possible to get a positive number for the value of Yahoo's core business. But it's still a small number. When Levine crunched the numbers in December, he concluded that Yahoo's core businesses were worth just $1.7 billion, less than 10 percent of Yahoo's overall market value.

So Yahoo's search engine, email service, news site, and other properties might not literally be worth less than nothing. But right now the stock market doesn't seem very optimistic about their chances.

It's not hard to see why Wall Street would value Yahoo's core business as close to worthless. Yahoo has several different ways to measure its profits, but all of them have been getting worse over the past two years:

At a time when other internet companies have enjoyed healthy growth, Yahoo's numbers are moving in the opposite direction. Analysts who have looked at Yahoo's cash flow think Yahoo's internet business would be worth around $4 billion as a separate company, a small fraction of its value a few years ago. In short, there's no sign that Mayer's turnaround efforts have been working. She has invested heavily in both engineering and media talent. But those investments haven't yet improved Yahoo's bottom line.

Yahoo is under intense pressure to split itself up

The big fear of Yahoo's Wall Street critics isn't just that Yahoo management will fail to turn a profit; it's that they'll burn up billions of dollars in a futile effort to turn Yahoo around. Yahoo has enough cash in the bank to continue its current losses for several more years, and after that it could sell its Alibaba and Yahoo Japan stakes to buy itself many more years of money-losing operation.

But while Yahoo's management and employees obviously like to have a big cash cushion, shareholders aren't interested in endlessly subsidizing a money-losing business. And so over the past year, Wall Street has been steadily ratcheting up the pressure on Mayer to separate Yahoo's core internet business from its stakes in Alibaba and Yahoo Japan.

To mollify Wall Street, Mayer announced a plan last summer to spin off Yahoo's Alibaba shares into a new holding company. Under tax law, a company can spin off part of its business tax-free if it's doing so for a legitimate business purpose, but it can't do so merely as a tax dodge. In the past, the IRS hasn't enforced this rule very strictly, but when Yahoo asked the IRS to bless its spinoff proposal, the IRS demurred. That meant Yahoo could face a multibillion-dollar tax bill. So in December, Yahoo announced that it was canceling the spinoff.

In the goofy world of tax law, another option is a "reverse spinoff." In this plan, Yahoo would essentially spin off the entire company into a new legal entity, leaving the existing corporation as a holding company for Alibaba shares (and possibly Yahoo Japan shares) and a few other assets.

You might think spinning off everything except Alibaba shares would have the same tax implications as spinning off Alibaba shares, but that's not necessarily the case. This could allow shareholders to get their Alibaba shares without the baggage of Yahoo the business, and without paying any taxes on Alibaba's increased value.

An activist hedge fund wants Yahoo to sell its core business

In a January letter, the hedge fund Starboard Value was scathing about Mayer's performance. "The management team that was hired to turn around the Core Business has failed to produce acceptable results," the firm wrote.

So Starboard urged Yahoo's board to choose a third option: selling Yahoo's core business to another company.

A spinoff would leave Mayer in control of Yahoo the business, which Starboard views as a disadvantage. The hedge fund believes a new owner could do more with the company than the current management, and would therefore pay more for the company than the current market value.

And Starboard isn't just making an idle suggestion. Starboard is an activist investment firm. Its strategy is to buy a stake in a company and then use it as leverage to force management to make changes. In 2014, for example, Starboard successfully ousted the management of the Olive Garden after writing an epic 300-page slide deck criticizing the company's management. The slide deck faulted the restaurant chain for stale breadsticks and mushy pasta, along with weightier criticisms of its real estate portfolio and business strategy.

Starboard is threatening to take that same approach at Yahoo. "If the Board is unwilling to accept the need for significant change," the company wrote on January 6, "then an election contest may very well be needed so that shareholders can replace a majority of the Board with directors who will represent their best interests."

Only failing companies face this kind of pressure

It's easy to get bogged down in tax and accounting details, but the big-picture lesson here is that Yahoo is failing under Mayer.

If Apple had made a prescient billion-dollar investment in Alibaba 10 years ago, Wall Street wouldn't be pressuring CEO Tim Cook to spin off the shares. And that's not just because Apple's success gives Cook leverage over Wall Street in general. It's also because so long as Apple continued to be profitable, there'd be no reason to worry about Cook raiding profits from one part of the business to cover losses in another part.

But there's a real danger that Mayer — or one of her successors — will dip into those Alibaba profits to help pay for Yahoo's continued losses. And because those Alibaba shares are worth a lot more than the rest of Yahoo put together, Wall Street's top priority is to make sure that a continued meltdown of Yahoo the company won't drain value from Yahoo's investments. The easiest way to do that is to put them into separate companies.

Reasonable people can debate whether the failure of Yahoo's core business is Mayer's fault or whether Yahoo was beyond saving when she arrived. Given the long line of failed CEOs that preceded her, I'm more inclined to go with option two. But either way, it's becoming clear that Mayer's turnaround plan isn't working.