Big changes may be coming for Yahoo as the company’s board meets this week and reportedly considers a plan to sell the company’s core business — the search and advertising divisions of the 20-year-old company that have been wilting in the shadow of rivals such as Google and Facebook.

But the proposal, as radical as it sounds, is being precipitated by a relatively mundane financial issue: taxes.

Most of Yahoo’s current $34 billion market value comes from the nearly 400 million shares that it owns in the fast-growing Chinese Web retailer Alibaba. When Alibaba went public last year, Yahoo’s stake ballooned to more than $30 billion. At least in the eyes of Wall Street, that investment far eclipses the value of its Web sites, which are among the most visited in the world.

Under pressure from its shareholders, Yahoo has been trying to find a way to unload those shares without paying a hefty tax bill. But settling on a plan has been difficult. And now a number of activist shareholders are calling for the company to sell-off its Web business instead.

Directly selling its Alibaba shares would mean paying capital gains taxes, which could run in the billions, tax experts said. In January, the tech giant announced it would spin off its Alibaba stake into a new company. But, as it turns out, that could leave it with a hefty tax bill too.

Yahoo said in September that the Internal Revenue Service had declined to rule on whether a spinoff would be a tax-free transaction. The IRS is also considering changing its rules on spinoffs, Yahoo said.

Without those assurances, Yahoo could be hit with a $9 billion tax bill, said Robert Willens, an independent tax consultant. “I think the spinoff would qualify for tax-free treatment, it meets all the requirements,” he said. But investors are nervous and some have asked the company to abandon its plans.

“If you stay on the current path, we believe the potential penalty for being wrong is just too great, and the potential reward for being right is not materially better than the alternative,” Starboard Value, the activist hedge fund, said in a November letter to the company.

Starboard has been one of the investment firms pushing Yahoo to sell its core Internet search and advertising business. That would leave the remaining company with its stake in Alibaba and Yahoo’s valuable business in Japan.

That approach could also leave Yahoo with a multi-billion tax bill, but a potentially much smaller one, said Laurence M. Bambino, the head of the global tax group at the law firm Shearman & Sterling. It could be “$9 billion versus $3 or $4 billion. You’re talking about a big amount of money either way,” he said.

If Yahoo were to go ahead with either approach, the IRS could take the company to court years later to collect taxes, experts said. An IRS spokesperson said the agency does not comment on specific taxpayers.

That’s what the board is discussing at its regularly scheduled meeting this week, according to The Wall Street Journal which first reported on the board’s discussions, citing unnamed people familiar with the plans. A Yahoo spokeswoman declined to comment on the story.

Regardless, the board’s meeting and the broader struggles at Yahoo are bringing sharp scrutiny to Yahoo chief executive Marissa Mayer, who was brought on three years ago to turn the company around. At that time, she was Yahoo’s fifth chief executive in five years, and cast as a savior for the firm.

Back then, Yahoo was facing a key problem: It was huge but was losing users, particularly on the desktop Web. Today, it is still well behind its rivals. In October, comScore reported Yahoo had a 12.6. percent share of the desktop search market, placing it behind Google's 63.9 percent and Microsoft's 20.7 percent for Bing.

Meanwhile, consumers have been shifting the bulk of their searches to mobile devices, where Google and Facebook are even more dominant. Mayer’s initial strategy was to acquire several mobile-focused startups while striking deals to increase Yahoo’s search footprint. She also built up the company’s focus on producing its own content, hiring Katie Couric to anchor a news team. Yet while Mayer has managed to stabilize Yahoo’s business — and even making some money off of mobile ads — she hasn’t managed to kickstart another period of growth.

According to a report from Recode's Kara Swisher, Mayer still has the support of the board, even if she's taken a beating in the press.

“She has not lost support of the board,” one source with "knowledge of the situation" told Swisher.

In a note to investors Tuesday night, analyst Brian Wieser said that Yahoo’s in a tough position, in the face of Google. “As it stands, Yahoo can remain a large player in search without external acquisitions, but anything other than #1 may be a weak position,” he said. When advertisers, particularly smaller ones, look at how they should spend their budgets, he said, they’re inevitably going to focus their money on where the most people are.

Still, he said, Yahoo’s core business, particularly its e-mail service, still has a large-enough user base that can help it buy some time as it considers its next moves — whether that’s a new tax strategy or a sale of itself.