Most of Yahoo’s $36.4 billion market value is derived from its 15% stake in Chinese online commerce company Alibaba Group Holdings (BABA) and its 35.5% stake in joint venture Yahoo Japan (YAHOF). These are not included in Yahoo’s deal with Verizon.

Investors will be hoping for a quick sale of these stakes, but Yahoo (YHOO) has been looking for years without success for a way to make money from the investments without incurring a huge tax bill. Yahoo declined to comment on potential scenarios on Monday.

Prior to running an auction for its core business, which included its advertising tools and internet assets such as search and email, Yahoo explored spinning off its stake in Alibaba to Yahoo shareholders, but abandoned the plan because the U.S. Internal Revenue Service would not provide assurances it could be carried out on a tax-free basis.

The scenario many investors are now rooting for is Yahoo Japan and Alibaba buying back these stakes from Yahoo in some way that saves on taxes. Even though they would likely buy back these shares at a discount, Yahoo investors would benefit, according to Eric Jackson, managing director at SpringOwl Asset Management LLC, which owns Yahoo shares.

“Hopefully by the end of this year, we have some sort of transaction, preferably with Alibaba buying its stake back and Yahoo Japan buying its stake back,” Jackson said.

Such a deal would likely involve some tax, due to the fact that the stakes have appreciated greatly in value, but it is unclear how much.

Bankers and analysts argue it is most likely that Yahoo will find a way to divest its Yahoo Japan stake, worth more than $8 billion on paper, before making any decision on the Alibaba stake, which is worth more than $30 billion.

Cap on Tax

Yahoo’s shares in Yahoo Japan date back to 1996, when the internet company launched a joint venture with Japan’s SoftBank Group (SFTBY).

To minimize its tax liabilities, Yahoo could do a “cash-rich split off” with Yahoo Japan, whereby Yahoo would swap its Yahoo Japan shares for cash and assets from Yahoo Japan, according to corporate tax law consultant Robert Willens.

Yahoo Japan would have to create a subsidiary, contribute cash and an operating business that has been active for five years, according to Willens. Cash can only make up two-thirds of the new company’s value, with at least one-third of the value coming from the operating business, according to Willens.

Then Yahoo Japan could give this subsidiary to Yahoo in exchange for Yahoo’s shares in Yahoo Japan, Willens said.

Yahoo itself hinted on Monday it prefers to deal with Yahoo Japan first, rather than Alibaba. Yahoo board member Tom McInerney, who is chairman of its strategic review committee, said on a conference call with analysts that the company views the stakes in Yahoo Japan and Alibaba differently.

For the Alibaba shares, “our goal is to preserve pre-tax value,” and the company has “no current intent sell those in a taxable transaction,” McInerney said.

Yahoo’s early investment in Alibaba, made in 2005, has appreciated in value so much that the company would likely have to pay more than $12 billion in tax if it decided to sell its stake, according to Morningstar analyst Ali Mogharabi.

McInerney said the company was more flexible with its shares in Yahoo Japan, whose value is a lot smaller than Alibaba.

A cash-rich split would come with challenges, as Yahoo Japan would need to trade some operating asset that it does not want with Yahoo as part of the deal, Willens said. Yahoo, by then a holding company, would end up owning this asset in addition to the Alibaba stake, and would eventually need to figure out what to do with it.

SoftBank, Yahoo Japan’s biggest shareholder, would also need to bless any deal involving shares in the Japanese company. Yahoo and Yahoo Japan did not offer any comment on Monday. Softbank could not immediately be reached for comment.

Alibaba Stake

Coming up with a solution to the Yahoo Japan stake is key in achieving the ultimate goal of spurring Alibaba into action to buy back its shares from Yahoo, analysts said.

Alibaba is the only company that can help Yahoo avoid most of the tax liabilities associated with returning cash from the sale of the stake to Yahoo shareholders. That is because an acquisition by Alibaba of Yahoo owning just the Alibaba stake could be structured as an asset swap, whereby Yahoo shareholders would be paid in Alibaba stock rather than cash.

Alibaba, which appears not to be in any rush to do any deal, may decide to play ball with Yahoo to avoid having a proxy or shell company for its shares trading at a discount. Alibaba did not respond to a request for comment.

Mogharabi at Morningstar expects the shares in Yahoo, were it to own just the Alibaba stake, to trade at a discount to Alibaba’s shares in the open market, because investors would be worried about taxes resulting from a sale.

“We believe the shares will trade at a discount as the risk of having to pay some or all of the deferred tax liabilities of those holdings remains,” Mogharabi said.