Starboard may use this structure to save Yahoo $16 billion

AOL CEO on Yahoo: Our focus on AOL strategy
AOL CEO on Yahoo: Our focus on AOL strategy

Activist investor Starboard Value wants Yahoo to slim down and merge with rival AOL, all without paying a $16 billion tax bill. Is there a single structure that makes it all possible?

Starboard announced Friday it had taken a stake in Yahoo and published a letter with a list of several proposals. Some of the plans were straightforward: slashing costs in the troubled display adverting division by several hundred million dollars and halting the company's ill-fated acquisition strategy, which Starboard said has cost the company over $1 billion in the last two years.

Marissa Mayer and Tim Armstrong.
Getty Images

But the greatest opportunity lies in Starboard's more ambitious proposal. The company wants Yahoo to unlock the value of its stakes in Chinese e-commerce giant Alibaba and Yahoo Japan, all without paying taxes. If this can be done, Yahoo shareholders will save a whopping $16 billion by Starboard's estimates.

At the same time, Starboard is urging Yahoo to merge with rival AOL, a combination that could lead to extensive savings if the companies eliminate overlap in their advertising businesses. AOL has also found a way to drive rapid advertising revenue growth, suggesting there is opportunity to turn Yahoo around if the businesses are combined. Starboard declined to comment to CNBC beyond the content of its letter.

There may be a structure that accomplishes everything Starboard wants in one fell swoop. A transaction known as a reverse Morris trust, used frequently in the media industry by mogul John Malone, allows companies to harvest stakes in listed companies without triggering a tax bill. Malone used the structure to spin off a 54 percent stake in DirecTV several years ago without paying taxes.

Read MoreWhat did Marissa Mayer ask Tim Armstrong over drinks?

Here's how it works: Yahoo would first create a new company that holds the stakes in Alibaba and Yahoo Japan. To qualify for the favorable tax treatment under U.S. law, that new company would also need to own an actual operating company in addition to the passive stakes, according to Columbia Business School professor Robert Willens. That company would be listed and trade just like a normal stock. Since Alibaba and Yahoo Japan are listed, and the operating business could be very small, the market could easily value the company at a fair price.

The remaining Yahoo business would then acquire AOL, likely by issuing new shares. For the structure to be tax free, Yahoo shareholders would need to wind up owning more than 50 percent of the combined company after the deal, Willens said. That probably makes sense, given that Yahoo generates over $1 billion of earnings before interest, taxes, depreciation and amortization. AOL, meanwhile generates about $500 million in EBITDA.

Starboard may want to go a step further, putting AOL's management in charge of the combined company. Indeed, Starboard appears to have developed a healthy relationship with AOL after taking an activist role at that company. In 2012, Starboard put pressure on AOL to sell a portfolio of patents. When a deal was struck to sell the patents to Microsoft for $1.1 billion, AOL shares jumped 43 percent in a single day. AOL CEO Tim Armstrong has remained at the helm and the stock has continued to rise over the last couple of years.

Putting AOL management in charge shouldn't be an issue if Starboard gets as far as combining the two companies. Yahoo shareholders would own most of the new company, giving them the power to elect members of the board of directors. Yahoo didn't respond to a request for comment from CNBC.

Of course, Starboard will need to win the support of Yahoo's current board to make any of this happen. That may mean staging a proxy contest to get directors of its choice on board, an effort Starboard is currently making at Darden Restaurants. But even the chance of pulling off such a lucrative deal should keep a floor underneath Yahoo shares for some time.

Read MoreYahoo-AOL: Unfortunately, this isn't 1999