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For Yahoo, AOL merger is a sideshow next to this

Frustration with Yahoo CEO Marissa Mayer is as high as ever. But some big investors in the company say they are choosing their battles carefully.

In late September, activist investor Starboard Value wrote a letter to Yahoo urging it to take several actions. The flashiest proposal was to explore a merger with rival AOL, which has achieved strong revenue growth recently while Yahoo has fallen behind.

Read MoreStarboard's real plan: A Yahoo Inc. without Yahoo

Yahoo President and CEO Marissa Mayer delivers a keynote address at the 2014 International CES in Las Vegas, Jan. 7, 2014.
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Yahoo President and CEO Marissa Mayer delivers a keynote address at the 2014 International CES in Las Vegas, Jan. 7, 2014.

While a merger between AOL and Yahoo has been suggested by observers for years, Starboard's letter clearly gave investors a fresh reason to raise the question. Both AOL investors and others have asked the company what it thinks about a deal with Yahoo more frequently in recent weeks, according to people familiar with the matter. AOL, Yahoo and Starboard declined to comment.

Even so, multiple Yahoo shareholders who asked not to be named say it would be a mistake to get too hung up on a potential AOL deal. The vast majority of the value that Starboard wants to extract comes from a far-less sexy proposal: Avoiding taxes on the disposal of its stakes in Alibaba Group and Yahoo Japan.

Back in September, Starboard said those tax savings were worth a whopping $16 billion. But anyone watching Alibaba's soaring share price would realize that the tax savings related to that divestiture have ballooned in the last few weeks.

Using Yahoo's disclosed figures and assuming a 38 percent tax rate, it's possible to calculate just how much shareholders could benefit if Alibaba can be set free in a tax-efficient manner. The tax savings from Alibaba alone are worth about $17 billion, or $17 per Yahoo share.

Applying a similar calculation to Yahoo's stake in Yahoo Japan, it's apparent that shareholders stand to gain about $3 billion, or $3 per share form a tax-efficient disposal. If Yahoo divests both stakes successfully, shareholders stand to gain $20 in value, compared with a current share price of about $50.

"There's nothing else that Yahoo can do that would create that much value," said a top-10 Yahoo shareholder who asked not to be named. "Anyone who owns Yahoo is doing it for the tax-efficient disposal of those stakes."

Read MoreActivist's plan aims to save Yahoo $16B in taxes

As for an AOL merger, it's harder to be precise, but the benefit to Yahoo shareholders appears far smaller. Even assuming a merger would generate between $1 billion and $1.5 billion in synergies (according to figures cited by numerous analysts), Yahoo would probably have to share some of those with AOL shareholders in the form of a premium.

Using an adjusted $1 billion of synergies and assuming a multiple of six times, the transaction would be worth about $6 per share of value for Yahoo shareholders. While not insignificant, it's peanuts compared with the tax-free disposals.

How would it all happen? Starboard has envisioned a structure that would achieve everything at once. Through a transaction known as a reverse Morris trust, AOL would issue shares in exchange for Yahoo's core business in a deal that left Yahoo shareholders with a majority stake in the combined entity. That would leave the stakes in Yahoo Japan and Alibaba inside the original company.

But it's also possible for Yahoo to simply spin out the core Yahoo business. While the Alibaba and Yahoo Japan stakes would still be stuck together, they could always be separated later on.

One hurdle is a lockup agreement that theoretically forces Yahoo to hold on to its Alibaba shares for one year after the Chinese e-commerce company's September IPO. But a spinout of the Yahoo core business might not violate that agreement in itself. And even a transaction that separates the Alibaba stake can be announced 60 days after the IPO, or just a couple of weeks from now.

Read MoreNevermind Alibaba, this is why Yahoo shares have surged

Mayer continues to acknowledge the urgency of a tax-efficient disposal of Yahoo's assets. In a post Tuesday connected with the company's acquisition of video-ad platform BrightRoll, she said Yahoo is "exploring smart, tax-efficient solutions for our stake in Alibaba."

As one investment banker recently said: "Marissa Mayer has taken a lot of heat for the core business struggling. But the more important question is how she handles Alibaba—where all the value is."