By Stephen Gandel
February 13, 2014

FORTUNE — Warren Buffett’s company appears to be looking to sell its entire stake in the company that used to own the Washington Post.

Berkshire Hathaway (BRKA) is the largest investor in Graham Holdings (GHC), which was renamed from The Washington Post Company last year after the company sold its namesake paper to Amazon (AMZN) CEO Jeff Bezos. Graham Holdings still owns the educational company Kaplan, as well as a number of television stations and news website pioneer Slate. Berkshire, through various entities, owns about $1.13 billion worth of Graham Holdings, or nearly a quarter of the company’s shares, and has owned the stock in the company for more than four decades.

According to a late Wednesday filing on the SEC’s website, Berkshire and Graham Holdings are negotiating a stock swap that would involve Berkshire handing its 1.7 million shares of Graham Holdings back to the company. In return, Buffett’s company would get the Berkshire shares that Graham Holdings owns, currently held in part through the Graham Holdings pension plan.

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But that wouldn’t be the end of the deal. Berkshire holds considerably more Graham Holdings shares then Graham owns of Berkshire. According to the filing, Berkshire may end up acquiring a division of Graham Holdings to make up the difference. It does not appear from the filing that it has been determined what division of Graham Holdings Berkshire might be interested in.

While Graham Holdings might lose its largest shareholder, the deal could also be good for the family-led company. Graham has been buying back its own stock for many years. Acquiring the shares owned by Berkshire would allow Graham to pick up a big chuck of its own shares in one transaction at a set price. Also, the tax-free nature of the swap could make it advantageous for all parties.

The deal is not final and could still be called off if, for example, the prices of the companies’ shares move on the news.

Berkshire has had a long history with Graham Holdings and its predecessor. Berkshire first bought shares of the company back in 1970s. He became a close confidant and personal friend to The Washington Post’s long-time CEO Katharine Graham, who died in 2001. In the late 1970s, Graham followed Buffett’s advice on how to restructure the company’s pension plan. As a result, Graham Holding’s pension plan is one of the best funded in corporate America. Buffett has also done two stints as a member of the company’s board of directors.

The deal is also another example of Buffett investing prowess. Berkshire paid about $11 million for its stake in Graham Holdings, giving Buffett’s company a profit of at least $1.1 billion, for a compounded return of roughly 12.3% a year over the past 40 years. Buffett’s total return is more than that, because that calculation doesn’t include the dividends Berkshire has collected along the way. That’s far better than the S&P 500 (SPX), which had a compounded return of 7.7% in the same time period.

Buffett has done stock swap acquisitions before. The most recent one was in December when he swapped his stake in ConocoPhillips for a division of the company that made lubricant used in transporting oil through pipelines.

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