Buffett and Moynihan had a private dinner together on August 6 at the Happy Hollow Club in Omaha, where Buffett is a member.
According to people briefed on the dinner, Buffett expressed bullishness on the banking sector, especially for institutions like Bank of America that have a strong deposit base.
Buffett also praised Moynihan's turnaround efforts, which have helped lift the stock more than 100 percent since Berkshire invested $5 billion in BofA in August 2011.
(Read more: Berkshire Hathaway's 15 biggest stock holdings)
Berkshire gets a dividend of 6 percent, or $300 million a year, for the money it, in effect, loaned to BofA through the purchase of preferred shares. (Read more below the video.)
Even more lucrative for Berkshire, though, are warrants it received as part of the deal that allow it to purchase $5 billion worth of BofA common stock at $7.14 per share.
With the stock now trading at $14.36, that's a paper profit of just over $5 billion.
It's not known whether the two men discussed Berkshire's eventual exit from the 10-year deal. That wasn't the purpose of the dinner, but it "very likely came up," sources said.
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