In its effort to raise capital and shed some of its non-core business units, Bank of America is selling First Republic Bank just two years after Merrill Lynch purchased the San Francisco-based private banking and wealth-management firm.

The terms of the deal were not made public, but according to DealBook buyers, including private equity firms General Atlantic and Colony Capital, will pay about $1 billion for the bank. Alois Pirker, an analyst with Boston-based Aite Group, says Bank of America is getting a decent price considering the market conditions.

“Bank of America didn’t buy First Republic, so it doesn’t look like they made a mistake. They’re just cleaning up what they inherited with the Merrill Lynch transaction. Ultimately, Bank of America is doing what any acquirer would do—deciding what to keep and what to shed,” Pirker says. Bank of America had announced its intention to sell First Republic as early as May.

Merrill first announced its plans to acquire First Republic in January 2007 for $1.8 billion. As of September 30, First Republic had $19 billion in total assets, $16 billion in deposits, and $15 billion in wealth management assets under management. “At the time, the acquisition was a nice one for Merrill,” Pirker says. “Merrill didn’t have much banking to offer and First Republic gave that to them. It was a good fit then. But Bank of America has no real need for something like [First Republic Bank.] They already have U.S. Trust to handle accounts above $10 million.”

Bank of America is in the midst of raising capital to help pay back $45 billion in loans it received from the government. On September 21, the bank announced moves that would “reduce its reliance on government support and return to normal market funding.” Click here for more on how Bank of America plans to pay back some its government debts. On September 30, Bank of America sold its Columbia Management Group to Ameriprise Financial for as much as $1.2 billion in cash.

In May, after the government’s bank stress test, Bank of America was ordered to raise $34 billion in common-equity. Bank of America then said it would raise the money by issuing common stock and selling assets like First Republic and Columbia Management group.