BofA is agreeing to sell 80.8 million shares of HCA Holdings Inc. back to the health-care company, raising $1.5 billion for the bank and spurring a 10% stock-price rise at the Nashville-based hospital operator.

The BofA-HCA agreement sets an $18.61-a-share price, .

Selling the shares, equal to 15.6% of HCA, is "consistent with our strategy of focusing on our core businesses, building liquidity and strengthening the balance sheet," Jerry Dubrowski, a Bank of America spokesman, tells Bloomberg News. "Our customers do not choose to do business with us because we have an investment in a health-care provider."

BofA CEO Brian T. Moynihan has sold at least $40 billion of assets and preferred shares to raise capital and make the company easier to run. The company's plans to eliminate the 30,000 jobs over the next few years were announced earlier this week, about the edge that could give competitors of the Charlotte-based banking behemoth.