HCA Inc. agreed to pay $20 million to shareholders who had accused executives of making false statements that helped boost the company’s stock price.

Under the deal, according to the Associated Press, the Nashville-based hospital management company didn’t admit to any wrongdoing.

The AP said that shareholders had alleged that executives misstated HCA’s financial condition between January and July 2005, inflating the stock price. The shares then fell nearly 10 percent when HCA subsequently reported worse-than-expected results.

Several insiders — including then-Senate Majority Leader Bill Frist, whose father and brother founded HCA — sold large amounts of stock before the price dropped, according to AP. It noted that the senator’s sales took place as he was considering a run for the Republican presidential nomination. (He eventually chose not to run.)

In September 2005, CFO.com reported that HCA had received a subpoena related to Sen. Frist’s stock sale. The company also was being investigated by the Securities and Exchange Commission, according to reports at the time.

In November, a group of private equity firms and management bought HCA for $21.3 billion plus $11.7 billion in debt. Investors included Bain Capital Partners LLC, Kohlberg Kravis Roberts & Co., and Merrill Lynch Global Private Equity. The deal also involved $16 billion in new debt, the AP noted.

The wire service said that the investigation had ended in April without action being taken against Sen. Frist.