NEW YORK — HCA Inc., the hospital company founded by the family of Senate Majority Leader Bill Frist, R-Tenn., agreed yesterday to be acquired by a group of private investors, including Frist's brother, for a record $21.3 billion in cash.

Without accounting for inflation, the deal, which also includes the assumption of $11.7 billion in debt, is the largest-ever leveraged buyout, just topping the $31 billion deal to take RJR Nabisco private in 1989.

The buyers include the private equity firm Kohlberg Kravis Roberts & Co., which engineered the Nabisco deal; Bain Capital; and Merrill Lynch Global Private Equity. HCA co-founder and former chief executive Thomas F. Frist Jr., who owns an estimated 4.4 percent of the company, also is part of the consortium.

Hospital companies are attractive to private equity firms because they have substantial and relatively stable cash flow. Nashville, Tenn.-based HCA, the nation's largest for-profit hospital chain, owns 176 hospitals and 92 surgery centers, many in cities that are growing faster than the rest of the country.

"We can take a longer-term view than the public markets, and from a long-term perspective, this is an outstanding company," said Stephen Pagliuca, managing director at Bain.

The consortium plans to invest $7.5 billion over five years on capital improvements, said Michael W. Michelson of KKR.

Private equity firms have become big players on Wall Street in recent years. Low interest rates have made it easier to borrow money, and the use of that leverage has allowed these firms to offer returns well above the stock market's.

Buyout firms typically put up 20 percent to 50 percent of their offer in cash and then borrow the rest, much as a home buyer uses a mortgage to fund the bulk of a purchase. Cash flow from the acquired company is then used to pay interest on the debt until the investors sell stock to the public again and get their money out.

Yesterday's deal represented a growing trend on Wall Street in which as many as half a dozen private equity shops join forces to fund deals that would be too large or too risky for a single firm.

HCA was taken private once before, in 1989, in a management-led buyout. The company went public again in 1992, merged with Columbia Hospital Corp. in 1994 and sold off its nonhospital businesses in 1997 as part of a restructuring.