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Dell Inc. neared an agreement on Monday to sell itself to a group led by its founder and the investment firm Silver Lake for more than $23 billion, people briefed on the matter said, in what would be the biggest buyout since the financial crisis.

If completed, a takeover would be the most ambitious attempt yet by Michael S. Dell to revive the company that bears his name. Such is the size of the potential deal that Mr. Dell has called upon Microsoft, one of his most important business partners, to shore up the proposal with additional financial muscle. The question will now turn to whether taking the personal computer maker private will accomplish what years of previous turnaround efforts have not.

The final details were being negotiated on Monday evening, and a deal could be announced as soon as Tuesday. Still, last-minute obstacles could cause the talks to collapse, the people briefed on the matter cautioned.

The consortium is expected to pay $13.50 to $13.75 a share, these people said. Mr. Dell is expected to contribute his nearly 16 percent stake to the deal, worth about $3.8 billion under the current set of terms. He is also expected to contribute hundreds of millions of dollars in fresh capital from his own fortune.

Silver Lake, known as one of the biggest investors in technology companies, would most likely contribute roughly $1 billion, these people added. Microsoft is expected to put in about $2 billion, though that would probably come in the form of preferred shares or debt.

Dell is also expected to bring home some of the cash that it holds in offshore accounts to help with the financing.

A spokesman for Dell declined to comment.

For decades, Dell benefited from its status as a pioneer in the market for personal computers. Founded in 1984 in a dormitory room at the University of Texas, the company grew into one of the biggest computer makers in the world, built on the simple premise that customers would flock to customize their machines.

By the late 1990s, its fast-rising stock created a company worth $100 billion and minted a class of "Dellionaires" whose holdings made for big fortunes, at least on paper. Mr. Dell amassed an estimated $16 billion and formed a quietly powerful investment firm to manage those riches.

But growing competition has sapped Dell's strength. Rivals like Lenovo and Samsung have made the PC-making business less profitable. Last month, the market research firm Gartner reported that Dell sold 37.6 million PCs worldwide in 2012, a 12.3 percent drop from the previous year's shipments. Perhaps more significant is the emergence of the smartphone and the tablet, two classes of devices that have eaten away at sales of traditional computers.

Mr. Dell has sought to move the company into the more lucrative and stable business of providing corporations with software services, spending billions of dollars on acquisitions to lead that transformation. The aim is to refashion Dell into something more like I.B.M. or Oracle. Even so, manufacturing PCs still makes up half of the company's business.

The company's stock had fallen 59 percent in the 10 years ended Jan. 11, the last business day before word of the buyout talks emerged. That has actually made Dell more tempting as a takeover target for its founder and Silver Lake, which see it as undervalued.

A Dell deal would be a watershed moment for the leveraged buyout industry: It would be the largest takeover since the Blackstone Group paid $26 billion for Hilton Hotels in the summer of 2007. No leveraged buyout since the financial crisis has surpassed the $7.2 billion that Kohlberg Kravis Roberts and others paid for the Samson Investment Company, an oil and gas driller, in the fall of 2011.

Private equity executives have hungered for the chance to strike a deal worth more than $10 billion, an accomplishment believed difficult because of the sheer size of financing required. Dell would take on more than $15 billion in debt, an enormous amount arranged by no fewer than four banks.

But the debt markets have been soaring over the last two years, as the cost of junk bonds has stayed low. Persistent low interest rates have prompted debt buyers to seek investments that carry higher yields

Dell was unusually well-placed to make a deal with private equity. The company carries $4.9 billion in long-term debt, which some analysts have regarded as a manageable amount. And its management has signaled a willingness to bring back at least some of the company's cash hoard held overseas, despite potentially ringing up a hefty tax bill.

It is unclear whether the company's biggest investors will accept a deal at the levels that the buyer consortium is advocating. Shares of Dell fell 2.6 percent, to $13.27, on Monday after reports of the proposed price range emerged.

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