Billionaire Carl Icahn, seeking to upend a $24.4 billion buyout of Dell Inc. by its founder and Silver Lake Management LLC, proposed an alternative that could have investors keep their stakes in the computer maker and get $12 a share in cash.

Under Icahn’s plan, shareholders will be able to choose between a $12 a share cash distribution or $12 in additional shares valued at $1.65 apiece, according to a May 9 letter included in a filing today. Icahn and Southeastern Asset Management Inc., which together own about 13 percent of Dell, are offering an alternative to the $13.65-a-share bid by Michael Dell and Silver Lake.

Southeastern and Icahn, in the sharply worded letter, said their proposal gives investors a chance to benefit from potential future growth at Round Rock, Texas-based Dell and that it is more valuable than the buyout proposal. The two investors plan to take additional stock in the third-largest computer maker, rather than cash, they said.

“It is insulting to shareholders’ intelligence for the board to tell them that this board only has the best interests of shareholders at heart, and then accept Michael Dell’s offer to purchase the company he founded for $13.65 per share, a price far below what we consider its value to be,” according to the letter, signed by Icahn and Southeastern’s president G. Staley Cates.

Dell rose 1.4 percent to $13.50 at 7:05 a.m. New York time before the stock market opened. Dell has risen 31 percent this year, and has lost $125 billion in market value since its peak in March 2000.

Dell Debt

Icahn and affiliates own about 4.5 percent of Dell’s shares, today’s filing shows. Financing for his proposal will come from existing cash at the PC maker and about $5.2 billion in new debt. That compares with about $16 billion of debt under the buyout proposal, according to the letter.

“Either give shareholders the real choice they are entitled to or face the legal liability for your failures,” Icahn and Southeastern wrote to the board.

David Frink, a spokesman for Dell, didn’t respond to a request for comment outside regular business hours. Representatives of Silver Lake and a special committee of Dell’s board, which fielded buyout proposals, also didn’t respond to requests.

Michael Dell and private-equity firm Silver Lake will have to determine whether to sweeten their offer, which was outlined in February, while Dell’s board considers whether the new proposal from Icahn might be deemed superior. Blackstone Group LP, the world’s biggest buyout firm, pulled out of bidding for Dell last month amid concerns over a worsening global PC slump.

Blackstone’s Withdrawal

As more consumers check e-mail, browse the Web and watch television and movies on smartphones and tablets, PC shipments plummeted 14 percent in the first quarter, the worst decline since researcher IDC began tracking data in 1994. The record drop in computer sales helped trigger the withdrawal, Blackstone said in a letter released at the time. Blackstone had made a non-binding offer to acquire Dell in March.

The PC market, although challenged, “is far from an obsolete technology, but one that is maturing and ultimately somewhat cyclical,” Icahn and Southeastern said in the May 9 letter. Furthermore, “the PC is not where the ultimate long- term opportunity lies for Dell, something we are confident Michael Dell is betting on, while leaving shareholders out in the cold.”

Icahn and Southeastern will work to persuade all shareholders to reject the Dell offer and will put up a slate of 12 directors to challenge the current board at the annual shareholder meeting if their proposal isn’t recommended by the board, according to the letter.

Michael Dell, who founded the PC provider in his Texas dorm room in 1984, needs to ensure majority control so he can pursue his plan to retool the struggling company as a maker of data- center gear and software for corporations -- without the scrutiny of public investors.

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