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.

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