Dell (DELL.DL) founder Michael Dell, with help from private-equity firm Silver Lake Partners, hopes to take his company private by paying $13.65 in cash for each share of Dell stock. However, Carl Icahn's Icahn Enterprises (IEP 0.06%) fund recently joined with Southeastern Asset Management (the largest shareholder aside from Michael Dell himself) to offer a rival buyout proposal.

The Icahn-Southeastern proposal entails using much of Dell's cash and adding some debt to pay a $12 special dividend to Dell shareholders. (This type of financial maneuver is called a leveraged recapitalization.) However, the proposal is particularly interesting because it gives shareholders the option of receiving the $12 in cash, or in additional Dell stock valued at $1.65 per share.

To persuade shareholders to adopt his proposal rather than accept Michael Dell's buyout offer, Icahn will need to convince at least half of the ownership base that the stub stock will be worth more than $1.65 per share. Otherwise, Dell shareholders would be better off taking $13.65 in cash from Michael Dell. On the other hand, if Icahn is too convincing about the stub stock's upside, everybody will want extra Dell stock rather than cash, which would defeat the purpose of his leveraged recapitalization plan.

Cash or stock?
Icahn and Southeastern have already announced that they will decline cash payments in favor of additional stock. Together, they own approximately 13% of Dell stock -- roughly 230 million shares. After receiving additional stock in lieu of the $12 cash payment, they would own 1.9 billion shares. Overall, they expect 20% of the shareholder base to take extra stock instead of cash.

However, Icahn and Southeastern face a thorny problem. Assume that you're a Dell shareholder. If you believe that the stub stock will be worth less than $1.65, you'll be better off taking a $13.65 cash payment from Michael Dell and Silver Lake rather than a $12 payment and a stub stock from Icahn and Southeastern.

On the other hand, if you believe that the stub stock will be worth more than $1.65, you'd probably be better off declining the proposed $12 cash payment in favor of extra stock. That's because you'd be paying just $1.65 a share for the extra Dell stock (which, by assumption, is worth more than $1.65).

To prevent the Dell-Silver Lake transaction from being approved, Icahn and Southeastern need to persuade at least half of the Dell shareholder base to vote against the agreement. They're trying to do this by calling the Dell-Silver Lake transaction "The Great Giveaway," and arguing that Dell could perform much better under new management. In other words, they need to convince shareholders that Dell would be significantly undervalued at $13.65 per share.

Who will take Icahn's money?
If Icahn can't convince many people that the stub stock will be worth more than $1.65 in his leveraged recapitalization, he'll lose the proxy battle, and the Dell-Silver Lake proposal will be approved. By contrast, if he convinces most Dell shareholders that the stub stock will be worth at least $1.98 and as much as $5.35, then it's likely that far more than 20% of shareholders will opt for additional Dell stock rather than cash. After all, according to Icahn's math, the "extra" stock would be worth at least $14.40, whereas the cash option is just $12.

If 50% of the shareholder base opts for additional stock, this would significantly reduce the amount of debt needed to finance the leveraged recapitalization, but it would also result in severe dilution of Dell stock. The Icahn-Southeastern proposal assumes that 20% of shareholders would opt for additional stock, which would raise the diluted share count from 1.8 billion to 4.42 billion. If 50% opt for additional stock, the share count would go to 8.34 billion. This increase in share count would leave the stub stock's EPS well below Icahn's projections.

Foolish conclusion
As I've stated before, I think the Dell-Silver Lake $13.65 per share offer is fair, and that shareholders should take the money and run. Dell's dismal Q1 adjusted EPS of $0.21 -- down 51% year over year -- seems to support management's contention that this will be a long, painful turnaround best undertaken as a private company.

If Carl Icahn and Southeastern Asset Management continue to pursue their leveraged recapitalization idea, they'll have to do a lot of work to convince Dell shareholders that the stub stock would be worth more than $1.65. However, if they do their job too well, a flood of shareholders will want "extra" Dell stock rather than a $12 cash payout. Striking the right balance -- i.e., getting most Dell shareholders to take $12 in cash and a stub stock rather than all cash from Dell and Silver Lake or all-stock from Icahn and Southeastern -- could prove to be an impossible task.