Earlier this year, Dell (UNKNOWN:UNKNOWN) founder Michael Dell and private equity fund Silver Lake Partners agreed to take Dell private for $13.65 per share in cash. The news sparked a brief bidding war for the company. Meanwhile, several prominent Dell investors complained that the buyout price was too low, even though it stood nearly 50% above the stock's late-2012 low.

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Late last week, Carl Icahn's Icahn Enterprises (NASDAQ:IEP) teamed up with Southeastern Asset Management to launch a competing bid for the struggling PC giant. Under this proposal, shareholders would receive $12 in cash but would continue to own a "stub" stock (with an estimated value of $1.65). Alternatively, shareholders would have the option to decline the cash payment in return for 7.27 additional shares.

Icahn and Southeastern expect 20% of shareholders to take the all-stock option rather than the $12 cash payment. Based on Dell's diluted share count of 1.8 billion, cash payments to the other 80% of shareholders would total $17.3 billion. Icahn's group states that it can pay that sum while only taking on $5.2 billion of new debt. However, a realistic look at the company's finances casts serious doubt on that notion.

Raising cash
If Icahn's group plans to pay out $17.3 billion to shareholders while adding just $5.2 billion of new debt, it will need to find $12.1 billion from other sources. According to Icahn's plan, this $12.1 billion would come from 1. cash on hand, 2. two additional quarters of cash flow before closing, and 3. selling the net financing receivables from Dell's captive finance unit.

At book value, a sale of the financing receivables could generate around $3 billion. This leaves roughly $9.1 billion to be covered by Dell's cash on hand and any additional free cash flow generated prior to closing the deal.

Icahn estimates the next two quarters of free cash flow at $1.4 billion. However, it is hard to understand how he arrived at this estimate. Dell generated FCF of less than $300 million in the first half of fiscal year 2013, although the company did manage to produce free cash flow of $1.5 billion in the first half of FY 2012. In light of the company's deteriorating performance recently, $1.4 billion seems like a very aggressive cash flow estimate.

Available cash
Dell had $15.3 billion of cash and investments at the end of last year. Assuming the company fulfills Icahn's aggressive FCF forecast, the company would have $16.7 billion by the end of July. However, not all of this cash is available for payouts to shareholders. Nearly all of Dell's cash is held overseas, which means that the company would have to pay up to 35% in federal corporate taxes (plus any applicable state taxes) when repatriating it to the U.S. To be conservative, I will apply a 30% discount factor to Dell's cash, leaving $11.7 billion available after taxes.

Furthermore, Boston Consulting Group recently recommended a change in Dell's operating model from "build to order" to "build to stock," to improve the company's competitiveness. Icahn's business plan for the company entails following through on BCG's suggestions. However, Dell has acknowledged that this would require a significant increase in working capital.

Dell has recently held approximately 11 days of supply in inventory, whereas competitor Hewlett-Packard holds 26 days of inventory. If Dell needs to match HP's days of inventory under a "build to stock" operating model, that would increase working capital (and decrease cash) by approximately $2 billion. Dell would thus have total cash and investments of $9.7 billion, from which Icahn wants to draw $9.1 billion to pay shareholders.

Too risky
Technically speaking, Icahn's numbers work: Assuming Dell produces FCF of $1.4 billion in the first half of FY14, the company would have enough cash to cover the payments to shareholders. However, this would leave Dell with less than $1 billion of cash on hand. It would be incredibly dangerous for a company of Dell's size to maintain such a small cash cushion, especially because of the rapidly changing nature of the markets Dell competes in.

Icahn's proposal would leave Dell starved for cash and with a heavy debt burden. It would entail selling the company's captive finance arm, which could make it harder to close some deals. All in all, it would represent a very risky gamble that would leave Dell no margin for error as it navigates the transition to a post-PC world. Compared to this prospect, the all-cash offer from Michael Dell and Silver Lake seems much more attractive for shareholders.