Dish brings its own benefits, such as wireless spectrum that could be valued at $10 billion, marketing experience and millions of subscribers. Ergen said that the savings, lower capital expenditures and bundling would create $37 billion in benefits.

"We remain confident that the Sprint board will share our view that the Dish proposal is superior by offering Sprint shareholders greater value with a higher price and more cash, while also creating the opportunity to participate meaningfully in a combined, and competitively unique, Dish/Sprint," a statement from the satellite TV company said Tuesday.

Dish argued that Softbank, an overseas telecom operator, cannot offer Sprint the opportunity to cut back office costs or cross-market products. "We will continue to work with the Sprint board's special committee and its advisers, as we have been over the past week," Dish said.

Son said that Dish's bid did not consider factors such as the cost of deploying a network over the company's spectrum, which he put at $6 billion. With synergies, he suggested, Dish's bid comes to $6.31 per share.

Complicating the analysis, Sprint and Dish both have pending offers for wireless broadband provider Clearwire Corp. Clearwire brings its own spectrum holdings and debt that would have to be considered in the merger scenarios. Not surprisingly, Softbank and Dish also have differing views of leverage that the post-merger companies would have. Ergen said that combining his pay-TV company with Sprint and Clearwire would generate a company with leverage, net of cash, of 4.7 times Ebitda.

Softbank, on the other hand, puts leverage of a merged Dish-Sprint-Clearwire at 5.9 times Ebitda, which Son described as a "very dangerous situation."

Son said that Ergen's plans to have debt at Dish and Sprint, rather than combine the balance sheets, would present its own issues. "Two separate companies with two different sets of lenders would make it very, very complicated to get the synergies," Son said.

Softbank projects that after acquiring Sprint and Clearwire it would have leverage of 3 times Ebitda. Sprint and Softbank have said that they could close their merger by July 1. There is a lot of math for Sprint's special committee to do over the next two months.

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