CHICAGO – Cablevision Systems Corp.’s founding family has offered once again to take the cable-television operator private, this time in a $7.9 billion deal that’s 15 percent higher than an unsuccessful bid last year.

The offer by Charles and James Dolan sent Cablevision shares up as much as 13 percent in trading Monday morning. Charles Dolan is chairman of Cablevision’s board, while son James serves as president and chief executive.

The offer they’ve made on behalf of the Dolan Family Group represents nearly a 13 percent premium to Cablevision shares’ Friday closing price of $23.93.

The Dolans said they offered to buy Bethpage, N.Y.-based Cablevision – which owns cable systems primarily serving the New York City area as well as Madison Square Garden, the New York Knicks basketball team and the New York Rangers hockey team – for $27 a share in a letter transmitted to shareholders on Sunday.

Though the Dolans’ offer to take the bid private in June 2005 also had a $7.9 billion price tag – at $33.50 a share – the latest proposal is higher after adjusting for the $10-a-share special dividend that Cablevision paid out last April. The Dolans had proposed that dividend after the company’s board rejected their buyout bid.

Moreover, the newest offer is entirely in cash. Terms of the Dolans’ previous offer included shares in the company’s Rainbow Media cable networks unit, which includes AMC, Independent Film Channel, WE: Women’s Entertainment, and various regional sports networks.

“I think this deal is more likely to be accepted by the board,” said Matt Harrigan, cable analyst at Janco Partners in Denver. “It’s an all-cash offer. I think the stock’s probably worth a lot more than $27, but I think at this point, people will be inclined to take the money.” Harrigan added that the deal could still be sweetened to some extent, though not significantly.

Some or all of the Rainbow Media Group assets could eventually be sold, as observers have speculated for some time, Harrigan said. This would be especially so for the AMC movie channel, which became less desirable to some cable operators after mixing more in the way of newer movies with its classic-film lineup.

Cablevision’s shares last traded $2.67 higher at $26.60, up more than 11 percent but pulling back after setting an intraday high at $27.15.

The new proposal indicates that the Dolans still believe the public markets are undervaluing cable stocks, many of which dropped by more than 50 percent from 2003 to 2005 on fears that telephone companies and satellite providers would be able to poach much of cable’s market share. That slump in cable stocks led Cox Communications and Insight Communications to take themselves private prior to the Dolans’ initial bid.

“The bid raises two obvious questions,” said Sanford Bernstein & Co. analyst Craig Moffett. “The first question is whether the bid will be deemed adequate by independent directors, and the second is whether one or more counterbidders will emerge at a higher price.”

Moffett added that it seems unlikely that other prospective bidders – such as Time Warner or Comcast Corp. – would pursue Cablevision, since if Cablevision goes private, it would easily be able to do deals with those companies anyway.

“Recall also that these same potential buyers declined to intervene 16 months ago, and that was for a cable-only deal that would be a far easier sell than the more complicated conglomerate asset collection for which they would need to bid today,” Moffett told clients.

As before, Charles and James Dolan said Monday that going private would relieve the company from “constant focus on short-term results.”

In last year’s offer, the Dolans offered to buy out the cable and telecommunications businesses of Cablevision and spin off the company’s Rainbow cable-networks arm and its sports and entertainment businesses.

The group said it has now taken into account feedback from the Cablevision board’s special committee and its advisers in connection with the going-private proposal made in 2005, and maintained that this time it’s offering “a simpler structure, enhanced value and value certainty.”