Cox Communications’ controlling shareholder on Tuesday sweetened its all-cash offer to buy the cable company and take it private, boosting the final price to $8.4 billion from an earlier offer of $7.9 billion.

The controlling shareholder, Cox Enterprises, raised its offer price for Cox Communications to $34.75 a share from an earlier offer of $32 a share, following through on a move widely expected by Wall Street analysts. Cox Enterprises is acquiring the 38 percent of Cox Communications that it doesn’t already own.

The revised bid values each Cox Communications subscriber at around $4,000 apiece, and, according to Bernstein Research cable analyst Craig Moffett, serves as a good benchmark for cable sector valuations.

Plans call for Cox Enterprises to structure the deal as a cash tender offer to begin in two weeks, followed by a merger that is expected to end by mid-December.

In reaching the new merger terms, Cox Enterprises also announced that it has entered into memoranda of understanding with Cox Communications shareholders who cried foul earlier this year at how Cox Communications and Cox Enterprises were negotiating the merger.