Shares in Compuware (Nasdaq: CPWR), the business-software maker, advanced to the highest price since April 2011 after rebuffing a $2.3 billion buyout offer from Elliott Management Corp. and announcing its first-ever dividend.

The shares rose 5.9 percent to $11.39 in New York, and earlier touched $11.52, the highest intraday price since April 2011.

The stock gained 13 percent before today since Elliott offered to buy the Detroit-based company on Dec. 17.

Elliott Management’s offer of $11 a share signficantly undervalues the company, Bob Paul, chief executive officer of Compuware, said in a statement today. Compuware is cutting annual costs by $60 million, initiating a dividend and spinning off its remaining Covisint shares to deliver “meaningful value” for shareholders, he said.

“The plans outlined today are a step in the right direction,” Kirk Materne, analyst at Evercore Partners Inc., said in a note. Compuware’s announcement indicates it is “leaving the door open” for headcount reductions and other potential divestitures, said Materne, who rates the stock overweight with a $13 price target.

Elliott Management said it’s still interested in Compuware.

“Compuware has granted our request for access to diligence to confirm an offer for the Company,” Jesse Cohn, portfolio manager at Elliott Management, said in an e-mailed statement. “We remain very interested in the company.”

Compuware’s products include mainframe applications, collaboration technology, project management tools, and application performance management services for cloud and mobile services.

Compuware said it is being advised by Goldman Sachs Group Inc. and Allen & Co.

Peter Karmanos, who also owns the Carolina Hurricanes, is in the process of stepping down as executive chairman of the software firm.

Karmanos co-founded the Detroit-based software development business nearly four decades ago.

The company detailed the plans in a recent filing with the Securities and Exchange Commission. The 69-year-old is expected to become a consultant for Compuware, earning $600,000 a year.

The move to leave the company’s board is effective March 31.

Karmanos stepped down as Compuware’s chief executive in 2011.

He will be succeeded as nonexecutive chairman by Gurminder Bedi, the company’s lead independent director.

Karmanos moved Compuware’s headquarters from suburban Farmington Hills to a new building in downtown Detroit in 2002. He had said earlier that he was aiming to retire by 2013, when he turns 70 and the company turns 40.

“I’d like to leave with a really great flourish at the end,” Karmanos told The Detroit Free Press in an interview last year.

Compuware has an operation in Durham at the American Tobacco complex.

Karmanos believes the company could triple its market value to $6 billion by 2013.