After weeks of silence, Wendy’s International and interests led by billionaire Nelson Peltz sniped back and forth yesterday over the future of the Dublin-based burger chain. The Peltz camp said two recent offers to buy the company were rejected, and it is seeking a special meeting so that shareholders can vote on the company’s future, its filing with the Securities and Exchange Commission said. 

Soon after, Wendy’s shot back with its own filing, saying “private actions and public statements have been inconsistent” on the part of Trian Fund Management and Triarc Cos., the Peltz-controlled companies that made the bids.

The filing also said a special committee formed a year ago to consider options for Wendy’s future, including a possible sale, will have further announcements “in the very near future.”

Despite yesterday’s fireworks, the situation remains as murky as ever.

“It drives me crazy,” said Pam Thomas Farber, daughter of founder Dave Thomas and a Wendy’s franchisee and investor. “It’s tiring. We don’t know what’s going to happen.”

In a letter to James Pickett, chairman of Wendy’s board, the Peltz side indicated it is concerned that Wendy’s might strike a deal with a different bidder without allowing shareholders to vote.

“If the special committee now intends to pursue a transaction with another party … we urge the board to ensure that any alternative transaction be subject to the approval of Wendy’s shareholders,” wrote Peter May, a top officer with both Trian and Triarc.

The concern that other interested parties could be on the prowl is probably legitimate, said Dennis Lombardi, executive vice president of Dublin consulting firm WD Partners.

Lombardi said restaurant stocks have been beaten up so badly that investors are taking notice. Wendy’s shares closed yesterday at $25.38; the 52-week high is $42.22.

When talk of a possible sale of Wendy’s surfaced, other possible bidders included a group led by David Karam, an Upper Arlington franchisee, and a group led by the former head of CKE Restaurants, the operator of the Carl’s Jr. and Hardee’s chains.

Investors also could view Wendy’s as a company that is primed for the kind of turnaround that has been engineered by competitors McDonald’s and Burger King, Lombardi said.

“There are a lot of ways to speculate,” he said. “You could understand financial buyers, strategic buyers and international buyers being interested. Wendy’s would be a wonderful way to get into the U.S. market.”

Nelson Peltz, who controls interests that own 9.8 percent of Wendy’s shares, began pushing for change at the company more than two years ago, including winning an effort to put handpicked candidates on the board.

Yesterday’s filing said Peltz-controlled companies were willing to pay $900 million in cash and additional stock for Wendy’s in one bid, or merge Wendy’s with Arby’s, which is owned by one of Peltz’s companies.

The letter said the deals would not have required third-party financing, which has been an issue, given the tightness of credit markets. Wendy’s contested the financing assertion.

“It’s difficult to judge whether the Wendy’s board made the right or wrong decision,” said John Owens, an analyst with Morningstar. “There’s not enough information disclosed in the letter. But I do think that it is in shareholders’ interest to vote on these offers.”

Wendy’s is to hold its regularly scheduled board meeting over two days beginning Tuesday, according to an internal memo to employees that was obtained by The Dispatch. The memo also said the company has not set a date for its annual shareholders meeting, which typically had been set by this point in past years.