Three-month stock chart for Cosette Communications on the TSX. (CBC)

Shares in Cossette Inc. jumped 33 per cent Tuesday morning after a U.S.-based private investment firm offered to buy the Quebec advertising and communications agency in a $131.5-million cash deal.

Shares were trading at $7.78, up $1.93, on the Toronto Stock Exchange.

The deal would take Cossette Inc. private and delist the shares, but leave the current management in charge if it goes through in December.

Connecticut-based Mill Road Capital LP is offering $7.87 per share in cash for all of Cossette's issued and outstanding subordinate voting shares.

That trumps a rival bid from Cosmos Capital Inc., which had been offering $5.25 per share for Cossette. That valued Cossette at about $87.7 million, but would have cost Cosmos less, since it already has nearly one-fifth of Cossette's stock.

Cosmos Capital Inc. wasn't immediately available for comment.

In the summer, Cosmos, which includes former Cossette senior executives who had broken with their former partners, had offered $4.95 per share for Cossette.

Cossette's board advised shareholders again on Tuesday to reject the Cosmos offer, which expires on Dec. 7, as it "significantly undervalues" the company.

Cossette's senior management team, which has 30 per cent of the company's shares, supports the Mill Road offer and considers it superior.

Mill Road is focused on investments in publicly traded companies under $250 million in size. Its current portfolio includes companies in retail, manufacturing, business services and consumer products industries.

"We are very pleased with this transaction for many reasons: it better reflects Cossette's true value and exemplifies our commitment to maximize value for all our shareholders," Cossette's CEO and president, Claude Lessard, said in a statement.

"Furthermore, it is occurring with a strategic partner that has already proven its respect for our organization," Lessard added.

National Bank Financial analyst Adam Shine said Mill Road's offer isn't likely to be exceeded.

"In the event, however, of a superior proposal, Mill Road has the ability to match or be paid a termination fee of $3.25 million," Shine wrote in a research note released Tuesday.

The offer is "very full and more than fair" for Cossette, Shine wrote, noting its struggles as a public company became more acute in the past two years in the face of lost mandates and recessionary pressures.

The deal is expected to close by the end of the year, assuming shareholders give their approval at a meeting scheduled for Dec. 18.

Shares in Cossette closed at $5.85 on Monday.