Aimia Inc.'s top shareholder has picked apart Air Canada's attempt to buy its loyalty program Aeroplan as "blatantly inadequate."

Christopher Mittleman, chief investment officer of Mittleman Brothers – which holds 17.6 per cent of Aimia's shares – made his argument in an open letter to Aimia's board less than a week after it rejected the approach by Canada's largest airline and its buyout partners.

"The offer for Aeroplan from the Air Canada-TD-CIBC-Visa consortium was misleading, coercive, and blatantly inadequate," Mittleman wrote in the letter. "I applaud the board for note acquiescing and continuing negotiations."

Air Canada, Toronto-Dominion Bank, Canadian Imperial Bank of Commerce and Visa Canada Corp. went public on July 25 with an offer to buy Aeroplan. The consortium framed the deal as being worth $2.25 billion, including $250 million in cash, and set Aug. 2 as the deadline for Aimia to respond.

Last Thursday, Aimia disclosed it turned down the original offer, as well as a sweetened $325-million bid, and said it counter-proposed $450 million. Air Canada and its partners have not indicated what their next move will be.

Meanwhile, Montreal-based Aimia has been playing the field. On Friday it announced a partnership with Porter Airlines that will take effect in 2020. It also recently confirmed it's held talks with the Oneworld airline alliance, which is home to many of Air Canada's rivals.

"Aeroplan is the lynchpin in the nexus of this powerful network, where TD, CIBC, Visa, Amex, and Air Canada generate hundreds of millions in net profits annually from their Aeroplan card holders," Mittleman wrote in his letter, adding he estimates the loyalty program is worth up to $10 billion to the consortium.

He suggested the group's $325-million offer represents a 1.4x EBITDA multiple, and is "clearly beyond the bounds of any conceivable range of reasonableness" for Aeroplan.

Mittleman added Aimia should not sell the business unless it receives at least $1 billion, plus a 20 per cent premium, from a buyer.

“In matters of valuation there is always a degree of subjectivity on inputs, assumptions, multiples, margins, growth, discount rate, etc. But there are limits," Mittleman wrote. "And veering too far from those limits takes one into the realm of ridiculousness, and posturing. The Air Canada-TD-CIBC-Visa consortium bids for Aeroplan were deep into that realm."