One of Aer Lingus' largest institutional shareholders has warned that International Airlines Group (IAG) might have to pay as much as €1.6bn (£1.25bn) to take over the Irish carrier.News emerged on Friday that the airline had rejected an improved deal, prompting Crystal Amber, the activist investor that holds a 2.8% stake in Aer Lingus, to suggest IAG placed a bid as high as €3 a share, claiming that the carrier was worth at least €2.75 a share."We think the board of Aer Lingus was absolutely right to reject an offer at €2.40," Richard Bernstein, investment adviser at Crystal Amber, was quoted as saying by The Sunday Telegraph."When [IAG boss] Willie Walsh bid for Vueling he bid €7 initially which was rejected, and then he paid €9.25 in the agreed deal so there's a bit of a precedent."IAG would need the approval of Ryanair, Aer Lingus' biggest shareholder with a 29.8% stake, for the takeover to go ahead.In December, Aer Lingus turned down IAG's initial approach, worth €2.30 a share, and on Friday it rejected an improved offer of €2.40 a share. Bernstein, who had previously suggested IAG should bid €2.60 a share, said the amount would be "insufficient" in light of the airline's strong fourth-quarter trading update on Thursday.On Friday, Aer Lingus shares closed at €2.50, after the group said operating profit for 2014 would surpass the €61.1m it reported a year earlier and that it had boosted fuel hedging to benefit from falling fuel prices.