Carillion has made an improved offer of £2.1bn for construction rival Balfour Beatty after conversations with its major shareholders. Carillion's merger proposal, which would create the largest construction firm in the UK, is at a 36% premium to the average share price in the month before the deal was leaked in late July. Philip Green, chairman at Carillion: "Given the scale of the prize for shareholders of both Balfour Beatty and Carillion from a merger of the two companies, the board of Carillion remains committed to moving forward in a constructive and collaborative way with the board and management of Balfour Beatty to create a world-class business and very significant value for the shareholders of both companies."Previous bids had floundered in the face of a resolute Balfour Beatty board, which dismissing its suitor's recent second approach to their investors as "opportunistic" and on Friday quashed Carillion's idea that £1.5bn of synergy cost savings could be made, saying any savings would be "materially lower".In its new proposal, Carillion said the cost-base of the combined group could be reduced by at least £175m per year by the end of 2016 and reiterated that these savings "would represent a capitalised value of over £1.5bn before any re-rating".To further sweeten the pill, it has offered Balfour Beatty shareholders a 58.268% share of the combined group as well as a cash dividend of 8.5p per share in order to bring shareholders on side.And addressing another snag to a deal, being Balfour's plans to sell its US-based Parsons Brinckerhoff division, Carillion stated that the auction process could continue but should the merger proceed it "would expect the disposal of Parsons Brinckerhoff not to be completed" and would reimburse the remaining Parsons Brinckerhoff bidders' reasonable costs.At 15:50 on Tuesday, shares in Balfour Beatty were up 3.02% to 255.5p, while Carillion's were just above flat at 337.7p.OH