Key TakeawaysLiberty Broadband shares surged Tuesday after the communications provider made a counteroffer to a merger proposal from Charter Communications.The counteroffer calls for Liberty Broadband investors to get 0.29 Charter shares for each Liberty share they own. Charter's proposal was for 0.228 of a share for each share of Liberty.Liberty currently owns a 26% stake in Charter, which offers internet, cable television, and mobile phone services under the Spectrum brand. Shares of billionaire cable mog ...