Welcome to FlyerTalk,
linda705,
You can use the ITA website to estimate the amount of taxes/fees/surcharges you can expect to pay on a BAEC redemption.
http://matrix.itasoftware.com/
For a HOU-HNL coach fare, ITA lists the following taxes/fees:
US Transportation Tax (US) $14.11
US Alaska/Hawaii Departure Tax (US) $16.40
US September 11th Security Fee (AY) $10.00
US Passenger Facility Charge (XF) $16.50
US Flight Segment Tax (ZP) $14.80
Note, not all of the above are fixed fees: the US Transportation Tax is calculated as a percentage of the base fare (7.5%) and thus works out as zero against a redemption fare.