Surely premeditated murder can't always be considered a sin?

My elderly mother (God bless her very soon to be departed soul) is infirm, virtually blind, bedridden and in acute pain. She no longer wants to live but being a devout Christian refuses to commit suicide. I can only see it as an act of mercy to end her suffering. This way my mother gets the release she craves and (as a bonus) gets to meet her maker, the health service is spared the expense of treating her and I get the inheritance before I'm too old to really enjoy it. Everyone wins.