The only time I would feel I would be able to kill someone, is if they did something horrible to someone else and I was there to witness it. Such as murdering someone else. And even then, I may just try to stop them and call the cops.
But for a price, I could probably kill someone that deserved it. Maybe. I would probably struggle with the decision.
As for killing a loved one or a random stranger? No amount of money would be enough.