Its not quite that simple.
Currently it costs a lot more to use the Death penalty than to imprison someone for 40 years or more, but that is because of the insane amount of checks, balances and red tape that goes along with it.
However when I reference Capital Punishment I am not speaking of the exact system we have in place at the moment, more rather hearing the verdict and taking "old yella" out the back to a merciful end at the barrel of a shotgun.
Someone goes on death row they are there for a Life Sentence before they actually face the chair, most people sentences to death die in prison during the long wait and the US actually Kills far less people than you would think. The Number of people that face the Electric Chair is relatively few, even in states such as Texas.
That's the whole system of applying the death penalty in the US that's stupid, it's not the death penalty that is expensive in itself. Besides, that's just more reason to abolish the death penalty.
By the way, if a guy killed your daughter you feel you should have the right to dispose of him as you see fit, right? Now imagine that specific guy had a family of his own, doesn't his family, by your logic, also have right to kill you after you murder him?