Is the cost of the private security contractors covered by Dept of Defense?

I have been unable to discover who pays for the mercenaries we call private security contractors. Is it covered by DOD, USAID, State or who? If it not in the DOD budget, is it disclosed as part of the cost or are we burying this as well? If it is not in DOD, why are we paying so much for the military and then paying them on top of that? It is especially troublesome in that our tax dollars have payed for the training of these mercs while they were part of our military. Now they are, in essence, beyond the rule of law in most cases yet we pay them. Why do we have as many private mercs or in some cases more than we do military in Iraq and Afghanistan? Doesn't it bother anyone that these companies will sell their services to the highest bidder and are willing to go anywhere that profit can be made? And another issue is that while we are setting up programs to "win the hearts and minds" with the military these mercs are free to attack and kill at will with few repercussions. It defeats the whole purpose of embedding troops in villages to get cooperation. It furthers the image that we are the barbarians and create more hate and discontent. Any thoughts?