Towing hitch

Hello guys, have you ever attached a trailer coupling? I would like to mount one on my V40 year 2003. Was recently with my dealer and he made me an estimate of 580 euros. I would have almost tipped over there. And that even for a rigid coupling. If this remains with this price, then it is still cheaper to rent a car and a trailer instead of building it. Has any of you ever built one on it yourself? Does that work easily? Does the bumper also have to be “cut up” a bit or is the hook mounted under it? Can you do a lot wrong? I am grateful for every help. Nice start of the week still…