Apartment bath leak to floor below

I have had a blocked bath drain for a few weeks. Today I decided to sort it out. I put a coat hanger down to try to dislodge some of the scum and hair and then got my plunger and cleared it of the rest. Not long after, I got a knock on my door from my downstairs neighbours who now have a leak in their ceiling. I'm guessing I have damaged the pipe bringing my bath water away. I called the management company and they're sending out a man. I'm just wondering what is going to happen next. I own the apartment. There is damage to the downstairs neighbour's apartment from a broken pipe and I'm also going to have to pay to have the pipe fixed. How much is all this going to cost me and is there any part of it I could do myself?

I'm guessing a tile or two will have to be pulled up to replace the broken pipe under the bath drain. Would I be better off just redoing the entire bathroom? I'm afraid this is going to cost me thousands. Hundreds I suppose I could handle. Lesson learned. Leave the coat hanger in the closet, although there were so many internet how to's encouraging coat hanger solutions.

Thanks