And leave the whole permitting responsibility to them; this is not a DPD permit, it is specifically a sewer permit which can only be taken out by a licensed sewer contractor. The city does not allow property owners to act as sewer contractors because of the liability of the city sewer system.
The cost depends entirely on how much work needs to be done; it can cost $10,000 or $40,000. If you own an older home and the line is broken, the line might need complete replacement or simply blasted with a new liner. Which means you need to have a number of bids from licensed sewer contractors, not the firms that advertise on TV and tell you they do everything.
Always ask if there are other options other than the one that the contractor is suggesting. Follow the answer up by finding someone who does a lot of the other option.
Always ask if there is a cheaper way of fixing the problem...ASK, ASK, ASK questions.