DIY? About $75 not counting equipment remtal(sheetrock lift)

Hire out? $300 and up.

You also have insulation issues to deal with - if it is wet it should be replaced. I would not recommend starting your first DIY job on a ceiling, but you can keep costs down by replacing insulation and installing the drywall and then hiring a taper to finish. Then you can prime and paint yourself.

For tips on installing drywall repair panels, see the link below.

Here is a link that might be useful: Drywall Repair Tutorial

Hmmm... I didn't realized that there was insulation underneath. It's a house with a flat roof built in the late 40's or early 50's. Do you think it will have insulation?

Ironically, there are several drywall repairs around the house, but none of them are all that accessible. There is another repair required at the staircase.

Paul

If you are located in an area with winter cold temps there is almost certainly insulation. Also, if you are in an area with lots of hot requiring AC, there is probably insulation. So I guess unless you are in someplace with constant 70 degree temps (San Diego?) then you probably have insulation between ceiling and roof. One way to find out: Cut out an area big enough to look or find other access to the area. Or, cut out a small square big enough to shine a flashlight through and look.