You could have the frame repaired in a couple of ways. The "strut" connecting the bottom bracket to the dropout is called a chain stay. A good repair man can replace the broken stay with a new one. A cheaper repair would be to have a welder re-weld at the break. It depends on how much you want to spend.

To replace the broken stay and repaint the frame could cost anywhere from $200 to $500, just welding the break and spray painting it could cost less than $100. Although the cheap way would be very ugly.