Redesigning a site can often be a more tedious and difficult job than designing one from scratch. People often need their sites redesigned because they lack responsive features. This could require and entirely different structure in order to be done properly. Then you have others who simply want to change the colors and layout, but they want the information and imagines to remain the same.
The cost of redesigning a site is also impossible to give without getting details on how much work needs to be done. This is why you need to sit down with the designer and explain your needs before a price can be set.