Whatever the problem is it's why the previous owner sold it cheaply. You might try to check for a sticking exhaust Vanos valve spool. I'm going from 3.0l experience, but I think the 4.4 Vanos works the same way.

__________________
1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)