Is there BOM Cost Report by Item Group showing cost of BOM components by item group total as of today or any point of time?
It depends upon how you have set this up, if you have defined the item with cost groups you can see this in any of the calculations and the complete button or on any works order. You also have the costing sheet analysis on the tab. The cost depends upon how you handle the costing version and the fallback principle.
Production - Reports - Analysis - Cost and Estimates is also useful.
There is no such report in standard,as this can be more specific.