Harsha, I understood your point but couldn't grasp why you're comparing the formulas when i am not using the time range anywhere. The answer lies somewhere in between what you and I are saying. Since I have introduced Quater totals in the model (doesn't matter I do not use the time range which has the quarters or not), I have introduced an intermediate level in the hierarchy between month and year, which will be consistent across the model.
That is my best guess unless someone has a better understanding
Harsha, I think you are missing the point. As mentioned previously, the new time range (which has the Quarter totals) isn't being used in the Snapshot Staging module. Snapshot staging has the model calendar which doesn't have Quarter totals.
For some reason, the existence of Quarter in one of the time ranges (even if that time range isn't being used anywhere) is causing the time formula to deviate from its obvious behavior. Let me know if this clarifies the issue.