Out of the box you can't change that setting conditionally on the fly based on the values of the prompt just next to it.
I can imagine you can "simulate" something like that if you set your prompt to auto submit (without "Apply" button) when you change values and using conditions to display or hide a section: you can create 2 versions of your "fiscal period" prompt and display one or the other based on the values of the company prompt using a condition ....
Honestly I wouldn't do that at all, just tell your users it's not supported, less issues for you in the future!
Thanks for your quick answer
This functionality will not be ever supported in OBIEE because it does not fit in normal functionality of reporting tool.
You can try to do workaround not sure how it will help because it is manual work...
1) create 2 presentation variable for 2 different scenarios like abc and xyz for product and date
2) create manual group by bin for company_name
3) pass xyz and abc variable to the report