How to assign different cost center to a work center with diff validity period

Dear SAP Gurus,

I want to assign a new cost center(which got created) for a existing work center effective 01.Jan.2016. I want to have the existing cost center assignment to continue till 31.12.2015.

Is it possible to do it now with different validity period (for both cost center) and if possible, can you please provide inputs on how to do the same.

Is the validity start and end date in costing tab refers to validity period of work center assignment to a cost center (I have highlighted in attached screenshot)

Thanks in advance.

Best Regards,

R.Velmurugan