Hi Joseph,
I didn't tried below suggestion but i am sure it will work.
Try a work around as system will not allow you delete Last Posting Period as SAP depend upon Posting Period for doing any transactions.
You can create Posting Period for Last Year and then Delete the Posting Period which you are not able to Delete.
After Deleting you can create Current Year Posting Period.
Hope this helps 
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Regards::::
Atul Chakraborty