Formula to change Quarter to Last Year

Hi All,

I'm not even sure if this is possible, so I thought to ask here. I have a table which includes a column that documents Quarters per current year.

When January 1st comes around, I need the current quarters documented to change to reflect the last year so I can distinguish the difference between last years quarters versus this years quarters. Including a dropdown to reflect each quarter per year was vetoed and I was asked to come up with a solution for this. I'm not sure if I'm articulating it well, so here's a screenshot of what I'm trying to accomplish:

I have no idea where to even start with building a formula to do this. Can anyone point me in the right direction? I appreciate any assistance!