Why FV=0 when calculating equivalent annual annuity?

Sometimes I just wished I had a professor next to me while studying to answer these small and probably easy questions that pop-up. I assume that the answer is very straight forward, but why do we set the FV to = 0 when comparing projects of different lengths?

I believe this is because we are trying to examine the yearly payout with future exhaustion. If there is a future value, that means the annuity payments have been understated and there are remaining dollars, similar to a personal retirement plan.

FV=0 is when the payment stops. Similar to a pension calculation loan calculations, thats when the cashflow stops.