You are going to open a can of worms!
I'll shoot out the first opinion and then watch the fun begin
BMW engines can run on 87 octane. Modern engines have knock sensors and computers to adjust to the lower octane. You will see minor reductions in performance and some gas mileage reduction.
I used to argue that if you could afford a BMW you should be able to afford premium. I've backed off on that. A local auto columnist and car junkie says he runs 89 in his premium cars and hasn't noticed a difference.
So for a .20 savings per gallon, I may test a tank or two of 89 and see what happens.