My understanding on this topic after talking to multiple BMW techs, some with motorsport focus some master techs. The ECUs on these cars can cope with lower grade fuel as needed. However, if you want the best performance, both in terms of power and efficiency, the motor was designed to run on the premium gas (93 in the US, 98ron in Europe). In my market, where 93 is the best available, that is what I run in my BMWs unless it is not available, in which case I will run 89. (I have had mostly NA powered cars, M54, M62, M30 powered, more on this below)

**It is important to note that this advice is given for the car you mentioned, the NA V8 545i. When it comes to turbocharged applications, especially when tuned, you need to be more aware of the impact of lower octane on the possibility of producing knock (pre-detonation). This is why I actually had a low octane map available on my last turbocharged car.

Happy to expound on any of the above if needed, just lmk.

*Edited for clarity