Doesn't have any impact on warranty.

The reason BMW and other manufacturers specify a higher AKI (octane rating) than the engine requires is because fuel varies so much from region to region in North America. I try not to call it octane, as motor fuel doesn't have any. By calling for 91, though, just about everyone will get a fuel that is 'good enough'. You may need 91 where you live, depending on your local fuel quality (and to some degree, on the ambient temperature, and the condition of your engine)

Using a lower AKI won't necessarily cause a reduction in power and fuel mileage. It may do so, because of the variability mentioned above. The only way to know is to test it, tank to tank, and measure the fuel consumption. It the consumption doesn't climb with a lower AKI fuel, it is a safe bet that your timing is not being retarded due to knock, and that the fuel has an adequate anti-knock rating (the actual anti-knock properties, not what it says on the pump). In either case, you won't hurt the engine, you just may spend some of your $/gallon savings in increased consumption, as a trade-off.

Another variable is ethanol, which does reduce mileage. Regular fuels sometimes have more ethanol than premium fuels. Other times they have less. Depends what fuel suppliers in your region are doing.

I ran 89 in my X5 for all the time I owned it. Ran great. Best mileage ever was on 89. 87 didn't run as well. No benefit to using 91 for me, given my local fuel. Same with our 325. Same with the Z4. The 535 got 91 or 94, as that engine (with the turbos) took more advantage of the better anti-knock properties. The X3 is now getting 91, but it runs fine on 89. I just like the fact that our 91 here doesn't have any ethanol at many stations, and the 89 has up to 5%.

Cost difference here is about $0.58 per imperial gallon from 87 to 91, half of that for 89. There is no reason to use a fuel with a higher anti-knock rating than the engine needs (not what BMW publishes, but what it actually needs), as it doesn't help your engine in any way. The other things that often go along with premium fuel (more detergent, no ethanol) can help your engine, but aren't directly related to the anti-knock index (AKI).

I think that the oft-heard line that if you can afford a BMW you should put the best fuel in it is absurd. You should put in a fuel that the engine requires in practice. Anything more is wasteful. You should also use a quality fuel, but AKI is not a quality measure, in the way that sediment, water content, and ethanol contamination are.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue