BMW recommends 93 octane with a minimum fuel grade of 91. They further state "Do not use any gasoline below the specified minimum fuel grade. Otherwise the engine could be damaged.".
Implied here - if the engine is damaged due to low grade (i.e.: 87 octane) fuel, repairs under warrenty may not be covered! With the price difference between 87 and 91/93 you'd have to fill up an awful lot to pay for an new engine!