BL Lac objects of the intermediate subclass (IBLs) are known to emit a substantial fraction of their power in the energy range 0.1--10 GeV. Detecting gamma-ray emission from such sources provides therefore a direct probe of the emission mechanisms and of the underlying powerhouse. The AGILE gamma-ray satellite detected the remarkable IBL S5 0716+714 (z simeq 0.3) during a high state in the period from 2007 September - October, marked by two very intense flares reaching peak fluxes of 200times10^{-8} ph / cm^2 s above 100 MeV, with simultaneous optical and X-ray observations. We present here a theoretical model for the two major flares and discuss the overall energetics of the source. We conclude that 0716+714 is among the brightest BL Lacs ever detected at gamma-ray energies. Because of its high power and lack of signs for ongoing accretion or surrounding gas, the source is an ideal candidate to test the maximal power extractable from a rotating supermassive black hole via the pure Blandford-Znajek (BZ) mechanism. We find that during the 2007 gamma-ray flares our source approached or just exceeded the upper limit set by BZ for a black hole of mass 10^9 M_sun
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