  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 200\times10^{-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 Lac's 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
