The Phase-Induced Amplitude Coronagraph (PIAAC) uses a lossless beam apodization, performed by aspheric mirrors, to produce a high contrast PSF. Thanks to the lossless apodization, this concept offers a unique combination of high theoretical throughput ($\approx$100%), high angular resolution ($\lambda/d$), small inner working angle (${\approx} 1.5 \lambda/d$), low chromaticity and low sensitivity to pointing errors or angular star diameter. Together, these characteristics make the PRC an ideal choice for direct imaging of extrasolar terrestrial planets (ETPs) from space. We show that a visible telescope smaller than 4m would then achieve the goals of the TPF mission, while other coronagraphs considered for TPF require telescope diameters typically 2 to 3 times larger. On a large size (8m) space telescope, ETPs can be searched for around a significantly larger sample of stars, thus enabling a much higher scientific return.