A lossless solar cell operating at the Shockley-Queisser limit generates an open circuit voltage (Voc) equal to the radiative limit. At Voc, the highly directional beam of photons from the sun is absorbed and subsequently externally re-emitted into a 4π solid angle, providing a large photon entropy loss. A solar cell can beat the Shockley-Queisser limit and approach the 46.7% ultimate limit by decreasing the output solid angle of the light emission at open circuit conditions. Here, we present a design for an InP single nanowire solar cell capable to operate 159 mV above the radiative limit. We first optimize the spontaneous emission factor (b-factor in the dataset) into a guided mode of the nanowire towards 68%. We subsequently launch a guided mode at the bottom straight part of the tapered nanowire yielding a photon escape probability of 81% for a tapering angle of θ=1.2 degrees and a top facet with a radius of 83 nm (transmission part of the dataset). When assuming homogeneous light emission along the nanowire, an outcoupling efficiency of 42% of the emitted light is obtained. The final optimization is the reduction of the emission cone towards 0.011 sr by focusing the guided mode with an external lens (lens part of the dataset).