A new Monte Carlo (MC) simulation program based on the GEANT code has been developed to study the most effective position of the target for the measurement of work functions using positronium (Ps) and thermal Ps with the time-of-flight (TOF) technique. We find that distances of <1.5 cm and >2 cm are suitable for the measurement of thermal and work function Ps, respectively. The kinetic energy of Ps emitted from the front surface of the micro-channel plate (MCP) is measured by slow positron bombardment. The kinetic energy of the emitted Ps is equivalent to the magnitude of the Ps work function, which was determined by measuring the TOF of ortho-Ps (o-Ps). Ps emission energy is measured for the first time to be 0.79 +/- 0.30 eV. This measurement is consistent with a general description of the production of work function Ps resulting from a common interaction of low-energy positrons with the electrons of the traversed material.