Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10<or=N(b)<30. Both the density at which the IN transition occurs and the location of the gas-liquid coexistence go through a maximum with increasing N(b). For longer chains, behavior expected from theory is found and both of these coexisting densities decrease with increasing length.