The future new cold neutron backscattering spectrometer IN16B at the Institut Laue-Langevin is being designed to maintain the extremely high energy resolution of the existing backscattering spectrometer IN16 (approximately 0.4 µeV full width at half maximum in a standard configuration). Simultaneously, a phase space transformation (PST) device will significantly increase the flux at the sample position at the expense of an acceptably more divergent incoming beam. A wide wavelength band (Δλ/λ ≈ 10%) has to be offered to the PST device in order to achieve a significant flux gain by a factor of at least 4. Thus, IN16B will have to be located at the end of a cold neutron guide, whilst the present IN16 is located at a side position along a guide. In order to optimize the layout of individual components and to estimate the instrument performance, the Monte Carlo simulation programs McStas and VITESS have been used. McStas and VITESS offer a general framework to compose virtual neutron scattering instruments and support both reactor and spallation neutron sources. In this paper, we report on studies to optimize the neutron delivery towards the PST device, with an emphasis on results from McStas. The simulations of IN16B were performed for two different hypothetical guide end positions, namely a shorter guide with 58Ni coating and existing gaps and instruments upstream, and a longer dedicated guide with a ballistic layout and supermirror coating. For the simulations, different models of the available cold neutron moderator sources have been taken into account. A neutron velocity selector and an elliptical focus guide were optimized for the purposes of IN16B. [ABSTRACT FROM AUTHOR]