Current low voltage (LV) network planning methods consist mostly of a static deterministic assessment of radial network alternatives. This straightforward approach does not take into account the uncertainty which comes with the introduction of PV generation, electric vehicles and other new technologies into the LV-network. Moreover, these technologies may call for a change in network topology, from radially oriented networks to more meshed variants. The focus on cost-efficiency requires the implementation of risk-based asset management into the LV-planning approach. The complete implementation of these two aspects into LV-network planning methods would result in a too complex network planning formulation. By using heuristic optimisation methods to reduce the number of network alternatives and scenarios which need to be assessed in combination with simplifications on the risk-based assessment of power quality, losses and service availability, a computationally feasible LV-network planning approach is developed in this work. A greenfield case study based on an existing Dutch neighbourhood shows how this approach can be applied in practice to yield the optimal network structure. Though the initial investments and availability of a meshed network are worse, the meshed network structure generates a 10% lower overall cost, due to reduced losses and improved power quality.