The distribution line planning task has become more complex due to several impacting factors. This paper presents a stochastic approach for implementing an optimization procedure with a statistical representation of the electricity prices, ambient temperature and load currents in the distribution network. The validation of this stochastic approach is based on the comparison results of both examined approaches (stochastic and deterministic), which are applied for the computation of the total average annual costs. Attention has been focused on reducing total average annual costs by optimizing the conductor profile of a power line and the transformer capacity. Thus, the Net Present Value of the total average annual costs can be evaluated during the planning period. The problem is formulated as a minimization of the Net Present Value of the total average annual costs of an examined distribution line project. The tool is implemented in MATLAB software by using the Monte Carlo method. The proposed stochastic approach has been applied in the solution of an example of a distribution line project, which is presented.