This paper provides a numerical approach based on a Monte Carlo simulation for valuing dynamic capital budgeting problems with many embedded real options dependent on numerous state variables. We propose a way of decomposing a complex capital budgeting problem with many options into a set of simple options, suitably accounting for interaction and interdependence among them. The decomposition approach is numerically implemented using an extension of the Least Squares Monte Carlo algorithm, presented by Longstaff and Schwartz (2001) applied to our multi-option setting. We also provide a number of applications of our approach to well-known real options models and real life capital budgeting problems. Moreover, we present a set of numerical experiments to provide evidence for the accuracy of the proposed methodology