This paper analyzes the performance of the A³MCNP™ (Automated Adjoint Accelerated MCNP) for determination of neutron fluence in a BWR core shroud. A³MCNP™ automatically prepares variance reduction parameters based on the CADIS (Consistent Adjoint Driven Importance Sampling) methodology that uses a 3-D energy dependent “importance” function. A³MCNP™ prepares necessary input files for performing adjoint transport calculations using the TORT Sn code. Using A³MCNP™, we have calculated DPA (displacement per atom) values (with a lσ uncertainty) at the H4 weld of a BWR core shroud in less than 5 CPU hour. For the same calculation, an analog Monte Carlo simulation requires about one month of CPU time. The trade-off between the accuracy of the adjoint function calculation and overall computation cost is examined. It is demonstrated that even for a very approximate adjoint function distribution, A³MCNP™ yields significant speedup over an analog Monte Carlo calculation.