Facility location decisions are typically made before demand is fully known, yet most applied studies solve a single deterministic model using expected or nominal demand. This paper formulates and solves a capacitated facility location problem using a real academic benchmark instance, then extends it to a two-stage stochastic program in which facility-opening decisions are made under uncertainty and allocation decisions are made as recourse once demand is realized. Using the standard evaluation framework from stochastic programming, we compute the Value of the Stochastic Solution (VSS) and the Expected Value of Perfect Information (EVPI) for this instance, and test the robustness of both quantities across alternative demand-scenario structures and shortage-penalty assumptions. We find that the deterministic solution, while 3.2% cheaper up front, leaves an expected 1,230 units of demand unmet once evaluated honestly against demand uncertainty, and that accounting for uncertainty at the facility-opening stage is worth $82,933 in expected cost (VSS), consistently an order of magnitude larger than the value of having perfect foresight about which scenario will occur (EVPI), across every scenario structure and penalty assumption tested. This gap between VSS and EVPI indicates that the primary benefit of stochastic optimization here comes from committing to a more robust first-stage decision, not from reacting optimally after the fact, a finding consistent with related results reported in the humanitarian logistics literature.