In the global effort for industrial decarbonization, repurposing closed coal-fired power plants into power-to-methanol (PtM) plants offers a promising pathway to reduce CO₂ emissions while leveraging existing infrastructure. This study introduces a novel combined optimization approach using mixed-integer linear programming (MILP) to simultaneously optimize the investment and operation of a PtM plant, assessing its economic viability. The model incorporates the operational flexibility of proton exchange membrane (PEM) electrolyzers in response to fluctuating electricity prices through a piecewise linear representation of its load–efficiency characteristic curve. A case study of a repurposed coal plant in Austria demonstrates the model's applicability and practical relevance. The results show that larger electrolyzer capacities, i.e., 434 MW, with flexible part-load operation can significantly reduce methanol production costs, i.e., EUR 0.8/kg, achieving competitiveness under high CO₂ pricing scenarios, i.e., EUR 500/ton. A sensitivity analysis is performed to identify the critical factors influencing production costs. This study concludes that the combined investment and operational optimization approach effectively captures the essential elements of PtM systems, enabling faster, better, and operation-informed investment decisions for innovative technologies to support the ongoing energy transition. These findings indicate that PtM technologies can be a viable solution for asset repurposing, grid stabilization, and decarbonizing hard-to-abate sectors.