This paper examines the value that can potentially be created by a vertically integrating energy system. Integration entails operational gains that must be traded off against the requisite cost of capacity investments. In the context of our model, the operational gains are subject to inherent volatility in both the price and the output of the intermediate product transferred within the vertically integrated structure. Our model framework provides necessary and sufficient conditions for the value (NPV) of an integrated system to exceed the sum of two optimized subsystems on their own. We then calibrate the model in Germany and Texas for systems that combine wind energy with Power-to-Gas (PtG) facilities which produce carbon-free hydrogen. Depending on the prices attainable for hydrogen in different market segments, we find that a synergistic investment value emerges in certain settings. In the context of Texas, for instance, neither electricity generation from wind power nor hydrogen production from PtG is profitable on its own in the current market environment. Yet, provided both subsystems are sized optimally in relative terms, the attendant operational gains from vertical integration more than compensate for the stand-alone losses of the two subsystems.