Engineering systems are typically subject to deterioration processes and shocks that might require multiple recovery actions and emergency operations during their service life. Decision-making in the context of maintenance, repairs, and post-disaster management has been the focus of multiple studies over the last decade. Decisions are typically informed based on the available knowledge about the system, and the cost of tools used to obtain such knowledge (such as Structural Health Monitoring) must be compared against the benefit they bring in terms of risk reduction. Due to the increasing availability of these tools, the interest in quantifying the value of the information they provide (i.e., the VoI) has been growing in the past few years. The quantification of the VoI requires the proper quantification of the uncertainties in the state of the system over time. Due to the multiple ways the system might evolve during the course of its life-cycle, the problem is affected by a curse of dimensionality which makes it computationally intractable when looking at multiple decisions throughout the life-cycle of the system. This paper proposes a novel formulation for the quantification of the benefit of Structural Health Monitoring using Renewal Theory. The long term value of the information is quantified using a new measure, which accounts for the benefits over the entire service life of the system. While different from classical VoI measures available in the literature, the obtained value can be used in a similar way to quantify the benefits of preventively installing Structural Health Monitoring. The proposed Renewal Theory formulation uses numerically solvable integral equations and circumvents the curse of dimensionality that is encountered when applying existing formulations to the entire life-cycle of the system.