The rapid growth of electric vehicles is leading to a substantial increase in retired and end-of-life batteries. Reusing these batteries in second-life applications has gained significant attention because it extends battery utilization while reducing investment costs. However, uncertainties in their remaining capacity and degradation rates pose major challenges for the optimal sizing and operation of energy systems, particularly when cycle and calendar degradation are not explicitly considered. This paper presents a mathematical framework for integrating second-life batteries into the optimal sizing of hybrid renewable microgrids. The proposed model simultaneously captures capacity degradation caused by depth of discharge, cycle number and severity, and calendar aging as a function of time and state of charge. By jointly optimizing investment, operation, and maintenance costs, the model determines the optimal capacities of generation and storage resources while satisfying reliability and load demand constraints. A case study demonstrates that, over a one-year planning horizon, second-life batteries reduce the total net system cost from $66 million to $63 million due to their lower upfront cost. However, this economic advantage disappears over longer planning horizons. When degradation is explicitly modeled, the total net cost increases from $66 million (assuming no degradation) to $101 million for new batteries and $132 million for second-life batteries. These findings show that neglecting battery degradation leads to overly optimistic long-term economic assessments and suboptimal microgrid designs. In contrast, the proposed framework provides a more realistic evaluation of second-life battery economics by explicitly accounting for cycle and calendar degradation across different planning horizons.