The widespread adoption of battery energy storage systems (BESS) has been hindered by the uncertainty of their financial value. In past research, this value has been estimated by optimizing the system's actions over the course of the battery's lifetime. However, these estimates did not consider the fact that battery actions decrease the lifetime itself. This paper uses realistic battery cycle degradation to re-evaluate BESS profitability and attempts to increase profits by mitigating this degradation. For this purpose, the paper develops an approximate linear model of degradation suitable for co-optimization with the set of battery actions. It is shown through simulation that 29.1% of the storage system's value is lost because of cycle degradation. However, co-optimization through the approximate model reduces this loss to just 3.3%.