Integrating a grid-connected battery into a Renewable Energy Community boosts Collective-Self-Consumption of photovoltaic produced energy and allow to perform Energy Arbitrage in the day-ahead and intraday electricity market. However, is it a cost-effective investment? The proposed analysis relay on Net Present Value assessment. Ageing affects are integrated and sensitivity analyses are conducted: considering community customers number, electricity mar-ket prices, battery cost, size and the decision to engage in energy arbitrage. Each scenario under-goes a 20-year hourly simulation using an ageing aware rolling-horizon 24-hours-looking-ahead scheduling, optimized with Mixed-integer linear Programming. Forecast errors, provid-ing of ancillary services, real time control and grid constrains are not taken into account. Simulations conducted on the Italian market indicates that a battery dedicated solely to collec-tive self-consumption is not economically appealing. However, integrating Energy Arbitrage, despite impact on battery lifespan, halves the payback period and enhances the attractiveness of larger battery investments. The Net Present Value is contingent upon battery size, customer number and market prices. However, if battery cost does not exceed 200 €/kWh the investment become cost-effective across all scenarios.