This paper assesses the profitability of battery storage systems (BSS) by focusing on the internal rate of return (IRR) as a profitability measure which offers advantages over other frequently used measures, most notably the net present value (NPV). Furthermore, this study proposes a multi-objective optimisation (MOO) approach to IRR estimation instead of relying on the simple linear optimisation and compares the results to the popular linear optimisation with battery cycle-cost penalty. The analysis is conducted under perfect foresight conditions by considering multiple revenue streams: arbitrage trading in the day-ahead and intraday markets, peak shaving, participating in the primary reserves market, and from photovoltaic (PV) power-generation unit. Data are collected for the German power market for 2017 and 2021. The results show that MOO approach yields similar IRR estimates to the cycle-cost model in 2017. However, higher market volatility and increased electricity prices in 2021 resulted in tangible differences. The analysis shows that, if such conditions are coupled with a low battery capacity price, the MOO method significantly outperforms the cycle-cost model. The effects of battery calendar lifetime and state of charge which decrease profitability are also considered. Nevertheless, a noticeable rise in profitability in 2021 relative to 2017 could provide enough compensation to address the issue of relatively poor viability track record.