Energy storage is a key solution to supply renewable electricity on demand and in particular batteries are becoming attractive for consumers who install PV panels. In order to minimize their electricity bill and keep the grid stable, batteries can combine applications. The daily match between PV supply and the electricity load profile is often considered as a determinant for the attractiveness of residential PV-coupled battery systems, however, the previous literature has so far mainly focused on the annual energy balance. In this paper, we analyze the techno-economic impact of adding a battery system to a new PV system that would otherwise be installed on its own, for different residential electricity load profiles in Geneva (Switzerland) and Austin (U.S.) using lithium-ion batteries performing various consumer applications, namely PV self-consumption, demand load-shifting, avoidance of PV curtailment, and demand peak shaving, individually and jointly. We employ clustering of the household's load profile (with 15-minute resolution) for households with low, medium, and high annual electricity consumption in the two locations using a 1:1:1 sizing ratio. Our results show that with this simple sizing rule-of-thumb, the shape of the load profile has a small impact on the net present value of batteries. Overall, our analysis suggests that the effect of the load profile is small and differs across locations, whereas the combination of applications significantly increases profitability while marginally decreasing the share of self-consumption. Moreover, without the combination of applications, batteries are far from being economically viable.