The introduction of local, often uncontrollable, generation units as well as larger loads such as electric vehicles (EVs) causes an increasing amount of stress on our energy supply chain, specifically on the distribution grids. Demand-side management (DSM) is often seen as a potential technology to counter-act this increasing stress on the (distribution) grid. An important and expensive asset within these grids are the power transformers. Thus, economic incentives for DSM can be obtained by decreasing transformer ageing. To study the potential of using DSM to decrease transformer ageing, we consider an ageing model of distribution transformers based on the load profile being supplied by the transformer. We combine this with an optimization problem to find optimal charging profiles of EVs w.r.t. transformer ageing. Furthermore, we compare the results of the optimization problem to three other charging strategies. We conclude that smart charging strategies can give improvements of up to two orders of magnitude in reducing the ageing incurred by EV charging over the base load. Furthermore, we show that for the considered scenarios, a DSM strategy that steers towards the flattening of a neighbourhood's load profile gives similar results to our approach, which directly optimizes transformer lifetime.