It is getting increasingly crucial for policymakers to acquire reliable price forecasts for battery electric vehicles (BEVs) to make choices and set priorities. Here, we examine the prospects for the wide deployment of BEVs, following an ex-post analysis of their learning rate and an ex-ante forecast of their price up to 2040. We make a clear distinction between the mainstream of BEVs and a hypothetical group of BEVs that are technically on a par with internal combustion vehicles (ICVs). To do so, we introduce a new index, in which the driving range and max-speed of a vehicle are coupled together, i.e., the Mobility-Diffusion coefficient. We highlight different shares of battery packs (i.e., 19 +/- 1%), and the ensemble of electrification components (e.g., battery pack, electric motor, power electronics), i.e., electrification cost (52 +/- 2%), in the price of a BEV. Our price projections suggest that there is no prospect of breakeven between BEVs and ICVs before 2040 for both groups of BEVs, because the current learning rates of 9 +/- 2% and 15 +/- 1% for the price and electrification costs, respectively, of BEVs. Strong and long-term support from policymakers is required to ensure competitiveness of BEVs with ICVs in the near future.