Neodymium is one of the more critical rare earth elements with respect to current availability and is most often used in high performance magnets. In this paper, we compare the virgin production route of these magnets with two hypothetical recycling processes in terms of environmental impact. The first recycling process looks at manual dismantling of computer hard disk drives (HDDs) combined with a novel hydrogen based recycling process. The second process assumes HDDs are shredded. Our life cycle assessment is based both on up to date literature and on our own experimental data. Because the production process of neodymium oxide is generic to all rare earths, we also report the life cycle inventory data for the production of rare earth oxides separately. We conclude that recycling of neodymium, especially via manual dismantling, is preferable to primary production, with some environmental indicators showing an order of magnitude improvement. The choice of recycling technology is also important with respect to resource recovery. While manual disassembly allows in principle for all magnetic material to be recovered, shredding leads to very low recovery rates (<10%).