Its amazing how much hardware you can pack into a single machine for 10k€. Last year our group bought two additional high-memory (768GB) nodes for around that price each (including support for a couple years from the vendor).
A few years before we bought 40 nodes with 128GB RAM each, for a similar price to last years high-memory nodes (and a fast interconnect and a lot of storage).
If you are at a larger research institution, you probably also have an IT department that can co-locate your hardware for next to nothing (compared to cloud). There you also will save a lot of ingress/egress, storage, backup, etc. costs.
Regarding the per student costs, even with cloud instances I would consider running a traditional HPC job system (grid engine, lsf, torque, ...). The MIT had a nice solution with Starcluster [1] to easily deploy a SGE on AWS. It looks a bit dead now though.