The ship is wood and his system required large amounts of copper, including sheeting covering what I understand to be a fairly large part of the hull. I imagine the fitting process was also not inexpensive given that.
A quick browse through Wikipedia suggests that entire Royal Navy had copper by the late 1790s.
This was done anyway as it was the primary way of getting rid of barnicles, shipworm and other attaching seacreatures. I don't see why this is an additional cost.