We mentioned in class that by excluding things extremely close to or extremely far from the camera, we can avoid numerical issues caused by dividing by a number very close to 0 or very large.

How to determine the values of -znear and -zfar? Does it depend on calculation power?

I would say that long as it doesn't lead to any oddities in the resulting image, I can imagine a lot of values for -znear and -zfar are possible.

Following Sneaky Turtle's comment, if your system uses double precision floating point values, it could be more feasible to have -znear "closer" to the camera (assuming computation isn't a limiting factor though it is definitely another consideration).