How many man hours does it take to code an OS?

What makes you think this is unfeasible? Just think of the complexity of a modern OS. In that light, 100 man years is probably too small a number.

100 man years is equal to 100 people, working 1 year (40 hours a week, 52 weeks a year). Relatively speaking, that isn't a lot.

Depends on what you want the OS to do. An embedded OS can be fairly simple and completed in 1 man week. Windows is fairly complex and will take longer. Also depends on what you call an OS. Just the Kernel or all the sundry around it?.

Linus Torvalds didn't start work on Linux until 1991, and he threw together a fairly decent kernel in a couple of months, which has now been developed to its current form, but probably way over 100 man years.

Bill Gates started on Windows in 1984 or 1985, I forget which, so it has a few years on Linux. Again, probably more than 100 man years to get to its current form, but Windows 1.0 was done in less than 1 year. Even if you consider that PCDOS 1 was done in the space of a few months, although that was based on efforts produced a few years earlier.

So, its feasible to make an OS in a short space of time. To make one to compete with Windows, Linux, etc, may take a bit longer.