Econ 101 provides an extremely limited understanding of economics.
Your assumption is that the company is a closed system -- a fixed pile of money. But in the real world it isn't, it's part of the overall economy. If people are spending more, the overall economy expands, which increases the earnings of our hypothetical business, which leads to them having more than $100.
The benefit of a minimum wage increase is in the way it puts money in the hands of people who will spend it.
on another note, most people assume incorrectly that this bottom portion of earners is a fixed group of people year in year out. Simply not true. look at us bureau census data. Over half of people earning minimum wage are under 24. If you don't have skills for a job, you work for min wage, gain skills and experience so you can get better jobs. When the government makes companies pay more for these teenagers they will hire less. these would-be workers will have more difficulty gaining skills/experience.
So we must never question our reading of "econ 101", because it surely reflects some immutable eternal truths, and everything that contradicts it must therefore be wrong.
/s