TLDR: It's not worth it, and it won't work.

"Specialty" coffees (e.g. espresso-based) require a significant investment in equipment and training. Trying to significantly undercut say Starbucks will require a lot of sunk costs up front. In other words, you will not be able to undercut them and turn a sufficient profit until you're established.

Furthermore, people are (generally) OK with paying current costs for specialty drinks. If you started up a coffee shop and sold drinks at half of *$ cost, you wouldn't suddenly have a lineup of customers. Marketing to actually get people in the door will cost a lot, especially when you're up against the behemoth competition.

BUT, let's say for the sake of argument, that you manage it. You have established yourself as a popular destination that makes good drinks for three bucks less than then competition. You've opened up a few franchises, and things are going well.

That's when Starbucks (or whoever) drops their price by $3.50 to squeeze you out. They can afford it. They can afford to give coffee away for probably six months in a major single market, without suffering too much.

Other TLDR: Capitalism is cruel.