Except: You aren't factoring in your labor let alone your equipment. Homebrew is some of the most expensive beer in the world.
I know we've argued this in other threads, but on a per beer basis I really do think it's economical. I could go buy 5 gallons of Chimay (approx 25 750ml bottles) at $8 each (plus tax). Or I could brew 5 gallons at +/- $50. I'll take the homebrew, as to me that's a bargain.
You have to do something with your time. You can't bank it up. So rather than the cost of your time this should be opportunity cost. If you have something better to do, go do it. If not, why not spend it brewing. It also takes time to go to the store and buy beer. No one factors that into the cost of bottled beer.
Equipment can be as expensive or cheap as you desire. From an overall hobby perspective, it can make the hobby expensive. On a per beer basis, I don't think equipment cost is applicable. The money is already spent, so it doesn't impact what it costs you to make that next beer. If you insist on including it, you should amortize it over every beer you've ever made which makes the per beer cost approach zero, eventually. Obviously, if you don't yet have the equipment that changes the analysis.
I can agree that I would never recommend that someone get into the hobby to save money on beer. But since I already have everything I need to make beer, the marginal cost of the next beer is pretty low. Which makes it economical for me.