Asking how much it costs to build an 8x12 shed is like asking how long is a piece of string. It depends (in this case, on what materials you choose to use, which will affect aesthetics and longevity).
If you pay full retail for the same materials as that (or any other) premade shed, you are likely to spend more than you'd spend just buying the premade shed or kit straight-out, especially if you also have to buy some tools and especially if you choose to build it better quality than the premade (which frankly I think would only make sense, not that some of the premades are SO badly built but if I'm doing it at all I'd rather do it to *last*). Unless you are in a hurry, I would also recommend that if you're contemplating building a coop yourself you NOT buy everything from Lowe's but rather spend at least a coupla months actively scavenging for materials. You will still have to buy SOME stuff but not nearly as much.
Then, there is another option you have not mentioned -- buying a secondhand shed. You have to find one in good condition i.e. originally good-quality AND still in good shape, but this is often doable and as long as you can find a way of moving it can save you a considerable chunk o' change.
Good luck, have fun,