The initial investment (and its associated cost of capital) is quite separate from economic (as opposed to accounting) depreciation: if you could get a valuable asset for free (doesn't matter how) whose market value falls every year thereafter, you have no initial investment and thus no cost of capital. However, you have economic depreciation. On the other hand, if you buy a valuable asset that maintains its value forever, you have a cost of capital, but no economic depreciation. In real life, you have both for most assets.
As an aside: the financing cost of the initial investment is irrelevant. What matters is the opportunity cost: what profit (or return) could you have made by investing the money in a different asset of the same risk instead (which is the cost of capital)?