The book and the Lecture both say that we should use the WACC as the discount rate to be applied in capital budgeting analysis.

But, if we are going to take out a loan to finance the project, why cannot we just simply use the (after tax) cost of the debt (of the loan) to evaluate the project?

Or, if we are using mostly internally generated funds (like Retained Earnings) to finance the project, why would we not just use the Cost of Equity to evaluate the project?

In each of these situations, should we still use the combination of total capital, characterized as the Weighted Average Cost of Capital?