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In questions, we are often told each of these figures – for which calculations should we be using each?
E.g. for Theoretical value, we should be calculating free cash flows/After-tax average cost of capital.
The before tax cost of debt is the rate of return required by the investors and is used when we are asked to calculate the market value of debt.
The after tax cost of debt is the cost to the company and is used to calculate the weighted average cost of capital which is used to appraise projects.
The cost of equity is used when we are required to calculate the market value of equity, and is also used in the calculation of the WACC.
All of this is explain in detail, with examples, in my free lectures. The lectures are a complete free course for Paper FM and cover everything needed to be able to pass the exam well.