Historical and future cost: HC are Book cost related to past. Future cost are the estimated cost related to the future.
Specific and composite cost: SC refers to cost of a specific source of capital, while composite cost is combined cost of various sources of capital. It is the WACC, in case of more than one form of source of capital composite cost is resorted to
Explicit cost and implicit cost: EC is the discount rate which equates the PV of cash inflows in other words, it is IRR. Implicit cost is also known as opportunity cost, it is the cost foregone in order to take up a particular project.
Average cost and marginal cost: AC is the combined cost of various sources of capital, MC is the average cost of capital which has to be incurred to obtain additional funds required by the firm.
Conceptual controversies regarding the relationship between the cost of capital and the capital structure: few are of the opinion that a firm can minimise the WACC and increase the value of the firm by debt financing. Others believe that the cost of capital is uneffected by the changes in the capital structure.
Problems with regard to considering the various costs
Problems in computing the cost of equity: it is a difficult task to calculate the expected rate of return on equity.
Problems in computing cost of retained earnings: (Opportunity cost of dividends of shareholders is ignored often)