The bold lines graph MM's original tax model discounting debt tax shields at the unlevered cost of equity using riskless debt rates of 0.

pi]] is the unlevered cost of equity after both corporate and personal equity taxes, the levered cost of equity in the revised tax model becomes

Assuming perpetual and constant cash flows and that the appropriate discount rate for the dividend tax shield is the unlevered cost of equity (Ku, per our terminology, see section 2), they calculate the extra value the share holders get because the deductible dividends and a modified expression to evaluate the debt advantage for Brazilian firms.

Fernandez (2004), controversially, argue that the debt tax shield should be calculated as the unlevered cost of equity times debt times the tax rate times (Ku x D x T) and that the appropriate discount rate is K u.

Another school of thought says that the discount rate for tax shields should be the unlevered cost of equity, see for instance, Harris and Pringle (1985), Ruback (2002), Tham and Velez-Pareja (2001, 2004).

This eliminates the possibility of using Kd, the cost of debt and Ku, the unlevered cost of equity.

We depart from a known and widely mentioned formula (3a) derived in Appendix A and that depends on the unlevered cost of equity, the cost of debt and the proper discount rate for the tax shield, both assumed as given after considering all economic factors that may affect them.

Where Ke is the levered cost of equity, Ku is the unlevered cost of equity, Kd is the cost of debt, D is the market value of debt, E is the market value of equity, [psi] is the discount rate for the TS and [V.

Where Ku is the

unlevered cost of equity, [psi] is the risk (discount rate) of the TS, D is market value of debt, E is market value of equity and [V.

The implications of this assumption were examined in Miles and Ezzell (1980), who noted that the approach not only assumed tax savings that would grow in perpetuity but that these tax savings were, in effect, being discounted as the

unlevered cost of equity to arrive at value.

Capital charges for Departments are based on a weighted average of the costs of both debt and equity capital whereas the SOE methodology uses an

unlevered cost of equity.

We derive a general formulation for the equity value (E) at a given period that depends on the value of debt (D) for the same period, and the values at the next period of equity and cash flow to equity (CFE), tax savings (TS) and its corresponding discount rate [psi], the cost of debt (Kd), and the

unlevered cost of equity (Ku).