The bold lines graph MM's original tax model discounting debt tax shields at the unlevered cost of equity using riskless debt rates of 0.04 and 0.08, all else the same.

Given that [[rho].sup.[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).

In this process we do not pretend either to describe the many factors that may influence the value of required parameters like [K.sub.u] (unlevered cost of equity), [K.sub.d] (cost of debt), or [K.sub.e] (cost of levered equity).

1) We can estimate the unlevered cost of equity, Ku, as follows, using the CAPM: Ku = Rf + [beta]u x MRP = 8% + 1.4 x 5% = 15.0%

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.sup.TS] is the market value of TS; i is the period of analysis.

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.

This can be accomplished by valuing the firm as if it had no debt, i.e., by discounting the expected free cash flow to the firm at the unlevered cost of equity. In the special case where cash flows grow at a constant rate in perpetuity, the value of the firm is easily computed.

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).