## MM Approach With Tax (1963)
In 1963 MM amended their model to incorporate corporate tax. Once taxes exist, the value of the firm increases (and KO decreases) with leverage, because interest on debt is tax-deductible (the interest tax shield).
### Key result
- Value of Levered firm > Value of Unlevered firm, due to the tax advantage on interest payments.
### Formulas
1. Value of Levered Firm
$$V_L = V_{UL} + (D \times T)$$
where $V_{UL}$ = value of unlevered firm, $D$ = debt, $T$ = tax rate. The term (D × T) is the present value of the tax shield.
2. Cost of equity in a levered company
$$Ke_g = Ke_u + (Ke_u - Kd)\times \frac{Debt}{Debt + Equity}$$
where $Ke_g$ = cost of equity of levered firm, $Ke_u$ = cost of equity of unlevered firm.
3. WACC in a levered company
$$Ko_g = Ke_u\,(1 - tL)$$
where $t$ = tax rate and $L = \dfrac{Debt}{Debt + Equity}$.