# 莫迪尼亚尼-米勒定理

## 无税的MM命题总结

1. 无税
2. 无交易成本
3. 个人和公司的借贷利率相同

• $k_e$ 是权益成本（股权的期望收益率）
• $k_0$ 是完全权益公司的资本成本（在无税条件下，无杠杆公司的$R_0=R_{WACC}$,$R_{WACC}$是公司的加权平均资本成本
• $k_d$ 是负债成本（利率）
• ${D}/{E}$ 是负债权益比

## 税的MM命题总结

$V_L =V_U + T_C D\,$
• $V_L$ is the value of a levered firm.
• $V_U$ is the value of an unlevered firm.
• $T_C D$ is the tax rate ($T_C$) x the value of debt (D)
• the term $T_C D$ assumes debt is perpetual

This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefore leverage lowers tax payments. Dividend payments are non-deductible.

$r_E = r_0 + \frac{D}{E}(r_0 - r_D)(1-T_C)$
• $r_E$ is the required rate of return on equity, or cost of levered equity = unlevered equity + financing premium.
• $r_0$ is the company cost of equity capital with no leverage(unlevered cost of equity, or return on assets with D/E = 0).
• $r_D$ is the required rate of return on borrowings, or cost of debt.
• ${D}/{E}$ is the debt-to-equity ratio.
• $T_c$ is the tax rate.

## 参考文献

1. （美）罗斯（Ross, S. A.）、（美）威斯特菲尔德（Westerfield, R. W.）、（美）杰富（Jaffe, J. F.）. 公司理财（原书第8版）[M]. 吴世农、沈艺峰、王志强，等译. 北京：机械工业出版社，2009年.