Abstract

This paper addresses the differences between the Modigliani-Miller [M&M] model (1958, 1963) and the Miles-Ezzell [M&E] model (1980, 1985). The main difference between these two models concerns the stochasticity of the free cash flows. While M&M assumes a strictly stationary process, M&E’s process is a martingale. However, this subtle difference has not been fully exposed, and previous literature has produced partly erroneous statements or inconsistent valuation models. Therefore, the main objective of this paper is to illustrate and accentuate the effect of these two mutually exclusive stochastic processes on the timely behavior of cash flows, discount rates, and values of the firm, equity, debt, and tax shield. For this purpose, we perform a numerical experiment that allows the determination of values and discount rates by means of the risk-neutral approach. We show that in the M&E model, all cash flows and values are path-dependent, while they are not in M&M’s world. Furthermore, in M&E’s model, all discount rates are time-invariant, except for the discount rate applied to tax shields, which depends on the lifetime of the cash flows. Contrarily, in the M&M setup, all discount rates change across time, except for the constant discount rate of the tax shield. This has consequences for the applicability of the well-known present-value formula for annuities and for building consistent valuation models for both finite and perpetual cash flows.

摘要

本文讨论了Modigliani-Miller [M＆M]模型（1958，1963）和Miles-Ezzell [M＆E]模型（1980，1985）之间的差异。这两种模型之间的主要区别在于自由现金流量的随机性。虽然M＆M采取严格固定的流程，但M＆E的流程却是a。但是，这种微妙的差异尚未完全暴露出来，并且以前的文献已经产生了部分错误的陈述或不一致的估值模型。因此，本文的主要目的是说明和强调这两个相互排斥的随机过程对现金流量，折现率和企业价值，股权，债务和税盾的及时行为的影响。以此目的，我们进行了数值实验，可以通过风险中性方法确定价值和折现率。我们证明，在M＆E模型中，所有现金流量和价值都与路径相关，而在M＆M的世界中则不然。此外，在M＆E的模型中，所有折现率都是随时间变化的，除了应用于税盾的折现率取决于现金流的寿命。相反，在M＆M设置中，除税收抵免的恒定折扣率以外，所有折扣率都会随时间变化。这对于众所周知的年金现值公式的适用性以及为有限现金流和永久现金流建立一致的估值模型具有影响。他们不在M＆M的世界中。此外，在M＆E的模型中，所有折现率都是随时间变化的，除了应用于税盾的折现率取决于现金流的寿命。相反，在M＆M设置中，所有折扣率均会随时间变化，除了税盾的恒定折扣率。这对于众所周知的年金现值公式的适用性以及为有限现金流和永久现金流建立一致的估值模型具有影响。他们不在M＆M的世界中。此外，在M＆E的模型中，所有折现率都是随时间变化的，除了应用于税盾的折现率取决于现金流的寿命。相反，在M＆M设置中，所有折扣率均会随时间变化，除了税盾的恒定折扣率。这对于众所周知的年金现值公式的适用性以及为有限现金流和永久现金流建立一致的估值模型具有影响。