Modigliani Miller

Overview


The Modigliani Miller theorem asserts that under a set of specified conditions,

  • no taxes
  • no bankruptcy costs
  • symmetric information
  • equal borrowing costs

the value of a firm is independent of capital structure.

Formulation


The assumptions imply that

{% V_E = \mathbb{E}(max(0,V-D)) %}
{% V_D = \mathbb{E}(min(V,D)) %}
where

  • {% D %} is the stated principal of the company's debt
  • {% V_E %} is the value of equity
  • {% V_D %} is the value of debt
  • {% V %} is the value of the firm


Then we have,
{% V_E + V_D = \mathbb{E}(max(0,V-D)) + \mathbb{E}(min(V,D)) = \mathbb{E}(V) %}

Tax Effect


When there are taxes, and in particular, when interest on debt is tax deductable, then the theorem no longer holds. Instead, the tradeoff between debt and equity is no longer one to one. The company can increase the market value of outstanding debt by more than the corresponding value of equity lost by issuing debt.

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