# What are Modigliani and Miller Proposition I and Proposition II?

A business can have a number of different possible capital structures.  A firm’s capital structure is defined as “mix of a company’s long-term debt, specific short-term debt, common equity and preferred equity.(source)”  In the paper “The Cost of Capital, Corporation Finance and the Theory of Investment”, Franco Modigliani and Merton Miller stated that if you consider two firms which are identical except for their financial structures, with one firm being unlevered and the other being levered, the two firms would have the same value ([pmath size=10]V_u = V_l[/pmath]).  According to the third edition of Corporate Finance: Core Principles & Applications, this means that a firm cannot change the total value of its outstanding securities by changing the proportions of its capital structure, or in other words, no capital structure is any better or worse than any other capital structure for the firm’s stockholders.  This is known as MM Proposition I.  The assumptions that they make, in order to come to their conclusion are that individuals can borrow as cheaply as corporations and that there are no transaction costs.  It also discards the effect of taxes.

If you are like me, you might be asking yourself, at this point, what about the effect of risk?  A levered company, by default is more risky than an unlevered company.  In MM Proposition II, Modigliani and Miller argue that the risk to equity holders increases with leverage.  In MM Proposition II, we are still ignoring taxes.  Remember when we looked at the Weighted Average Cost of Capital, last week?  Well, we are going to use it again.

We defined [pmath size=10]WACC=(E/V)*R_e+(D/V)*R_d*(1-T_c)[/pmath].  This week, we are ignoring [pmath size=10](1-T_c)[/pmath].  In order to determine the cost of equity ([pmath size=10]R_e[/pmath]), we use the formula:

[pmath size=10]R_e = R_0 + (R_0 – R_d)*(D/E)[/pmath]

Where:
[pmath size=10]R_E[/pmath] = Cost of equity
[pmath size=10]R_0[/pmath] = Cost of capital for an all-equity firm
[pmath size=10]R_d[/pmath] = Cost of debt
[pmath size=10]D[/pmath] = Value of the firm’s debt or bonds
[pmath size=10]E[/pmath] = Value of the firm’s stock or equity

According to the third edition of Corporate Finance: Core Principles & Applications, the cost of equity capital [pmath size=10]R_E[/pmath], will be positively related to the firm’s debt-equity ratio and the firm’s WACC will be invariant tot he firm’s debt-equity ratio.

Using the cost of equity number, in a number of simulations can help a company determine the effects of taking on additional debt capital.

As a quick programming note, before I end this post,  I have turned on comments on the blog.  If you would like to be part of a discussion surrounding these posts, feel free.  I would love to hear your thoughts.