## What is the M&M Theorem?

The M&M Theorem, or the Modigliani-Miller Theorem, is one of the most important theorems in corporate finance. The theorem was developed by economists Franco Modigliani and Merton Miller in 1958. The main idea of the M&M theory is that the capital structure of a company does not affect its overall value.

The first version of the M&M theory was full of limitations as it was developed under the assumption of perfectly efficient markets, in which the companies do not pay taxes, while there are no bankruptcy costs or asymmetric information. Subsequently, Miller and Modigliani developed the second version of their theory by including taxes, bankruptcy costs, and asymmetric information.

## Interpreting the Modigliani-Miller Theorem

- The basic theory assumes a perfectly efficient market, without issues of taxes and other financial costs.
- The first proposition of the M&M says that the value of leveraged firms (capital structure with a mix of debt and equity) and unleveraged firms (capital structure with only equity) are the same. If not, there would be an arbitrage opportunity and will eventually become equal.

- Arbitrage is the opportunity to earn profit through market fluctuations with the common practice of buying at a lower price to sell at a higher price immediately.

**V(unlevered) = V(levered)**

(Where V(unlevered) = company with no debt financing and V(levered) = company with some debt financing)

- Investors that purchase shares of a leveraged firm, one with a mix of debt and equity financing, would receive the same profits as when buying shares of an unleveraged firm, which is financed entirely by equity.
- The second proposition states under the theory with no taxes suggests that the cost of equity of a company is proportional to the company’s debt level.

- When debts increase in a company, there are more chances of going default.
- Investors demand a greater return on their investments with the increase in risk.

**re = ra + D/E (ra – rd)**

(Where re = cost of levered equity, ra = cost of unlevered equity, rd = cost of debt, D/E = ratio of debt to equity)