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# What is the Modigliani–Miller Theorem? ## Definition of the Modigliani-Miller Theorem

• The theory suggests that a company’s capital structure and the average cost of capital does not have an impact on its overall value.
• The company’s value is impacted by its operating income or by the present value of the company’s future earnings.
• It doesn’t matter whether the company raises capital by borrowing money, issuing new shares, or by reinvesting profits in daily operations.

## 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)

## The Modigliani-Miller Theorem in Practice

• In the real world, companies are not free from the obligation to pay taxes and other transactional costs.
• Considering this, the Modigliani-Miller Theorem has been revised to accommodate the real-world scenarios better.
• The first proposition under this revised theorem suggests that the value of a levered company is greater than the value of an unlevered company, with the tax-deductible interest expense.

V(levered) = V(unlevered) + (T * D)

(Where V(unlevered) = company with no debt financing, V(levered) = company with some debt financing, T = tax rate, and D = amount of debt)

• The second proposition considers the relationship between the cost of equity and the level of debt, as risks are still involved.
• The formula for WACC used under this proposition states that when the level of debt increases, there is a guaranteed drop in the WACC.
• With this, there is an optimal capital structure when the debt level is 100%.

re = ra + D/E (ra – rd)(1 – T)

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

• Assumptions made here include taxations on earnings after interest, the inexistence of transactional costs, and the same borrowing rate for individuals and firms.