The Modigliani-Miller Theorem: Definition, Formula & Examples

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  • 0:04 The Modigliani-Miller Theorem
  • 1:22 MM Theory on Capital Structure
  • 6:20 Lesson Summary
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Lesson Transcript
Instructor: Sanghamitra Das

Sanghamitra has a master's in Finance and has a professional working and teaching experience of over a decade.

Most often investors try to understand the capital structure of the firm the best way possible before investing. This can be a big task but the MM Theory simplifies the decision making process based on the capital structure of the firm.

The Modigliani-Miller Theorem

Let's imagine that you have a surplus of money in your bank and you're looking to invest it somewhere for a longer period. One of the investing options of investing for a longer term is investing in a firm's equity. The returns that the firm would generate would depend on the profit of the firm, which is influenced by the firm's external factors, typically beyond the firm's control.

It's important to note that any firm will utilize the money taken from you as an investor and give a portion of ownership to make you an equity holder. The firm will use the funds for business expansion and generate profits from operations. A share of this profit will be given to you and that would be the return you would expect for investing your money with them. In real-world situations, the percentage of returns may vary between firms depending on macro (industry-specific) and micro (firm-specific) factors. One of the most important factors influencing investment decisions is the capital structure of the firm. As an investor you may choose to invest in an equity-only firm or a debt-equity firm. To ease this decision making process, Nobel Laureates Franco Modigliani and Merton Miller created a theory of capital structure widely known as the MM Theory. Let's proceed with an example of two manufacturing firms, Firm A and Firm B, to understand the implication of the MM Theory and how it can help in decision making.

MM Theory on Capital Structure

The MM Theory explains the effects a firm's capital structure may have on the value of the company for investment purposes. The definition states that ''the market value of a company is calculated using its earning power and the risk of its underlying assets and that its value is independent of the way it finances investments or distributes dividends.'' A simple way to arrive at the market value mentioned in the theory is to multiply the firm's number of shares outstanding by the current stock price. The theory indicates that from an investor's point of view the value of a levered firm (with debt) and unlevered firm (without debt) is the same. The MM Theory is based on certain set of assumptions:

  1. No taxes
  2. No transaction costs
  3. Equivalence in borrowing costs for both companies and investors
  4. Symmetry of market information

With the assumptions in place, the MM Theory communicates that the capital structure decision is irrelevant to the value of the company, while the same decision becomes very relevant when taxes are introduced. Within the theory formulated by Miller and Modigliani there are two propositions, which are discussed further in the context of one of the most important assumptions, the taxes.

Let's first take a look at Proposition 1 in the MM Theory. The first proposition is that the market value of any firm is independent of the amount of debt or equity in capital structure. This means: VlA = VlB in a no tax scenario . Here VlA represents market value of Firm A. Let's assume Firm A is the levered firm, or the firm with debt. Vl B represents the market value of Firm B, which is the unlevered firm, or the firm without debt.

In a taxable scenario, Proposition 1 changes to VlA = VlB + (TX*DB). Here TX represents the tax rates and DB represents the value of debt of the firm. In a taxable environment, Firm A has an advantage being a levered firm, since it can deduct the interest payments from its earnings, which further reduces the taxable earnings.

Now let's take a closer look at Proposition 2 in the MM Theory. The second proposition in MM Theory states that the cost of equity is directly related and incremental to the percentage of debt in capital structure. Let's continue with the example of Firm A with debt and equity, and Firm B without debt, only equity, in a no tax scenario. The expected return on equity of Firm A can be calculated based on the following formula: RE Firm A = RE Firm B + D/E *(RE Firm B - RD).

Here, RE denotes the cost of equity, or the expected rate of return on equity. Let's assume that RE for Firm B is 9%. RD denotes the cost of debt, or the expected rate of return on borrowings. Let's assume it to be at 6%

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