I describe the famous theorem here.

Before MM, the conventional wisdom was that highly-levered firms (firms that issue a lot of debt relative to equity) offered their investors higher risks and higher expected returns than less-levered firms. MM said that financial structure was essentially irrelevant. [NOTE: “investors” includes both shareholders and bondholders. As Daniel Davies pointed out, I incorrectly used the term “shareholders” in the original article. I hope to run a correction to the article soon. Also, the “conventional wisdom” is probably better described as a view that firms could better appeal to risk-averse investors by using less leverage, and that is the conventional wisdom that MM overturned.]

Let us return to our Food Court economy, in which investment projects consist of developing and testing new recipes. A low-risk project might be an attempt to find a recipe for sesame noodles that tastes good without using peanuts. A high-risk project might be an attempt to grow meat in a lab, which would reduce the need to kill animals for meat.

What MM says is that you cannot turn the sesame noodle project into a high-risk, high-return investment by funding it with debt. Conversely, you cannot turn the cultured meat project into a low-risk, low-return project by funding it with equity. Investors must bear the underlying risk of the project, regardless of how it is financed.

## READER COMMENTS

## Ashish

## Aug 1 2005 at 10:09am

For limited liability corporations, it will be better to issue debt than equity. In first example you cited, if the firm decided to finance the telecom infrastructure project with a $5 billion in equity and $5 billion through debt, then shareholders will lose only $5 billion.

## Arnold Kling

## Aug 1 2005 at 10:35am

Ashish, it is correct that if the firm has 0 net worth to begin with, then limited liability will mean that issuing $5 billion of debt would put a lot of the burden of a failed project on the debtholders.

However, it is wrong to say that therefore it would be “better” for shareholders to issue debt. Bondholders are not stupid. They charge a higher interest rate to compensate for the probability of default. The more levered the firm and the riskier the underlying projects, the higher the interest rate.

## Ian Lewis

## Aug 1 2005 at 1:53pm

I hope I am not being nit-picky, but are you sure that it is a “theorem”? As far as I understood, Theorems only existed in Mathematics and nowhere else. I understand that Modigliani-Miller uses mathematics, but it is an Economical Theory. No? Just curious.

## Patrick Tehan

## Aug 1 2005 at 2:05pm

I don’t think MM said it was essentially irrelevant because they stated it’s only irrelevant in a world based on assumptions we know aren’t true (for instance no taxes). Since we know there are taxes (and tax shields), the fact that firms aren’t financed completely with debt means that financing is relevant with regards to bankruptcy and agency costs.

## dsquared

## Aug 2 2005 at 2:30am

Ian: The MM Theorem is a theorem, proved over a set of axioms. The economic theory is the assertion that the MM Theorem accurately models dividend policy.

## dsquared

## Aug 2 2005 at 2:34am

Btw, Arnold, I think that this is quite a confusing way to present the MM result and the first paragraph quoted above is a mistake. Highly levered firms *do* have higher expected returns and higher risks (to their shareholders) than less levered firms. The MM result is that the risks exactly offset the returns and that firm equity value is invariant to leverage. Investors *can* change the risk-return profile of their investment by choosing a level of leverage – that’s the whole basis of MM – the theorem just proves that they don’t get a free lunch by doing so.

## Arnold Kling

## Aug 2 2005 at 7:50am

D-squared,

You’re right that it would be better to talk about the invariance of firm value relative to how the cash flows are carved up.

## Ian Lewis

## Aug 2 2005 at 9:19am

Hi dsquared,

Can you please explain what it is that makes it a theorem? What I am curious about is if the axioms are Mathematical Axioms or Economic Axioms. Because, then I would understand if it is an Economic Theorem or a Mathematical Theorem.

TIA

## Lauren Landsburg

## Aug 2 2005 at 1:29pm

For a few more explanations of Modigliani-Miller, see these articles in

Concise Encyclopedia of Economics,David R. Henderson, ed.:Biography of Merton Miller

Biography of Franco Modigliani

Article on Corporate Debt by Annette Poulsen

## dsquared

## Aug 3 2005 at 11:00am

Ian; it’s a mathematical theorem; specifically, what you do is prove using the normal mathematical methods, that the solution to a particular optimisation problem is invariant to one of its parameters, under various axioms.

You then make the economic argument that the optimisation problem is usefully analogous to the problem of valuing a firm, the axioms are a reasonable description of how a company generates cash flows and the invariant parameter is analogous to “leverage”. This is how mathematical economics is done and in my opinion the analogies are usually not terribly good.

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