Franco Modigliani

Franco Modigliani (June 18, 1918 – September 25, 2003) was an Italian-American economist at the MIT Sloan School of Management and MIT Department of Economics, and winner of the Nobel Memorial Prize in Economics in 1985.

Born in Italy, he left Italy for the US in 1939 because of his Jewish background and antifascist views. In 1944 he obtained his Ph.D. from the New School for Social Research working under Jacob Marschak. In 1946, he became a naturalized citizen of the United States, and in 1948, he joined the University of Illinois at Urbana-Champaign faculty.

When he was a professor at the Graduate School of Industrial Administration of Carnegie Mellon University in the 1950s and early 1960s, Modigliani made two path-breaking contributions to economic science:

• Along with Merton Miller, he formulated the important Modigliani-Miller theorem in corporate finance. This demonstrated that under certain assumptions, the value of a firm is not affected by whether it is financed by equity (selling shares) or debt (borrowing money).

• He was also the originator of the life-cycle hypothesis, which attempts to explain the level of saving in the economy. Modigliani proposed that consumers would aim for a stable level of income throughout their lifetime, for example by saving during their working years and spending during their retirement.

In 1962, he joined the faculty at MIT, achieving distinction as an Institute Professor, where he stayed until his death. Among his students was Nobel laureate Robert Merton, the 1997 winner.

Modigliani also co-authored the textbooks, "Foundations of Financial Markets and Institutions" and "Capital Markets: Institutions and Instruments" with Frank J. Fabozzi of Yale School of Management.

Active until the end, Modigliani enlisted fellow Nobel laureates Paul Samuelson and Robert Solow in 2003 to write a letter published in The New York Times chiding the Anti-Defamation League for honoring Italy's prime minister, Silvio Berlusconi. Berlusconi had recently defended Mussolini's conduct toward Jews during World War II.

Modigliani was a trustee of the Economists for Peace and Security

Modigliani-Miller Theorem

The Modigliani-Miller theorem (of Franco Modigliani, Merton Miller) forms the basis for modern thinking on capital structure. The basic theorem states that, in the absence of taxes, bankruptcy costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. It does not matter if the firm's capital is raised by issuing stock or selling debt. It does not matter what the firm's dividend policy is. Therefore, the Modigliani-Miller theorem is also often called the capital structure irrelevance principle.

Merton Miller's analogy to illustrate the principle uses a pizza: cutting a pizza into more or less pieces does not change the underlying amount of pizza.^{[citation needed]}

Modigliani won the 1985 Nobel Prize in Economics for this and other contributions.

Miller won the 1990 Nobel Prize in Economics, along with Harry Markowitz and William Sharpe, for their "work in the theory of financial economics," with Miller specifically cited for "fundamental contributions to the theory of corporate finance."

Propositions

The theorem was originally proved under the assumption of no taxes. It is made up of two propositions which can also be extended to a situation with taxes.

Consider two firms which are identical except for their financial structures. The first (Firm U) is unlevered: that is, it is financed by equity only. The other (Firm L) is levered: it is financed partly by equity, and partly by debt. The Modigliani-Miller theorem states that the value of the two firms is the same.

Without taxes

Proposition I: $V_{U}=V_{L}\,$ where $V_{U}$ is the value of an unlevered firm = price of buying a firm composed only of equity, and $V_{L}$ is the value of a levered firm = price of buying a firm that is composed of some mix of debt and equity.

To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does. The eventual returns to either of these investments would be the same. Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.

This discussion also clarifies the role of some of the theorem's assumptions. We have implicitly assumed that the investor's cost of borrowing money is the same as that of the firm, which need not be true in the presence of asymmetric information or in the absence of efficient markets.

Proposition II:

File:MM2.png

Proposition II with risky debt. As leverage (D/E) increases, the WACC stays constant.

$y=c_{0}+{\frac {D}{E}}\left({c_{0}-b}\right)$

• $y$ is the required rate of return on equity, or cost of equity.
• $c_{0}$ is the cost of capital for an all equity firm.
• $b$ is the required rate of return on borrowings, or cost of debt.
• ${D}/{E}$ is the debt-to-equity ratio.

This proposition states that the cost of equity is a linear function of the firm's debt to equity ratio. A higher debt-to-equity ratio leads to a higher required return on equity, because of the higher risk involved for equity-holders in a company with debt. The formula is derived from the theory of weighted average cost of capital.

These propositions are true assuming the following assumptions:

• no taxes exist,
• no transaction costs exist, and
• individuals and corporations borrow at the same rates.

These results might seem irrelevant (after all, none of the conditions are met in the real world), but the theorem is still taught and studied because it tells us something very important. That is, if capital structure matters, it is precisely because one or more of the assumptions is violated. It tells us where to look for determinants of optimal capital structure and how those factors might affect optimal capital structure.

With taxes

Proposition I:

$V_{L}=V_{U}+T_{C}D\,$

where

• $V_{L}$ is the value of a levered firm.
• $V_{U}$ is the value of an unlevered firm.
• $T_{C}D$ is the tax rate ($T_{C}$) x the value of debt (D)

This means that there are advantages for firms to be levered, since corporations can deduct interest payments. Therefore leverage lowers tax payments. Dividend payments are non-deductible.

Proposition II:

$y=c_{0}+{\frac {D}{E}}\left({c_{0}-b}\right)(1-T_{C})$

where

• $y$ is the required rate of return on equity, or cost of equity.
• $c_{0}$ is the cost of capital for an all equity firm.
• $b$ is the required rate of return on borrowings, or cost of debt.
• ${D}/{E}$ is the debt-to-equity ratio.
• $T_{c}$ is the tax rate.

The same relationship as earlier described stating that the cost of equity rises with leverage, because the risk to equity rises, still holds. The formula however has implications for the difference with the WACC.

The following assumptions are made in the propositions with taxes:

• corporations are taxed at the rate $T_{C}$ on earnings after interest,
• no transaction cost exist, and
• individuals and corporations borrow at the same rate

Miller and Modigliani published a number of follow-up papers discussing some of these issues.

References

ISBN links support NWE through referral fees

• Brealy and Myers, Principles of Corporate Finance.
• G. Bennett Stewart III, The Quest for Value (HarperCollins, 1991).
• F. Modigliani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review (June 1958).
• M. Miller and F. Modigliani: "Corporate income taxes and the cost of capital: a correction." American Economic Review, 53 (3) (1963), pp. 433-443.
• J. Miles und J. Ezzell: "The weighted average cost of capital, perfect capital markets and project life: a clarification." Journal of Financial and Quantitative Analysis, 15 (1980), S. 719-730.

External links

• Franco Modigliani autobiography
• About Franco Modigliani from nobel-winners.com
• Memorial for Franco Modigliani - MIT Sloan
• his pioneering analyses of saving and of financial markets.
• School performance in the early years was good though not outstanding

• MIT Sloan Lecture Notes, Finance Theory II, Dirk Jenter, 2003

• Corporate Finance: The Modigliani-Miller Theorems

• Ruben D Cohen "An Implication of the Modigliani-Miller Capital Structuring Theorems on the Relation between Equity and Debt"

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