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# Modigliani

[moh-dee-lee-ah-nee, moh-deel-yah-; It. maw-dee-lyah-nee]
Modigliani, Amedeo, 1884-1920, Italian painter, b. Livorno. In Paris after 1906, Modigliani first worked as a sculptor and was influenced by cubism and African art. Soon, however, he developed a unique style in painting, characterized by an elongation of form, a purity of line, a sense of sculptural mass, and a languorous atmosphere reminiscent of Florentine mannerism. Although known to other artists and many Parisian intellectuals, he remained largely unknown to the public during his short life, which was one of poverty, dissipation, and disease. Shortly after his death from tuberculosis, his magnificent portraits and figure studies became highly prized by collectors. Modigliani is particularly well represented in the Art Institute of Chicago and the Museum of Modern Art, New York City.

See biography by W. Fifield (1978); studies by J. Modigliani (1958), J. T. Soby (1963), A. Werner (1967), C. Mann (1985), A. S. Pfannsteil and B. Schuster (1986), A. Kruszynski (1996), D. Autkrystof (2000), K. Wayne (2002), M. Restilinni (2003), and M. Klein et al. (2004).

Modigliani, Franco, 1918-2003, American economist, b. Rome. Jewish, antifascist, and trained as a lawyer, he fled Mussolini's Italy in 1938, settling in the United States in 1939, where he studied economics. After teaching at various universities, he became a professor at the Massachusetts Institute of Technology in 1962 (emeritus in 1988), Modigliani won the 1985 Nobel Memorial Prize in Economic Sciences for his pioneering work in economic theory. He developed a life-cycle theory about the fluctuations in personal savings over an individual's lifetime, which states that people save to spend their money during retirement. He also demonstrated that corporate debt had less affect on how investors value a company than did the company's profitability, and helped devise an economic forecasting model used by the Federal Reserve Bank.

(born June 18, 1918, Rome, Italy—died Sept. 25, 2003, Cambridge, Mass., U.S.) Italian-born U.S. economist. He fled fascist Italy for the U.S. in 1939 and earned a doctorate from the New School for Social Research in 1944. He taught at several universities, including the Massachusetts Institute of Technology (1962–88; thereafter professor emeritus). His work on personal savings prompted him to formulate the life-cycle theory, which asserts that individuals build up savings during their younger working lives for use during their own old age and not as an inheritance for their descendants. In order to analyze financial markets, he invented a technique for calculating the value of a company's expected future earnings that became a basic tool in corporate decision making and finance. He received the Nobel Prize in 1985.

Self-portrait by Amedeo Modigliani, oil on canvas, 1919; in the Museum of Contemporary Art of the elipsis

(born July 12, 1884, Livorno, Italy—died Jan. 24, 1920, Paris, France) Italian painter and sculptor. After studying art in Italy, he settled in Paris (1906), where he exhibited several paintings at the Salon des Indépendants in 1908. Following the advice of Constantin Brancusi, he studied African sculpture and in 1912 exhibited 12 stone heads whose simplified and elongated forms reflect African influence. When he returned to painting, his portraits and nudes—characterized by asymmetry of composition, elongation of the figure, and a simplification of outline—reflected the style of his sculpture. By almost eliminating chiaroscuro, he achieved a sculptural quality by the strength of his contours and the richness of juxtaposed colours. In 1917 he began painting a series of female nudes that, with their warm, glowing colours and sensuous, rounded forms, are among his best works. His work reflects his lifelong admiration for Italian Renaissance masters, as well as the influence of Paul Cézanne and Brancusi. He died at 35 of tuberculosis.

(born June 18, 1918, Rome, Italy—died Sept. 25, 2003, Cambridge, Mass., U.S.) Italian-born U.S. economist. He fled fascist Italy for the U.S. in 1939 and earned a doctorate from the New School for Social Research in 1944. He taught at several universities, including the Massachusetts Institute of Technology (1962–88; thereafter professor emeritus). His work on personal savings prompted him to formulate the life-cycle theory, which asserts that individuals build up savings during their younger working lives for use during their own old age and not as an inheritance for their descendants. In order to analyze financial markets, he invented a technique for calculating the value of a company's expected future earnings that became a basic tool in corporate decision making and finance. He received the Nobel Prize in 1985.

Self-portrait by Amedeo Modigliani, oil on canvas, 1919; in the Museum of Contemporary Art of the elipsis

(born July 12, 1884, Livorno, Italy—died Jan. 24, 1920, Paris, France) Italian painter and sculptor. After studying art in Italy, he settled in Paris (1906), where he exhibited several paintings at the Salon des Indépendants in 1908. Following the advice of Constantin Brancusi, he studied African sculpture and in 1912 exhibited 12 stone heads whose simplified and elongated forms reflect African influence. When he returned to painting, his portraits and nudes—characterized by asymmetry of composition, elongation of the figure, and a simplification of outline—reflected the style of his sculpture. By almost eliminating chiaroscuro, he achieved a sculptural quality by the strength of his contours and the richness of juxtaposed colours. In 1917 he began painting a series of female nudes that, with their warm, glowing colours and sensuous, rounded forms, are among his best works. His work reflects his lifelong admiration for Italian Renaissance masters, as well as the influence of Paul Cézanne and Brancusi. He died at 35 of tuberculosis.

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.

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

Miller was awarded 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."

## Historical background

Miller and Modigliani derived the theorem and wrote their groundbreaking article when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. In contrast to most other business schools, GSIA put an emphasis on an academic approach to business questions. The story goes that Miller and Modigliani were set to teach corporate finance for business students despite the fact that they had no prior experience in corporate finance. When they read the material that existed they found it inconsistent so they sat down together to try to figure it out. The result of this was the article in the American Economic Review and what has later been known as the M&M theorem.

## Propositions

The theorem was originally proven 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:

$k_e =k_0+ frac\left\{D\right\}\left\{E\right\}left\left(\left\{k_0 - k_d \right\} right\right)$

• $k_e$ is the required rate of return on equity, or cost of equity.
• $k_0$ is the cost of capital for an all equity firm.
• $k_d$ is the required rate of return on borrowings, or cost of debt.
• $\left\{D\right\}/\left\{E\right\}$ is the 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, capital structure matters precisely because one or more of these assumptions are 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)
• the term T_C*D assumes debt is perpetual

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:

$r_E = r_0 + frac\left\{D\right\}\left\{E\right\}\left(r_0 - r_D\right)\left(1-T_C\right)$

where

• $r_E$ is the required rate of return on equity, or cost of equity.
• $r_0$ is the cost of capital for an all equity firm.
• $r_D$ is the required rate of return on borrowings, or cost of debt.
• $\left\{D\right\}/\left\{E\right\}$ 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. Their second attempt on capital structure included taxes and identified that as the level of gearing increases by replacing equity with cheap debt the level of the WACC drops and an optimal capital structure does indeed exist at a point where debt is 100%

The following assumptions are made in the propositions with taxes:

• corporations are taxed at the rate $T_C$ on earnings after interest,
• no transaction costs 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.

The theorem was first proposed by F. Modigliani and M. Miller in 1958.

## Economic consequences

The Modigliani-Miller theorem, which justifies near limitless financial leverage, has largely boosted economic and financial activities. But it also brought increased complexity, lack of transparency, higher risk and uncertainty in those activities.

## References

• Brealey, Richard A.; Myers, Stewart C. (2008). Principles of Corporate Finance. 9th edition, Boston: McGraw-Hill/Irwin.
• Stewart, G. Bennett (1991). The Quest for Value: The EVA management guide. New York: HarperBusiness.
• Modigliani, F.; Miller, M. (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment". American Economic Review 48 (3): 261–297.
• Miller, M.; Modigliani, F. (1963). "Corporate income taxes and the cost of capital: a correction". American Economic Review 53 (3): 433–443.
• Miles, J.; Ezzell, J. (1980). "The weighted average cost of capital, perfect capital markets and project life: a clarification". Journal of Financial and Quantitative Analysis 15 719–730.

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