Theorems in Corporate Finance
The investigation of the determinants of corporate capital structure is and has been one of the most active inquiries in finance for decades. . . .
The 1958 Modigliani-Miller Theorem. If the financial markets are competitive then, ceteris paribus, the value of the levered firm equals that of the unlevered firm, i.e., Vl = Vu, where the l and u denote levered and unlevered, respectively.
The 1958 Modigliani-Miller Theorem was initially designed to show that the corporation's capital structure decisions are not value increasing or decreasing; it has, however, become apparent that the theorem is far more general. If the firm is viewed as a nexus of contracts then the question of an optimal composition of contracts arises naturally. Modigliani and Miller limited the contract set to debt and equity and their theorem says that the composition of the contract set is irrelevant. By expanding the contract set it is possible to generalize the theorem. A generalized version of the theorem would say that, ceteris paribus, the composition of the contract set is irrelevant.
As an example of the generalized Modigliani-Miller theorem, suppose financial futures contracts are included in the nexus of contracts. Consider a financial futures contract on a stock index such as the S&P 500. The futures contract is a promise to pay the realized value of the index then, i.e., F, for a specified price of f dollars then. Let f be the number of futures contracts purchased by the corporation; let P be the corporate payoff then. The unhedged corporate payoff may be specified as P while the hedged corporate earnings may be specified as P + f (f - F). The second term is the capital gain or loss on the hedge. Note that both the corporate earnings and the index value are random from an ex ante perspective.
The 1961 Miller-Modigliani
Theorem. If the financial markets are competitive then, ceteris
paribus, the value of the corporation paying dividends equals that of the corporation
paying no dividends, i.e., Vd = Vn, where d and n represent dividend
and no dividend, respectively.
The 1963 Modigliani-Miller Theorem. If the financial markets are competitive and corporations are taxed then, ceteris paribus, the value of the levered firm equals that of the unlevered firm plus the value of the debt tax shield, i.e., Vl = Vu + T, where the l and u denote levered and unlevered, respectively, and T denotes the value of the debt tax shield.
The 1977 Miller Theorem. If the financial markets are competitive and both corporations and investors are taxed then the equilibrium value of the levered firm equals that of the unlevered firm, i.e., Vl = Vu, where the l and u denote levered and unlevered, respectively.
The 1980 DeAngelo-Masulis Theorem. If the financial markets are competitive but corporations cannot costlessly protect tax credits and shields then the equilibrium value of the levered firm equals that of the unlevered firm plus the values of the tax shields and credits; in some market equilibria the levered value plus the shields and credits exceeds the unlevered value, i.e., Vl = Vu + T + C > Vu, where the l and u denote levered and unlevered, respectively, and T and C represent the tax shield and credit values, respectively.
The 1984 Green Theorem. If the corporation can select investment levels in two projects, one of the projects is riskier than the other, in the Rothschild-Stiglitz sense, and corporate outsiders cannot observe the relative scale of the investments then, ceteris paribus, current shareholders bear an agency cost if the firm finances its investments with debt. The corporation can, however, eliminate the agency cost by appropriately structuring a convertible bond issue, i.e., Sc > Sl, where Sc denotes current shareholder value given a convertible bond issue and Sl denotes current shareholder value given a straight bond issue.
The 1984 Myers-Majluf
Theorem. If the firm is endowed with a project that may either be
good or bad and the firm insiders know the project type but firm outsiders do not then, ceteris
paribus, the firm may reject the good project if outside equity must be issued to
finance it. The current shareholders bear an agency cost due to the asymmetric information
if the firm issues equity. If the firm can issue safe debt to finance the good project
then it will not be rejected and the current shareholders will not bear an agency cost.
The 1986 Brander-Lewis Theorem. Suppose the financial markets are competitive but the product market is characterized by Cournot duopoly. Suppose the manager, acting in the interests of current shareholders, selects the financing scheme for the corporation and then selects the scale of production. Then the manager includes enough debt in the financing scheme to make the probability of default positive and the value of the levered firm exceeds that of the unlevered firm, i.e., Vl > Vu.
The Froot, Scharfstein and Stein Theorem: If the firm is endowed with a project that may either be good or bad and the firm insiders know the project type but firm outsiders do not then, ceteris paribus, the inside manager of a firm with a good project has an incentive to hedge to reduce or eliminate the agency cost of any new investment.
Froot et. al. had to assume that outside finance was more costly but MacMinn has shown that the hidden knowledge suffices to generate an agency cost and that the inside manager will maximize the corporate value net of investment expenditure and agency cost in selecting the investment level, i.e., see MacMinn (2005).
Froot, K. A., D. S. Scharfstein, et al. (1993). "Risk Management: Coordinating Corporate Investment and Financing Policies." Journal of Finance 48(5): 1629-1658.
MacMinn, R. D. (2005). The Fisher Model and Financial Markets. Singapore, World Scientific Publishing.
Modigliani, F. and M. H. Miller (1958). “The Cost of
Capital, Corporation Finance and the Theory of Investment.” American
Growth, and the Valuation of Shares.”
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Miller, M. H. and F. Modigliani (1963). “Corporate
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Miller, M. H. (1988). “The Modigliani-Miller
Propositions After Thirty Years.” Journal of Economic Perspectives 2(4):
M. H. (1977). “Debt and Taxes.” Journal of Finance 32(2):
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R. C. (1984). “Investment Incentives, Debt and Warrants.” Journal of
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S. C. and N. S. Majluf (1984). “Corporate Financing and Investment Decisions
When Firms Have Information That Investors Do Not Have.” Journal of
Financial Economics 13: 187-221.
J. and T. Lewis (1986). “Oligopoly and Financial Structure:
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Monday, 31 October 2011 12:17 -0700
Comments to: Richard MacMinn