Bankruptcy, Limited Liability, and the Modigliani-Miller Theorem

This paper examines the validity of the Modigliani-Miller theorem in the presence of bankruptcy. The theorem asserts that the value of a firm and the set of return patterns that the capital markets offer to private investors are independent of firm debt-equity ratios. The usual proof of the theorem is based on the presumption that, in perfect capital markets, borrowing by firms and borrowing by individuals can be perfect substitutes. It is unclear whether this presumption is valid when there is a positive probability that either the firm or the individual who borrows to invest in the firm goes bankrupt. On the one hand, Joseph Stiglitz (1969) and Robert Merton have argued that the Modigliani-Miller theorem remains valid even with bankruptcy if agents who borrow to invest in a firm can limit their liability to the amount of collateral they put up. On the other hand, Vernon Smith (1972) has argued that a margin loan which is secured by a pure equity collateral has a different return pattern from a direct loan to the firm and cannot serve as a substitute for the latter (see also David Baron). ' Smith's argument raises a number of issues. First, it brings out the important fact that return patterns for limited liability borrowing and lending depend on the composition of the portfolio that serves as collateral. If a firm goes bankrupt, a pure equity collateral is worthless, whereas a collateral that contains some bonds may still earn a positive return because the bonds have a privileged claim to the firm's remaining assets. In general, margin contracts with different collateral compositions will generate different return patterns, both for the borrower and the lender. Given this multiplicity of return patterns on margin loans, one would not expect that all margin loans can be used as substitutes for direct loans to the firm. This intuition is confirmed by Smith's demonstration that a particular margin loan, namely the loan on pure equity collateral, cannot serve this purpose. The question remains open whether this is actually needed for the ModiglianiMiller theorem. It might be enough, if some appropriate margin loan could be used as a substitute for lending to the firm. In pursuing this problem, one finds a gap in the standard proof of the ModiglianiMiller theorem. Usually one applies an arbitrage argument to show that, as a firm changes its debt-equity ratio, investors in shares and bonds adjust their portfolios so as to leave their overall return patterns unchanged. No such arguments are given for other securities related to the firm; in particular, for margin investments and for margin loans that serve to finance those margin investments. Without an analysis of *Professor of economics, University of Bonn. Research on this paper was supported by NSF grant SOC 75-13437 at Princeton University and by the Deutsche Forschungsgemeinschaft. I have benefited from the advice of Dwight Jaffee and an anonymous referee. 'In a similar vein, Stiglitz (1972) asserts: "The value of the firm decregses because there is a divergence in the estimation of the chances of bankruptcy between the lender and the borrower" (p. 467). This analysis rests upon a form of market segmentation that is without economic merit: In his model, there are two groups of agents, optimists and pessimists. The optimists invest all their wealth in the firm's equity, valued to make the rate of return equal to that on the riskless asset. The pessimists are indifferent between the risky firm's bonds and the riskless asset. It follows that the optimists, being more optimistic than the pessimists, must prefer the risky bond to the riskless asset, and hence to the equity. Yet, Stiglitz assumes that the optimists invest in the equity and not in the risky bond. Of course, if one group invests all its wealth into one asset, that asset need not satisfy a marginal equality condition at all. A correct analysis of his model leads to the results of this paper.