one which maximizes the value of the firm. Consider a perfect capital market (no transaction or bankruptcy costs; perfect information); firms and individuals can borrow at the same interest rate; no taxes; and investment returns are not affected by financial uncertainty. Assuming perfections in the capital is a mirage and unattainable as suggested by Modigliani and Miller. Modigliani and Miller made two findings under these conditions. Their first 'proposition' was that the value of a company is independent of its capital structure. Their second 'proposition' stated that the cost of equity for a leveraged firm is equal to the cost of equity for an unleveraged firm, plus an added premium for financial risk. That is, as leverage increases, risk is shifted between different investor classes, while the total firm risk is constant, and hence no extra value created. Their analysis was extended to include the effect of taxes and risky debt. Under a classical tax system, the tax-deductibility of interest makes debt financing valuable; that is, the cost of capital decreases as the proportion of debt in the capital structure increases. The optimal structure would be to have virtually no equity at all, i.e. a capital structure consisting of 99.99% debt. Variations on the Miller-Modigliani theorem If capital structure is irrelevant in a perfect market, then imperfections which exist in the real world must be the cause of its relevance. The theories below try to address some of these imperfections, by relaxing assumptions made in the Modigliani–Miller theorem. Trade-off theory Trade-off theory of capital structure allows bankruptcy cost to exist as an offset to the benefit of using debt as tax shield. It states that there is an advantage to financing with debt, namely, the tax benefits of debt and that there is a cost of financing with debt the bankruptcy costs and the financial distress costs of debt. This theory also refers to the idea that a company chooses how much equity finance and how much debt finance to use by considering both costs and benefits. The marginal benefit of further increases in debt declines as debt increases, while the marginal cost increases, so that a firm optimizing its overall value will focus on this trade-off when choosing how much debt and equity to use for financing. Empirically, this theory may explain differences in debt-to-equity ratios between industries, but it doesn't explain differences within the same industry. Pecking order