Equilibrium in the Pricing of Capital Assets, Risk-Bearing Debt Instruments, and the Question of Optimal Capital Structure

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After integrating risky debt instruments into the generalized asset pricing model developed by Sharpe and Lintner, we have demonstrated that the required return-to-equity capital in this model is a linear function of the debt-to-equity ratio with a slope equal to the difference between the unlevered cost of equity and the direct cost of debt. Consequently, we take the average cost of capital to be invariant with respect to leverage. The particular nature of the debt instrument issued by the firm does not affect this result.

Our analysis supporting the net operating income valuation construct is of interest in that it takes into account not only the variance of the probability distribution of equity returns but also the covariance relationships between these returns and all other returns in the system. Further, we need not rely on assumptions of “equivalent return” classes or arbitrage possibilities to arrive at our solution. More important, our conclusion is quite general in that we demonstrate indifference toward finance with any instrument regardless of its inherent risk characteristics.