Abstract–Valuation of Corporate Bonds, Leverage, and Security Yields

In recent capital-market equilibrium theories it has been customary to entertain the assumption that corporate bonds are riskless. Attention has therefore been directed to the valuation of shares, since it is trivial to deal with the valuation of bonds under the assumption of riskless bond yield. In order to study the effect of leverage on equity and bond yields at the equilibrium while removing the assumption of riskless bonds, one must first deal with a valuation model for risky bonds. Consequently, one must face the necessity of making explicit the stochastic relationships between the risky bond returns and the risky share returns. To do this, each firm decides a dollar amount to be paid to the bondholders at the end of a period during which it generates random gross yields. The total return to bondholders is a random variable since it is possible that a firm's gross yield may be less than the dollar amount promised, a case of default. The total return to shareholders as a random variable is therefore conditional upon the choice of the promised amount to the bondholders. In other words, the explicit stochastic relationships between the bond returns and share returns will be conditional upon the choice of promised returns to bondholders by all firms. Employing the usual assumptions found in the capital-market equilibrium theories and the negative exponential utility function of final wealth, the model then generates conditional equilibrium prices of bonds and shares, and the resulting conditional equilibrium leverage and expected yields.