A Theoretical Model for Valuing Preferred Stock

This paper develops a model of preferred stock value which includes the possibility of dividends on the preferred stock being omitted. The analytical framework used is based on the option-hedging methodology of Black and Scholes. Precise valuation formulae are obtained for cumulative and noncumulative preferred stock in a variety of contexts. The values obtained are quite different from those for either riskless or risky perpetual bonds, which have previously been proposed as being similar to preferred stock. SINCE 1970, AN AVERAGE of 3 billion dollars worth of capital has been raised annually by corporations in the United States in the form of preferred stock. In spite of this impressive figure, there has been very little theoretical analysis of preferred stock valuation. While previous analysis (e.g., Merton [9] and Ingersoll [7]) has treated preferred stock as a corporate consol bond, this view is not taken here, for an essential feature of preferred stock is that omission of the dividend is permissible and does not precipitate bankruptcy, whereas this would happen if a bond coupon payment were missed. Corporations can and do fail to pay preferred dividends from time to time, particularly in times of severe economic depression. Herein is developed a theory of preferred stock valuation. The return-generating process for the firm is assumed to be a continuous time diffusion and the option hedging arguments of Black and Scholes [2], Cox and Ross [4], and other authors can be used to derive a functional form of preferred stock value in terms of firm value and dividend arrearage. The key to the valuation theory lies in a particular assumption about the conditions under which preferred stock dividends are omitted. This assumption is that all dividends are omitted whenever firm value falls below some critical amount. All the theory is developed subject to this assumption. Section I of this paper discusses whether such an assumption is reasonable. This section carefully examines conditions under which rational management, seeking to maximize common shareholder wealth, would pay dividends as suggested. In Section II, the basic model is described and solved. Some generalization is obtained in Section III, where allowance is made for the possible coexistence of other claims such as bonds. Illustrative solutions to the model are provided