Pricing New-Issue and Seasoned Preferred Stocks: A Comparison of Valuation Models

Ferreira, Eurico J., Spivey, Michael F., Edwards, Charles E., Financial Management

Over $1 billion in preferred stock is traded on the New York Stock Exchange each month -- a volume sufficient to make an investigation of alternative valuation techniques meaningful to both current and prospective investors evaluating opportune trading times. An understanding of alternative valuation models for preferred stocks will also be useful in more general assessments of shareholder wealth, since common stock value equals firm value less the value of its senior securities.

The trading value of nonconvertible preferred securities can be derived by using discounted cash flow methods (perpetuity model) or the option pricing theory (OPT) models presented in the literature. A number of studies ([1], [6], [9], [11], [12] and [17]) have considered these models and the pricing of preferred stocks, but no previous study has compared the merits of alternative models. It is worth investigating whether pricing techniques more complicated than the widely used perpetuity model might provide significantly better estimates of preferred stock prices.

This paper uses three models to estimate the prices of fixed-rate-dividend nonconvertible preferred stocks, looking separately at entirely new issues and at outstanding (seasoned) issues of preferred stock. Model estimates were generated with the security perpetuity pricing model, Merton's OPT-derived pricing model, and a numerically solved OPT-derived pricing model. The parameters necessary to use these models were first approximated using estimation samples of new-issue and seasoned preferred stocks, and subsequently used to price validation samples of preferred stocks.(1) We then compared each model's predicted prices with actual market prices.

Our results suggest that the simple perpetuity model more accurately prices new issues of preferred stocks. The evidence regarding seasoned issues is less conclusive; however, the option models appear more accurate. In general, results of the perpetuity model appear to be less sensitive to violations of key assumptions than is true for the OPT-derived models.

The remainder of this paper is organized as follows: Section I presents the models that are used to estimate the prices of preferred stocks. Section II discusses the data used in the estimation procedure. Section III develops the methodological procedures used to price the securities. Section IV presents the empirical results of the models and compares their ability to price issues of preferred stocks. The final section concludes the paper.

I. Valuation Models

Fixed-dividend preferred stocks traditionally have been valued using the perpetuity model, which assumes an infinite and constant stream of dividend payments. Under these conditions

[P.sub.0] = D/k,(1)

where [P.sub.0] is the preferred stock's value, D is the constant annual dividend, and k is the required rate of return.

Alternatively, Merton [12] has suggested the use of Equation (2) to value preferred stocks, when they are viewed as consol bonds. [Mathematical Expression Omissions] where

d = (C/r)/V,

a = 2r/[[sigma].sup.2], [Mathematical Expression Omitted]

Equation (2) is Merton's original equation which was later modified by Ingersoll [9], where P(a, ad) and P(a+1, ad) are incomplete gamma functions, [Gamma](a) and [Gamma](a+1) are gamma distributions, C is the preferred stock's annual dividend, r is the risk-free rate of interest, V is the firm's value, and [[sigma].sup.2] is the instantaneous variance of the change in V. Equation (2) holds only if several major conditions are met:(2) (i) no dividend payments are made to common stockholders, (ii) the market value of the firm follows an Ito diffusion process with variance ([[sigma].sup.2]) per unit of time proportional to the square of the market value of the firm (V), and (iii) for simplicity, the preferred issue is the only senior obligation of the firm, so that the firm's value (V) equals the sum of the market values of the common and preferred stocks. (Ingersoll [9] later states that the firm's value (V) in Equation (2) may be represented by the sum of the market values of the common and preferred stocks even when the firm's capital structure includes additional senior securities.)

An OPT-generated model, such as Equation (2), requires the use of capital-market parameters related to characteristics of the issuing firm and a risk-free interest rate that are presumably simply and objectively obtained. In many cases, it is desirable to expand the valuation process to incorporate such considerations as common stock dividend payments and call provisions, and their effect on the security's value.(3) A second OPT-derived model incorporating these additional conditions is represented by Equation (3) and the set of conditions indicated below: [Mathematical Expression Omitted] where [[sigma].sup.2] is the instantaneous variance of the change in the firm's value per unit of time, V is the firm's value, r is the risk-free rate of interest, P is the preferred stock's value, and t represents time.(4) In addition, Black-Scholes [2] and Merton [12] have shown that V follows a …

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Publication information: Article title: Pricing New-Issue and Seasoned Preferred Stocks: A Comparison of Valuation Models. Contributors: Ferreira, Eurico J. - Author, Spivey, Michael F. - Author, Edwards, Charles E. - Author. Journal title: Financial Management. Volume: 21. Issue: 2 Publication date: Summer 1992. Page number: 52+. © 2009 Financial Management Association. COPYRIGHT 1992 Gale Group.

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