# Valuation of Common Stock - Financial Management

In principle, the valuation of common stock is no different from the valuation of other types of securities, such as bonds and preferred stock. The basic procedure involves capitalizing (that is, discounting) the expected stream of cash flows to be received from holding the common stock. This is complicated by several factors, however.

First, the expected cash flows from holding a common stock take two forms: the cash dividend payments made during the holding period and/or changes in the price of the stock (capital gains or losses) over the holding period. All the cash flows received by the common stockholder are derived from the firm’s earnings and can be either paid to shareholders in the current period as cash dividends or reinvested in the firm to (it is hoped) provide higher future dividends and a higher stock price.

Second, because common stock dividends are normally expected to grow rather than remain constant, the relatively simple annuity and perpetuity formulas used in the valuation of bonds and preferred stock are generally not applicable, and more complicated models must be used. Finally, the expected cash flows from common stock are more uncertain than the cash flows from bonds and preferred stock. Common stock dividend payments are related to the firm’s earnings in some manner, and it can be difficult to forecast future long -term earnings and dividend payments with a high degree of accuracy.

To better understand the application of the capitalization of cash flow valuation method to common stock, it is best to begin by considering a one -period dividend valuation model and then move on to consider multiple -period valuation models.

One-Period Dividend Valuation Model

Assume that an investor plans to purchase a common stock and hold it for one period. At the end of that period, the investor expects to receive a cash dividend, D1, and sell the stock for a price, P.What is the value of this stock to the investor today (time 0), given a required rate of return on the investment, ke?

In the capitalization of cash flow valuation method, the discounted present value of the expected cash flows from the stock is calculated as follows:

P0 = D1/(1 + ke)+P1/(1 + ke)

For example, if Ohio Engineering Company common stock is expected to pay a $1.00 dividend and sell for$27.50 at the end of one period, what is the value of this stock to an investor who requires a 14 percent rate of return? The answer is computed as follows:

Thus, the investor who purchases the stock for $25, collects the$1 dividend, and sells the stock for $27.50 at the end of one period will earn the 14 percent required rate of return. Multiple-Period Dividend Valuation Model The dividend valuation process just described can be generalized to a multiple-period case. The expected cash flows to the investor who purchases a share of common stock and holdsit for n periods consist of dividend payments during each of the next n periods (D1, D2, . .. , Dn) plus an amount, Pn, from the sale of the stock at the end of the nth period. Capitalizing these expected cash flows at the investor’s required rate of return, ke, gives the following valuation equation: P0 = D1/(1 + ke)1 + D2/(1 + ke)2 + .... + Dn/(1 + ke)n + Pn/(1 + ke)n Consider again the Ohio Engineering Company common stock. Suppose that the investor is considering purchasing a share of this stock and holding it for five years. Assume that the investor’s required rate of return is still 14 percent. Dividends from the stock are expected to be$1 in the first year, $1 in the second year,$1 in the third year, $1.25 in the fourth year, and$1.25 in the fifth year. The expected selling price of the stock at the end of five years is $41. Using Equation and the appropriate present value interest factors (PVIFs), the value of the stock to the investor is computed as follows: Note that the current value of a share of Ohio Engineering common stock is the same (that is, P0 =$25.00) regardless of whether the investor plans to hold it for one, five, or any other
number of years.

INTERNATIONAL ISSUES
Global Equity Markets

Large multinational corporations have increasingly been turning to international markets to raise both equity and debt capital. Large, non -U.S. -domiciled corporations may sell equity in the United States because of the size and liquidity of the market for new issues in this country. For example, during 1993 Daimler- Benz, the large German conglomerate best known for its Mercedes-Benz automobiles, offered its equity in the U.S. capital market. By selling its stock in multiple country capital markets, Daimler hoped to reach more potential investors and perhaps realize some capital cost savings.

By dealing in global equity markets, multinational firms can take advantage of institutional differences from one country to another that may temporarily disadvantage a firm that is limited to selling its shares in a single capital market. Many multinational firms now have their shares trading in the United States, Japan,and Western European markets, such as London and Paris. The existence of these markets permits nearly 24- hour -per-day trading in the stock of large multinational firms. Around -the -clock trading provides investors with opportunities to buy and sell shares at almost any time they wish.

In addition, multinational firms can increase their name and product recognition abroad, to the benefit, it is hoped, of the firm’s bottom-line performance. As a truly global capital market emerges, it is clear that national borders will be less important in determining where, and in what form, capital will be acquired by a firm. Rather, firms can be expected to sell their shares in those markets with the greatest demand (and hence the lowest cost to the firm).

A General Dividend Valuation Model

In each of the valuation models described, the current value of the stock, P0, is dependent upon the expected price of the stock at the end of the expected holding period. Although this seems straightforward, providing accurate forecasts of stock prices when applying the models to specific stocks can be difficult. A final generalization permits the elimination of Pn from the model while showing that the dividend valuation models discussed are consistent with one another.

First, the value of the stock at the end of the nth period, Pn, must be redefined.Using the capitalization of cash flow approach, it can be shown that Pn is a function of all expected future dividends that the investor will receive in periods n + 1, n + 2, and so on. Discounting the stream of dividends at the required rate of return, ke, gives the value of the stock at the end of the nth period:

Substituting Equation and simplifying yields the following general dividend valuation model:

Thus, the value of a firm’s common stock to the investor is equal to the discounted present value of the expected future dividend stream. As was shown, the valuation of a firm’s common stock given by the multiple -period model (Equation ) is equivalent to the valuation given by the general model. The general dividend valuation model is applicable regardless of whether the stream of dividends over time is fluctuating or constant, increasing or decreasing.

Note that the general dividend valuation model treats the stream of dividends as a perpetuity having no finite termination date.Whereas this assumption is reasonable for firms that are going concerns, shorter time horizons must be used when considering firms that might be either acquired by other firms or liquidated in the foreseeable future. Some rapidly growing firms reinvest all their earnings and do not pay current cash dividends. In fact, some profitable firms have never paid cash dividends for as long as they have been in existence and are not expected to do so in the near future.

How can the general dividend valuation model be applied to the common stock of a firm such as this? It must be assumed that the firm will be able to start making regular, periodic cash dividend payments to its shareholders at some time in the future. Or, these returns could consist of the proceeds from the sale of the firm’s outstanding common stock, should the firm be acquired by another company, or a final liquidating dividend (distribution), should the firm be liquidated.

As stated in Chapter, the primary goal of firms should be the maximization of shareholder wealth. The general dividend valuation model indicates that shareholder wealth, as measured by the value of the firm’s common stock, P0, is a function of the expected stream of future dividend payments and the investor’s required rate of return. Thus, when making financial decisions that are consistent with the goal of maximizing shareholder wealth, management should be concerned with how these decisions affect both the expected future dividend stream and the discount rate that investors apply to the dividend stream. The relationship between financial decision making and shareholder wealth is illustrated in Figure. A primary emphasis of the financial management function is attempting to define and measure this relationship.