Equity

Most equity takes the form of common stock. Proportionate ownership of the firm is according to the number of stock shares owned. Preferred stock, a second form of equity is much less important and will be examined later. Common stock generates benefits for owners in three major ways. First, the stock owner is entitled to receive distributions of profits in the form of dividends as declared by the board of directors. Second, the value of each share of stock has the potential to grow as the worth of the firm increases in the market. Third, stockholders have the right to control management through the election of board of director members. Typically each share of stock is entitled to one vote. Selection of board members is then theoretically accomplished in an equitable way with share holders being entitled to vote in proportion to their ownership of the firm.

### Classified common stock

An unusual distinction sometimes found in a firm's common stock is the classification of common shares. This is often done in firms that have strong family ties. Family members may retain one class and the general public the other. A typical classification scheme is to designate one class as "A" and another as "B." By their very names an attempt is made to enhance the perception of one and detract from the perception of the other. Promoters attempting to enhance the appearance of the inferior classification designate it as "A" to take advantage of the general publics' perception of "A" grades being superior to "B" grades. Since many people have learned from their earliest days of school that earning an "A" is better than earning a "B" this often works. In fact the A shares do often have the benefit of some guarantee regarding dividend payments. For example, the firm's charter may specify that B shares will never receive larger dividends that A shares. Nor will B shares receive dividends when A shares receive none. The benefit conveyed to holders of the B shares is substantially enhanced voting power. For example, A shareholders receive one vote per share owned and B shareholders may receive ten votes per share owned. Consequently, when it comes time to select board members, the holders of B shares have, in this illustration, ten times as much power per share owned as do A share owners.

### Shareholder voting techniques

#### Simple majority voting

The simplest form of vote counting is known as simple majority voting. Each shareholder gets to vote his or her shares for each board position. A person or group who controls over half of the votes thus is able to control the firm. In fact control of just over half the votes enables one to entirely control the firm. We will designate this party as S as they have a stronger position. Consider a simple case where 25 shares are outstanding and five directors to be elected. Thus, 25 votes are available for each seat. You could conceivably own nearly half of those shares, 12, and have no representation on the board. Since the holder of 12 shares here has a weaker position, we designate them as W. If one person controls the other 13 shares, he or she simply selects the winning candidate for each and every seat on the board of directors. Repeatedly, the vote for each slot is 13 for their candidate and 12 for your candidate. The holder of 13 shares, S, elects all five directors.

#### Cumulative voting

The calculation that allows a shareholder to determine exactly the number of representatives, R, that can be elected with control of, C, shares of stock follows. Given that there are D directors being elected and O shares outstanding:

(1)
\begin{align} R=\frac{C(D+1)}{O} \end{align}

It is also possible to calculate the needed votes, N, required to elect R representatives to a board.

(2)
\begin{align} N=\frac{RO}{D+1}+1 \end{align}

#### Strategic voting

In reality the distribution of shares controlled by different groups is seldom as clear as described above in the simple majority and cumulative voting illustrations. Votes are typically cast through a proxy system wherein individual shareholders transfer voting rights to another according to their perceptions of how they will be handled.

# Issuing new stock

When a company sells stock to the public for the first time it is known as an initial public offering. Since non-financial organizations seldom have expertise in selling such stock, the services of an investment banker are typically used.

## Preemptive rights

A notion that dates back to old English common law is the idea that managers of a firm should not be able to effectively appropriate some of the firm's ownership and sell it to outsiders. Specifically, a problem emerges when an existing firm needs additional capital in the form of equity. For the firm to sell a substantial block of new shares, a price lower than the existing market price for those shares may be necessary. A simple understanding of supply and demand reveals that if a firm has but 100 shares outstanding and wishes to sell an additional 25 shares, the new offering will be large in comparison to the firm's existing position. For every four outstanding shares, one new one must be sold. If the firm were to simply start selling the new shares, it is possible that the per share price will fall as the growing supply of shares reaches the market. Simple recognition of that eventuality encourages managers to anticipate the lower per share price and incorporate it into the plan from the start. Unfortunately a shareholder who just purchased one of the previously existing shares and paid the previously existing price would find new share purchasers getting identical shares at the new lower price.

A rights offering is the technique designed to sustain fairness in such situations. Each shareholder receives one right for each share owned. The new offering of shares will be sold at a subscription price, S, which is significantly below the existing market price, M, per share. Existing shareholders are entitled to buy new shares at the lower subscription price in proportion to their existing ownership. The way this is accomplished is to first determine how many shares are outstanding for each new share being issued. For example, if 100 shares are outstanding and 25 new shares are to be issued, there are 100 divided by 25 or four outstanding shares for each new share. This number, the quotient of the number of shares outstanding divided by the number of new shares being issued, is designated N. From this information along with the market price per share, the intrinsic value of each right, V, can be estimated. When the stock is selling with rights attached the equation is:

(3)
\begin{align} V=\frac{M-S}{N+1} \end{align}

A simple explanation for the 1 that appears in the denominator is that M includes the value of one right, hence it must be accommodated in the denominator as well as in the numerator. Later, when the rights are distributed to shareholders and they are no longer attached to each share of stock, the stock price will decline by approximately the value of the extracted right. This change is represented by:

(4)
$$M'=M-V$$

Consequently M will decrease by V to an ex-rights price of $M'$ which can also be calculated from the equation:

(5)
\begin{align} V=\frac{M'-S}{N} \end{align}

Note that in this second equation the numerator no longer contains the value of one right, and consequently the denominator is simply N.

# Estimating beta

### Sample equity problems

page revision: 13, last edited: 27 Jan 2010 17:34