Pre Emptive Rights

The concept of preemptive rights dates back to old English common law. The idea is that a person should not have his property misappropriated by managers of a business he owns. Consequently, when additional shares are sold by a firm at a price below the existing market price, the preemptive right entitles existing shareholders to acquire those lower cost shares in proportion to their firm ownership position. The logic of selling new shares at a price significantly below the existing market price stems from the presumption that the market is clearing given present supply and demand conditions. Microeconomic principles tell us that if a substantial block of stock is introduced to the market, the market price of that stock will likely need to fall to induce an adequate number of buyers to acquire it. Thus, when such lower priced new stock is sold it should equitably be offered to existing shareholders first. The lower price at which new shares may be purchased is known as the subscription price. A rights offering is the technique designed to accomplish this distribution.

The mechanics of a rights offering begins with issuance of certificates known as rights to existing shareholders. Normally, one right is distributed for each share of stock outstanding. The number of shares being issued relative to the number of shares outstanding determines how many rights are needed to acquire one new share. For example, if 100 shares of stock are outstanding and a firm wishes to issue 25 new shares, it already has four shares outstanding for every new share it will issue. This can be found as the number of shares outstanding divided by the number of new shares to be issued, N. In this instance 100/25 = 4. Consequently, each buyer of one new share would need four rights plus the subscription price per share.

Number of rights required to obtain a new share = N. Number of shares outstanding = S. Number of new shares to sell = I.

(1)
\begin{align} N=\frac{S}{I} \end{align}

Given the data listed above, the calculation would be:

(2)
\begin{align} N=\frac{100}{25}=4 \end{align}

The rights' intrinsic value, V, can be determined from the benefits it provides. First, the rights offering entitles people to buy shares of stock below their market price, M, at a subscription price, S. This benefit is M - S. In order to make this purchase the N rights calculated above must be submitted along with the subscription price. Note that the market price M then includes the value of one right. Then, we calculate the value of each right by dividing (M - S)/(N + 1).

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

The remaining information needed to illustrate this relationship is the market price of the stock, lets assume $30 per share and the lower subscription price, lets assume$25 per share.

(4)
\begin{align} V=\frac{30-25}{4+1}=\1 \end{align} Thus, we have found the value of one right, V, to be1. At some point in time the rights must be distributed to shareholders. Later they can be exchanged along with the subscription price for the new shares. Note that after the new shares are issued, they will be identical to existing shares. Up until the time when the rights are distributed a new purchaser of the stock will be entitled to receive the rights when they are issued. However, at some point in time the company must take action. First, it will determine who is entitled to receive rights. At the close of business on a date of record, a copy of all share holders is taken. After the company is able to go through the mechanics of identifying and distributing rights to identified stockholders, those stockholders will receive the rights. People who sell their stock after the date of record will still receive the rights. Similarly, those who buy the stock after that date will receive the stock without receiving the rights. Thus, the stock is said to "go ex-rights" the first day during which new buyers of the stock do not receive un-issued rights. Logically, the price of each share of stock will drop by the value of the one right that was just removed from it on its ex-rights date if all other things remain unchanged. If we can calculate the intrinsic value of that right as V, the market price per share of the stock, M, will decline by V to a lower price M'. The equation for this change would be:

(5)
$$M'=M-V$$

Later after the stock trades ex-rights, the right valuation calculation is modestly different. The market price M no longer exists, it has been replaced by M' the exrights price. The M' in the numerator no longer contains the value of one right. Thus we find:

(6)
\begin{align} V=\frac{M'-S}{N} \end{align}

The value of the stock undoubtedly changes over time. For example, at a later time it may be selling ex-rights for 33 per share. We then calculate the new value of each right as: (7) \begin{align} V=\frac{\33-25}{4}=\\$2. \end{align}

Consider the instance of an investor who owns four shares in this company. He will receive four rights, one for each share owned. He will then be entitled to buy one new share at the subscription price.

Finally, all of these calculations merely identify the intrinsic value of each right and associated relationships. Market prices can be expected to follow these intrinsic prices with some logic.

page revision: 14, last edited: 27 Jan 2009 01:31