This section is from the book "Business Finance", by William Henry Lough. Also available from Amazon: Business Finance, A Practical Study of Financial Management in Private Business Concerns.
If a corporation has a million dollars par value of stock outstanding, with a market value of, say, $150 per share, and determines to issue $500,000 more of the same class of stock, with a subscription privilege to the present shareholders of buying the new stock at $125; what, under these conditions, is the value of the "right" to purchase one of the new shares?
At first glance it seems obvious that the answer is $25, but a little reflection makes it clear that this answer does not take into consideration the effect on the market value of all the shares produced by the new issue. If the corporation were to realize $150 from the sale of each of the new shares, and if the new capital were to be invested as profitably as the old capital, the market value of the shares would remain unchanged. But the company realizes only $125, and there must therefore be a general reduction in the market value of shares after the new issue has been brought out. The question, then, as to the value of a "right" requires some mathematical calculations. Perhaps the best method of presenting the solution of our problem, is to quote the following algebraic equations adapted from a statement in the Wall Street Journal:
number of rights needed to get one share
value of stock plus rights
Selling price - x
yx + 100
value of one share to be bought = value ex-rights
yx + 100
market price - x
yx + x
market price - 100
x (y + 1)
market price - 100
market price - 100/y + 1
By applying this formula to the example just cited, we reach the following conclusion:
X = (150-100/2+1) =(50/3)=16.66
The value of this "right" is not therefore $25, as would have been at first supposed, but $16.66. The same result may be reached by the arithmetical method as follows:
At the beginning of the operation there is in existence.
$1,000,000 par value of outstanding stock, which at the market value of $150= .......................
The $500,000 of new stock, being sold at $125, brings into the treasury of the corporation.....
Aggregate value of the $1,500,000 par value of stock outstanding at the conclusion of the transaction = ..............................
Dividing 15,000 (the number of shares with a par value of $100 each) into $2,125,000, we have the value of each share as $141.66. Inasmuch as the "right" entitles the holder to purchase a share for $125, the value of the "right" is the difference between $141.66 and $125, or $16.66.
It should be explained at this point that the term "right" is used on some stock exchanges to indicate the privilege of subscribing to one share of the new issue. On the New York Stock Exchange, however, the term is used as indicating the privilege that is granted to one share of all the stock then outstanding. In the hypothetical case above stated, the "right" to buy one share of a new issue at the special price would be granted to each two shares of the formerly outstanding stock.
Under the customary practice of the New York and many other stock exchanges, the "right" granted to each of the outstanding shares would be the "right" to subscribe to one-half a share of the new issue at the special price. The result of the above calculations should be divided by two, therefore, in order to give the value of the "right" under the New York definition of the word. The value of the "right" as defined in New York would be, then, $8.33.