How to Calculate the Theoretical Value of Shares Rights

The enlargement of capital of a company that quotes in the market provokes important changes on the quotation. Such as explained before , an enlarging of capital makes the old shares to quote, on one side, and the rights of subscription on the other.

Also, once the period of enlargement ends, during a time the old and new shares quote separately. This always occurs when both types of shares do not have the same rights during the first months after the enlargement. For example, if an enlargement is done in the middle of the year, it is logical that the new shares will receive dividends in proportion with the time they have been on the market. In this case, the new shares will receive half the payment of dividends than the old shares.

To understand the changes that are produced due to an enlargement of capital, it is necessary to analyze the following types of quotations:

  • ex-before quotation (C0): it is the quotation of shares before enlargement
  • theoretical ex-post quotation (C1): also denominated theoretical ex-right quotation, it is the quotation that in theory the old shares have during the enlargement. Logically, this quotation has to be lower than the ex-before quotation, due that from the old share has been stripped the right of subscription that quotes on its own.

To calculate the value of the ex-post  quotation you have to know:

  • number of old shares (N0)
  • quotation of the shares before the enlargement (C0)
  • stock exchange capitalization (V0) that is the value of the company on the market before the enlargement.

Before the enlargement, the stock exchange capitalization is equal to:

V0 (before enlargement) = N0 x  C0

Once begun the enlargement, the stock exchange capitalization (V1) will be, if we denominate the new shares N1 and P the issuing value of these shares:

V1 (after enlargement) = N0 x  C0 + N1 x P

The stock exchange capitalization can be calculated starting from the ex-post quotation (C1):

V1 (after enlargement) = (N0 + N1) x  C1

Equaling the two former equations, you can find the value of the theoretical ex-post quotation:

C1 = N0 x  C0 + N1 x P
N0 + N1

ex-post quotation on the market: it is the real quotation of the old shares after the enlargement and it is a convenience of the supply and demand

theoretical value of the right subscription (d): in theory the right has to have the same quotation of the difference between the ex-before quotation and the theoretical ex-post quotation

d = C0 - C1 = (C0 – P) N1
         N0 + N1

If you include the proportion there is between the old and new  shares (n) the former values will be calculated as follows:

n = N0
 N1
C1 = C0 x n + P
          1 + n

d = C0 - P
          1 + n

If the new share has less rights than the old ones (as for example a less dividend), in the calculation of the value that can be attributed to these minor rights (D):

d = C0 – (P + D)

          1 + n

Note that if these minor rights do exist, the theoretical value of the rights (d) will be lower.

value of the right of subscription on the market: it is the real quotation that the rights have on the market as consequence of the offer and the demand.

Example: let?s suppose that a company makes an enlargement of capital in the following conditions:

  • proportion (n): 5 shares (a new share for each 5 old ones)
  • issuance value (P): 200% in relation with the nominal value that is 500 m.u. per share. So the issuance value will be of 1,000 m.u. per share.

Quotation before the enlargement (C0): 300% or 1,500 m.u. per share

The theoretical value of the share will be:

C1 = C0 x n + P = 1,500 x 5 + 1,000 = 1.416 m.u.
     1 + n        1 + 5

and the theoretical value of the rights will ascend to:

d = C0 – C1= 1,500 - 1.416 = 84 m.u.

If the market value of the old shares and the rights where of 1.470 m.u. and 90 m.u respectively, it would be an indication that the market has overestimated their value more than expected. In this case, an investor that wishes to acquire a new share without owning any old shares would have to pay:

Issuance value 1,000 m.u.
                          5 rights (5 x 90)                     450 m.u.
  Total               1,450 m.u.

Due that the quotation of the old shares are above the 1,450 m.u. for the new shareholder would be more advisable to buy new shares than old ones.

In this case, he should take into account the greater dividends that the shareholders have option to from the old shares with respect to the new ones.