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Arriving at the individual values of listed Companies with cross holdings

Instances of crossholdings, that is Company A holding shares in Company B and Company B holding shares in Company A are few and have by and large been reduced. There are however exceptions. Such cross holdings pose a challenge in terms of our ability to ascertain the individual values of each of the Company. While, we will deal with a general form or method to ascertain the values, it would be a good idea to take a live example to bring out and showcase the method.

You have a situation of a Company, say, Company X, which has its own operations and business and in addition has shares in other  companies either in  subsidiaries or in  associate Companies  or  other Companies. Where all of the Companies are listed , ascertaining the independent market value (in the current context,by value, we mean the market capitalization)attributable to Company X, does not pose a big challenge.To ascertain the value of Company X, independently, all that one has to do is to ascertain the market value of its holdings (assuming that all are listed) in other Companies, deduct the same from the total market value of Company X to arrive at  the independent market value of Company X.

The exercise becomes a little more complicated when there are cross holdings.As people are aware, market capitalization is nothing but the total no of shares of a Company multiplied by the share price of each or in other words, it is the cost at which all the shares of a Company can be acquired. This is hypothetical, since share price can move up once someone tries to take control of the company, what is commonly known as “acquisition or takeover premium”.For the current exercise we will take that the current share price would stay put at all levels of acquisition.

We have two Companies, Company A, which has 21% holding in Company B .Total market Capitalisation of Company A in the bourses is , say Rs 300 Crs.This , obviously includes or embeds, share of the market capitalisation component of Company B also.

Company B has a holding of 11% in Company A and has a market capitalization of Rs 250 Crs, which, of course, again includes  the share of market capitalization of Company A embedded in Company B.

To ascertain the independent market value of each of the Company, we will have to frame out a simultaneous equation and solve the same.

Let us term the independent market capitalization of Company A, without the effect of its holding in Company B as “Mx’  and let us term the independent market Capitalisation of Company B, without the effect of its holding in Company A as “My”

The two part equation is as follows:

Part I 

Mx   + 0.21 My = 300

Part II

0.11 Mx +My = 250

We can solve this simultaneous equation and arrive at the following:

Multiplying Part I both sides by 100 we get

100 Mx   +21 y    =30,000

Multiplying Part II both sides by 21 we get

2.31 Mx + 21 My  = 5,250

Therefore,  97.69 Mx = 24,750

Mx = Rs 253.3524 Crs

My = Rs 222.1312 Crs

This exercise allows us to ascertain the independent market values of each. It is simple but useful in several cases where the cross holdings are significant. It also helps is evaluating the value of the independent business. Of course, the value is derived from known and available market capitalization numbers.The exercise can help us declutter the embedded values and look at the value of the business as a standalone.




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