Large Shareholder

Note on the relationship between large shareholdings and takeover activities: Sanjay Banerji

If the raider is a large shareholder (L), then the problem of free riding gets mitigated and the takeover premia decreases. Suppose that the large shareholder currently owns a fraction of  

1 shares. The large 2

shareholder is capable of making improvements in the current value of the firm to a new value Z . This value, although currently known to (L) but the ordinary shareholders do not know its exact value. In other words, Z is a random variable which has a cumulative probability distribution of F ( Z ) . We will work below with uniform distribution. The essence of the free-riding problem is this: In order take-over to be profitable, the bidder must receive a surplus ( which is equal to the gains from takeover minus its costs which include among other things, price it pays to the tendering shareholder) . On the other hand, shareholders in equilibrium will tend shares only when they expect to receive the full post takeover value of the firm. In order to gain control, the large shareholder will bid

1   shares with a premium of  2

. Suppose that other costs of bidding are negligible, then a take-over will occur (a) if it is profitable for bidder and (b) dispersed shareholders also tender.

In order takeover to be profitable for the large shareholder, it must be:

1 1 Z  (   )  0 2 2

(1).

The small dispersed shareholders do not know the exact value of Z They must form an estimate (forecast) of Z , given that they know the takeover is profitable , i.e, satisfies the equation (1). That is, by observing a bid premium,  , all they know that new and improved value of the firm, now lies from Z c  (1  2 ) to Z max . Hence, small shareholders will tender if :

  E[ Z Z  (1  2 ) ]  0

(2).

The questions are now: What is the relationship between  and  ? What is the relationship between Z c and  ? To answer this, let us assume that Z is distributed uniformly on (0,1) Then, The equation (2) becomes:

2 1 1 Z Z c 1  (Z c )2 1  Z c   E[ Z Z  Z ]   c Zf ( Z )dZ    Z 2 1  Z c 2(1  Z c ) 2 c

1

Inserting this value in (1), we get:

1 c 1 1 Z c 1  2 Z  ( )  0  Zc  2 2 2 1  2

and  ( ) 

1 1  2

Conclusions:

1.  is a decreasing function of 

2. Z c is a decreasing function of  .

Intuitions: The greater the initial shareholdings, lesser amount of shares needed to acquire control. Hence, firms with smaller productivity gains will find it profitable to acquire a controlling stake. Hence, the expected value of the improvement declines, leading to tendering shares at a lower premium. 3. Suppose that large shareholder spends resources to investigate the possibility of a takeover, it can be shown that amount of resources spent is an increasing function of the iitial shareholdings. Implications: The size and breadth of market for corporate control (hence, the frequency of corporate takeovers) vary positively on the amount of initial share holdings of the bidder. Hence, large (but not large enough) initial shareholdings is expected to make the market for takeover very active. A note on Uniform Distribution:

A random variable Z is said to be uniformly distributed in a  Z  b, if the density function is:

f ( z) 

1 if a  Z  b, and 0 otherwise. ba

The expected value

b

b

a

a

E[ Z ]   Zf ( Z )dZ  

2 b ZdZ 1 Z a (b) 2  (a) 2 b  a    ba 2 ba 2(b  a ) 2