Question

several disgruntled stockholders intend to replace as many directors as possible moody company has seven directors and 100,000 shares outstanding

(a) how many shares should the dissident stockholders control to elect at least one director under a majority voting system?

(b) how many shares should the dissident stockholders control to elect one director under a cumulative voting system?

(c) how many directors can the disgruntled stockholders elect if they control 4001 shares?

(d) these dissident stockholders want to elect four board members how many additional shares must they acquire to achieve their objective? (assume that they own 4001 shares at the present time)

Answer 1

(a). Under majority voting system,maximum number of votes a voter can cast for one director =Number of shares held.

Hence , he must hold majority shares to elect a director. He will need (100,000/2)+1 =50,001 shares to be certain to elect at least one director.

Answer: 50,001

(b)Under cumulative voting system , a shareholder can decide to cast all his votes(Number of shares held*Number of directors being elected) to one candidate. Thus, if a shareholder has 1,000 shares , he can cast all his 7,000(1000*7) votes in favor of one director.

N=Number of directors to be elected by dissident shareholders=1

D=Total number of directors to be elected =7

S=Total number of shares=100,000

X=Number of shares necessary =((S*N)/(D+1))+1

X=((100,000*1)/(7+1))+1=(100000/8)+1=12,500+1=12,501 Shares

ANSWER: 12,501 shares

(c).If they control 4001 shares

X=4001

Number of directors that can be elected =N=((X-1)*(D+1))/S=((4001-1)*(7+1))/100,000=(4000*8)/100000=0.32

The dissident stockholders will not be able to elect a single director with control of 4001 shares

(d)To elect 4 directors (N=2)

Number of shares needed X=((S*N)/(D+1))+1=((100000*4)/(7+1))+1=(400000/8)+1=50,000+1=50,001 shares

If they own 4001 shares , additional shares needed =50001-4001=46,000 shares

46,000 shares