Question

Can some explain letter b. Can you show the work for the formula I am confused also how we came up with the 300000 number?

The Rainbow Corporation had traditionally been a constant dollar-dividend paying company, with the board enjoying the support of retired investors holding 65% percent of the voting shares. A dissident group of high-salaried young investors holding 30% percent of the voting shares prefers reinvestment of earnings to save personal taxes and, hence, wants to elect board members supportive of its cause. The company has 600,000 shares of common stock outstanding and the board has 13 members-all to be reelected shortly.

(Please Show Work)

a. How many directors can the young stockholders elect under...

i. cumulative voting rules?

ii. majority voting rules?

b. What percentage (%) of voting shares and/or proxies must the dissident group have to be able to elect 7 out of the 13 board members?

• a.) i.) Under Cumalative Voting rule, we will have:

  Number of directors	14
  Total Shares	600000
  Shares I have	180000
  Members I can Elect = Shares I have/(Total shares)*(Number of seats+1)	4.2

  That, is we can re-elect 4 members.

  ii.) Under Majority rule I can re-elect:

  Number of directors	13
  Total Shares	600000
  Shares I have	180000
  Members I can Elect = Shares I have/Total shares*Number of seats	3.9

  b.)

  Cumilative rule:
  N= Number of shares Outstanding
  D = Number of directors that can be elected
  d= Number of directors we can elect at 1
  X = Number of shares jones needs to elect directors
  X=(NXd)/(D+1)
  7	No. of seats we require
  Shares I have	300000

  We require 50% voting shares in order to generate 7 out of 13 seats in case of cumilative Voting rights.

Answer 1

a.) i.) Under Cumalative Voting rule, we will have:

Number of directors	14
Total Shares	600000
Shares I have	180000
Members I can Elect = Shares I have/(Total shares)*(Number of seats+1)	4.2

That, is we can re-elect 4 members.

ii.) Under Majority rule I can re-elect:

Number of directors	13
Total Shares	600000
Shares I have	180000
Members I can Elect = Shares I have/Total shares*Number of seats	3.9

b.)

Cumilative rule:
N= Number of shares Outstanding
D = Number of directors that can be elected
d= Number of directors we can elect at 1
X = Number of shares jones needs to elect directors
X=(NXd)/(D+1)
7	No. of seats we require
Shares I have	300000

We require 50% voting shares in order to generate 7 out of 13 seats in case of cumilative Voting rights.

Explanation to part b:

The equation is similar to that is done in part a(i)

Under Cumulative rule we saw in part a(i) that Members I can elect= Shares I have / Total Shares * (Number of seats +1)

i. e. d=X/N*(D+1)

The same equation applies here but our requirement is to find X i. e, Shares I have. Thus by rearranging the equation, we get

X=N*d/(D+1)

By solving this,

=600000*7/(13+1)

=42,00,000/14

=3,00,000 shares

percentage (%) of voting shares and/or proxies must the dissident group have to be able to elect 7 out of the 13 board members=

Shares I require / Total shares *100

=300000/600000*100 = 50%

Thus solved.