Blue Moon Corporation has one million shares of common stock outstanding. In a typical annual election for the board of directors, shareholders representing 70 percent of the shares outstanding exercise their right to vote. The company has nine members on it board of directors, all of whom are elected annually.

a. If the company uses a majority voting procedure to elect its board, now many votes are requied to elect
1. One director
2. Two directors
3. A majority of the members of the board of directors.

b. If the company uses a cummulative voting procedure, how many votes are required to elect
1. One director
2. Two directors
3. A majority of the members of the board of directors.

a. Number of votes cast = 0.7 x 1,000,000 = 700,000

i. 350,000 + 1
ii. 350,000 +1
iii. 350,000 +1
b. i. Number of shares = [(1) x (700,000)] / [(9) + 1] + 1 = 70,001
ii. Number of shares = [(2) x (700,000)] / [(9) + 1] + 1 = 140,001
ii. Number of shares = [(5) x (700,000)] / [(9) + 1] + 1 = 350,001

a. In a majority voting procedure, each director position is voted on separately. In order to be elected, a candidate must receive more votes in favor than against.

1. To elect one director, a simple majority is required. This means that more than 50% of the votes cast must be in favor of the candidate. Since 70% of the shares exercise their right to vote, we need to calculate 70% of one million shares:

(70/100) * 1,000,000 = 700,000 shares

So, 700,000 votes are needed to elect one director.

2. To elect two directors, we apply the same logic as before. We need to calculate the number of votes needed for each director and sum them up.

For the first director:
(70/100) * 1,000,000 = 700,000 votes

For the second director:
(70/100) * (1,000,000 - 700,000) = 210,000 votes

Therefore, to elect two directors, a total of 700,000 + 210,000 = 910,000 votes are needed.

3. To elect a majority of the members of the board of directors, we calculate the number of directors needed to constitute a majority (which is half the total number of directors, rounded up to the nearest whole number):

Majority of directors = (9 / 2) + 1 = 5

To find out how many votes are required to elect this number of directors, we need to sum up the votes needed for each director until we reach the majority:

For the first director:
(70/100) * 1,000,000 = 700,000 votes

For the second director:
(70/100) * (1,000,000 - 700,000) = 210,000 votes

For the third director:
(70/100) * (1,000,000 - 700,000 - 210,000) = 63,000 votes

For the fourth director:
(70/100) * (1,000,000 - 700,000 - 210,000 - 63,000) = 18,900 votes

For the fifth director:
(70/100) * (1,000,000 - 700,000 - 210,000 - 63,000 - 18,900) = 5,670 votes

Therefore, a total of 700,000 + 210,000 + 63,000 + 18,900 + 5,670 = 997,570 votes are needed to elect a majority of the members of the board of directors.

b. In a cumulative voting procedure, shareholders can allocate their votes to one or more candidates, giving them more flexibility in voting. The formula for calculating the number of votes required to elect a director in cumulative voting is:

Votes required = (Shares held) / (Number of directors to be elected + 1)

1. To elect one director, we need to calculate the votes required. Since 70% of the shares exercise their right to vote, we calculate 70% of one million shares:

(70/100) * 1,000,000 = 700,000 shares

Therefore, 700,000 votes are required to elect one director.

2. To elect two directors, we calculate the votes required for each director.

For the first director:
700,000 votes

For the second director:
(70/100) * (1,000,000 - 700,000) / (2 + 1) = 140,000 votes

Hence, a total of 700,000 + 140,000 = 840,000 votes are required to elect two directors.

3. To elect a majority of the members of the board of directors, we repeat the calculation as before.

For the first director:
700,000 votes

For the second director:
(70/100) * (1,000,000 - 700,000) / (2 + 1) = 140,000 votes

For the third director:
(70/100) * (1,000,000 - 700,000 - 140,000) / (3 + 1) = 46,000 votes

For the fourth director:
(70/100) * (1,000,000 - 700,000 - 140,000 - 46,000) / (4 + 1) = 12,000 votes

For the fifth director:
(70/100) * (1,000,000 - 700,000 - 140,000 - 46,000 - 12,000) / (5 + 1) = 3,000 votes

Therefore, a total of 700,000 + 140,000 + 46,000 + 12,000 + 3,000 = 901,000 votes are required to elect a majority of the members of the board of directors in a cumulative voting procedure.