Suppose a firm has 15 million shares of common stock outstanding and six candidates are up for election to five seats on the board of directors.

a.
if the firm uses cumulative voting to elect its board, what is the minimum number of votes needed to ensure election of one member to the board?

minimum number of votes

b.
if the firm uses straight voting to elect its board, what is the minimum number of votes needed to ensure election of one member to the board?

Consider the following calculations

Explanation:

a.) Under cumulative voting scenario,

Total number of votes available = Common Shares Outstanding × No of directors

                                            = 15 x 5 million

                                            = 75 million

As there are six candidates for the five board positions, the five candidates with highest number of votes will be elected to the board and the candidate with the least total votes will not be elected.

Minimum votes needed to ensure election =1/6 x 75 million + 1 vote to break any ties

                                                              = 12,500,001 votes

If one candidate receives 12,500,001 votes, the leftover is total 62,499,999 votes.

No matter how these votes are spread over the remaining 5 director candidates, it is impossible for each of the 5 to receive more than 12,500,001. This would require more than 5 × 12,500,001 votes, or more than the remaining 62,499,999 votes.

b.) Now, in case of straight voting,

Vote on board of directors occurs one director at a time.

=> Number of votes eligible for each director = Number of Shares Outstanding = 15,000,000

Minimum number of votes needed to ensure election is through simple majority i.e. = 15,000,000/2 + 1 = 7,500,001 votes

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