CVA practice question 17 of 35

If there are five directors to be elected, and 500 shares are outstanding and voting for the election of directors, the minimum number of shares…

Choose your answer, then check it against the explanation.

If there are five directors to be elected, and 500 shares are outstanding and voting for the election of directors, the minimum number of shares necessary to elect one director would be 84 shares. Proof: 84 shares time five directors to be elected equals 420 votes, all cast for one director. Assuming the rest of the stock (416 shares) votes en bloc as the majority, such total of 2,080 votes distributed among five directors would be 416 votes each. Therefore, ndividual representing the minority and receiving its 420votes is sure to get one of the places on the board, the majority getting the other four places. The minority in this example must be sure to vote all of its 420 votes for one director; if it distributed the 420 votes among two, it obviously would not win any places on the board. Cumulative voting, move over, requires a majority of the stock to be able to elect a majority of the board. In the above example, five directors, ______________ shares are necessary, or a majority of the _____________ shares total.

Answer options

Correct Answer:

Explanation

The question asks for the number of shares required to elect a majority of the board of directors under cumulative voting. With five directors, a majority is three. The formula to determine the minimum number of shares required to elect a specific number of directors is:

Shares Required = [ (Total Shares Outstanding × Number of Directors to Elect) / (Total Number of Directors + 1) ] + 1

Applying the numbers from the scenario:

Shares Required = [ (500 × 3) / (5 + 1) ] + 1

Shares Required = [ 1500 / 6 ] + 1

Shares Required = 250 + 1 = 251

Therefore, 251 shares are necessary to elect a majority of the board. This number represents a majority of the 500 total shares outstanding.

Why Incorrect

A. 200 shares are insufficient to elect three directors, and 400 is not the total number of shares in the problem.

B. 150 shares are insufficient to elect three directors, and 300 is not the total number of shares in the problem.

D. 249 shares do not represent a majority of the 500 total shares and would be insufficient to guarantee the election of three directors.

References

1. NACVA, Business Valuations: Fundamentals, Techniques and Theory (FT&T). The concept and formula for cumulative voting are core components of the curriculum, specifically within the sections that discuss control premiums and discounts for lack of control. The formula provided in the explanation is the standard method taught for calculating the shares needed to secure board representation.

2. Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). John Wiley & Sons. In Chapter 14, "Value of Control," Damodaran discusses the mechanisms that minority stockholders can use to exercise influence, including cumulative voting, and presents the underlying formula for calculating the required shares for board representation (p. 338).

3. Lease, R. C., McConnell, J. J., & Mikkelson, W. H. (1983). The market value of control in publicly-traded corporations. Journal of Financial Economics, 11(1-4), 439-471. This foundational academic paper discusses how voting rights, including cumulative voting, affect the value of equity and the concept of control, which is a key topic in the NACVA CVA body of knowledge. https://doi.org/10.1016/0304-405X(83)90019-7

Question 17 of 35

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