Consider a firm that has dual-class shares with 250 million Class A shares (having 1 vote each)and 75 million nonlisted Class B shares having 8 votes each.The shares are otherwise identical.If one requires 51% of the votes to control the firm,what number of Class B shares must one control?

Question

Quizplus · Accepted Answer

For a total of 325 million shares, the firm requires 162.5 million votes to gain control (51% of 325 million). Each Class A share has only one vote, while each Class B share has eight votes. Let's call the number of Class B shares you need to control "x." Then the number of votes you control is:
250 million + 8x
To gain control, this must be at least 162.5 million, so we can write:
250 million + 8x ≥ 162.5 million
8x ≥ -87.5 million
x ≥ -10.9375 million
But the number of Class B shares you need to control must be a positive number, so we take the ceil function of -10.9375, which is  -10.0 rounded up to -10 + 1. This gives us 11 million shares, which we can convert back to Class B shares by multiplying by 4/3:
11 million shares * (4/3) = 14.67 million Class B shares
We round up to the nearest whole number to get 54.2 million shares. Therefore, controlling at least 54.2 million Class B shares is needed to gain control of the firm.

Consider a Firm That Has Dual-Class Shares with 250 Million