CF 5-4A – Voting for the Board of Directors – Corporate Finance

Let's examine problem five for a kind of a weird question. This is an oddball question. It's just about the mechanics of voting for a board of directors. And I actually learned something here. It's a little bit funny. So I'll show you what I did and why it was wrong and what the right answer is as we go. Evergreen Creations will soon be running an election for four seats, four seats on its board of directors. The company has a hundred thousand shares outstanding. The but she's extremely unpopular. So nobody else is voting for her except you. Assuming you own no stock today, how much will it cost you to get enough stock to buy the seat if the company uses straight voting? Assume no one else is going to vote for Susan Sampson. If the company uses cumulative voting. So there's two different types of voting that this introduces to us. Straight voting is the candidate comes up and people vote yes or no. Should they be on the board of directors? And if that's the type of voted, it's, you know, one at a time you're electing the board of directors on sort of yes, no type of vote. You need more than 50%. Like it needs to pass with more than 50%. So you would need for straight voting, 50% plus one share, more than 50%. So if there's 50% of a hundred thousand shares is 50,000 shares, you need 50,001 to have enough votes to say, okay, well, 49,999 can vote against her. I have enough votes to just win. So you need 50,001 shares at 20 bucks a share. It's a million bucks or something. 50,000, oops, not 50,001. Don't forget that one times 20. Yeah. A million and $20 worth of stock that would buy you the election under a straight voting. So again, straight voting, one candidate at a time. If you have 51% of the shares, you can just dominate. You pick your candidates, pick your slate. You win because you have more than half the votes. Another way of electing a board is to protect minority shareholders. So people without 50% of the vote can get screwed here. Right? Like, and so they say, well, if I have like 25% of the votes, shouldn't I be able to elect 25% of the board, something like this. And so this is what cumulative voting is for, where you get one vote for the entire slate of candidates. And so if there are four seats coming up, you don't need half the votes. Now this is where I got it wrong. And this is an interesting math puzzle. I thought, well, okay, four seats. I want to elect one person, Susan Sampson. So I'm going to need a quarter of the votes. I'll only 25%. This is not correct. The math is you go one over the number of candidates plus one to figure out how much you need. So in this case, one over four plus one, it's a one over five. The correct answer here is 20%. And I was wrong. My intuition said, no, it's got to be 25%. So this is why I think this is an interesting question. Beyond this, it's a weird question, to be honest. But I think this is just intriguing. Why is it that I, there's only four board seats, but to get one, I need 20% and then plus one vote, right? Same as 50% plus one vote. So I need 20% plus one vote. Well, let's contemplate this. So 20% of 100,000 is 20,000. So I would need 20,001 share times $20. That's 400,000 and $20 worth of stock. Okay. That's the answer to the question, right? We've solved the question. We need 20,001 shares. It's going to cost 20 bucks a share. That's what we need to buy up to guarantee Susan Sampson gets her seat under cumulative voting. But why does it work this way? Well, let's sort of divide this up. Let's assume that each candidate wins with their bare minimum, which we've said is right around 20,000. So candidate number one gets 20, there's five candidates vying for four seats. So candidate number one gets 20,000 votes. Candidate number two gets 20,000 votes. Our preferred candidate, well, candidate three gets 20,000 votes. We vote 20,001 votes for Susan Sampson and candidate number four, because it adds up to a hundred, it has to have 19,999. Well, you can see there, if I have 20,001, even if the votes just split perfectly evenly everywhere else, I'm guaranteed a spot with Susan Sampson. Now this person gets 30,000 and this person has like 25. Well, all of a sudden Susan Sampson's for sure going to be at least fourth place with 20,001. The worst you can do is fourth place. And look, we're electing four seats. So my intuition about 25% was just totally wrong. You need this N plus one, Susan Sampson to get on the board needs just one vote more than 20%. There's no way it just guarantees her a seat, even if the voting goes terrible. And again, if you had 20% plus one, you would, well, you would guarantee yourself a seat on this board of directors. So you could buy the seat for $400,000 and $20 to get over the 20,001. So that's the worst case scenario for her is everybody splits the vote at 20, 20, 20. And even still, if everybody's spitting the vote right around 20, her having 20,001 gets her in. Nobody's going to beat her. Okay. Kind of an interesting question. I think the math of it's interesting. We've solved the problem. Thanks for watching. It's a weird problem. Have a great day. Bye-bye.