# Why is the Modigliani-Miller theorem logical?

Quoting this SE question, who put it nicely, the M&M theorem basically states that:

...in a no-frictions world, two identical firms have the same enterprise value, regardless of their financial structure.

Given a firm A, whose liabilities are 50% equity, and 50% debt, and a firm B which is financed 100% by equity, the value of firm A and the value of firm B are the same.

But I'm not sure if this is logical in the real world, even under the assumptions of "absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market":

Let's look at the example of a company that's originally controlled by a single person who needs to find a way to finance the company, and let's look at two different options:

1. Going public, keeping 75% to himself, and selling the remaining 25% to the public thus securing the required funds.
2. Going public, keeping 87.5% to himslef and selling the remaining 12.5% to the public, and the "rest" of the money that needs to be raised (the equivalent of 12.5% in the other universe of the first option) will come from debt with some interest rate.

In the first option, it seems to me like the company should have a higher value: both companies are public so they pay fees to their stock exchange and need to take out money on making reports, but in the second option the company also has a debt that it will actually need to return, while in reality the money that came from selling shares (the equity) isn't a debt that needs to be repaid so the money will stay inside the company.

From my understanding stocks get their value (and therefore the motivation for people to buy shares, a.k.a the expectation to earn money) from a few things, and non of them make a difference between the two options:

1. Value - Theoretically the value of each share is derived from the value of the company - the total assets (and potential) minus the debt (and risk). This isn't real money that comes out of the company's pocket.
2. Dividends (or expectation of future dividend) - these are not a factor here since in both cases they are the same amount (it's just that in the 2nd option the original owner takes more money to his pocket since his stakes are higher). Also there is no legal obligation to pay dividends, so the owner doesn't have to ever pay dividends.
3. Share buybacks - The company isn't legally obligated to buy shares back, so again money won't come out of the company's pocket.
4. Share appreciation - the expectation that someone else (simply another player on the market or someone trying to acquire the company) will buy your share gives it value.

All of these, in my opinion, shouldn't change wether I give 25% to the public or 12.5% percent, and the only thing that's different here, is that in the 2nd option the company also has debt, which should decrease the company's value since this is actual money that needs to be paid to someone, and it will come out of the company's pocket.

Therefore, as the different distribution of shares (25% to the public vs 12.5% to the public) doesn't make a difference in the amount of money that the company loses (or earns), all companies shouldn't take debt, unless the money from the IPO isn't enough. (and under the assumption that the owner has more than 50% of the shares to have complete control of the company)

Summarizing in one sentence - the two companies have the same capital and the same potential, but the latter also has a debt it must pay in a few years.

Where is the flaw in my logic?

Remark: I wanted to ask why is this theorem correct, but as this isn't math, I think the word "logical" is better suited. This is just a side note, that sadly got most of the spotlight in the comments, to let people know that I understand that this isn't a mathematical theorem with a proof like in math courses. If this prevents you from understanding my question, imagine I'm using the word "correct".

• Logical just means that the theorem is correct, not that it is realistic. For example, the theorem that triangle angles add up to 180 degrees is logical but not realistic when we deal with earth surface which is not flat
– 1muflon1
Commented Nov 1, 2023 at 10:29
• @1muflon1 I don't mean logical in the mathematical sense, I just wanted people to be aware that I know that this theorem is not a basic truth of the universe, but more of a "theory" that seems to hold, and avoid comments like "This theorem isn't actually 'correct'", but seems like now this brought other pointless comments, ignoring my main question and going to redundant irrelevant areas Commented Nov 1, 2023 at 10:49
• Theorems are never truths about the universe; they are truths about formal systems. But this is a place for economics, not the philosophy of science. Commented Nov 1, 2023 at 12:31
• @MichaelGreinecker Bruh Commented Nov 1, 2023 at 12:38
• (Theorems are basic truths in the universe of the underlying postulates, that can be proved using a finite amount of mathematical logical [in the sense of mathematical logic, not "human logic"] steps. really not the point of this discussion...........................................) Commented Nov 1, 2023 at 12:40