<p>Putting some hypothetical numbers:  pre IPO let’s say the assets are worth 75mm and therefore the founder has equity worth 75mm.  Now in option 1 we sell 25mm of new shares to the public so now we have assets = 75mm+25mm cash =100mm, and on the other side we have equity =100mm.   In option 2 we sell 12.5mm of equity and 12.5mm of debt, so have again assets =100mm, versus now 87.5mm equity and 12.5mm debt.</p>
<p>The MM theorem says that the value of the company is determined by the assets which are generating the income, which is the same in both Options.  However it’s still useful to look at the income statement.  Let’s say the EBIT generated by the assets is 15mm.  Then in Option 1 you simply have 15mm income versus 100mm equity for a 15% ROE.  In Option 2 the income available to the equity holders is 15mm - interest of (at 8% say) 1mm = 14mm, on equity of 87.5mm which is a ROE of 16%.  So you have a higher ROE because the company is more levered and therefore the equity is more risky in Option 2.  The MM theorem argues that the correct discount rate for the equity cashflow in Option 2 results in the equity being worth 87.5mm, so that the increased ROE is exactly offset by the increased discount rate.</p>
<p>You also make the point that the company is somehow worth more in Option 1 because there’s no debt to be repaid. But think about Option 2 after repayment of the debt.  You just have 87.5mm assets (75mm +12.5mm cash) and 87.5mm equity. Ok this company has then issued fewer external shares than option 1 but the founder’s equity is still worth 75mm in both cases.</p>
<p>Hope that provides a clear example.</p>

CC BY-SA 4.0
2023-12-19T11:02:45.937Z
I'm not sure I agree with the first sentence in the 2nd paragraph - the value of the company should be determined by the assets generating the income minus the debt (and maybe other factors), which is not the same in both options, because in option 1 there is effectively no debt. Also, I don't understand the point you make in the last paragraph - how are they worth the same if they have exactly the same stats but one company also had debt and therefore less money (which means less money to use to invest back in the company so it can grow).
snatchysquid
CC BY-SA 4.0
2023-11-11T11:54:06.653Z
2023-11-11T11:54:06.653Z
dm63
<p>Quoting <a href="https://economics.stackexchange.com/questions/6927/why-was-modigliani-miller-so-relevant-and-innovative-when-it-came-out">this</a> SE question, who put it nicely, the M&amp;M theorem basically states that:</p>
<blockquote>
<p>...in a no-frictions world, two identical firms have the same enterprise
value, regardless of their financial structure.</p>
<p>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.</p>
</blockquote>
<p>But I'm not sure if this is logical in the real world, even under the <a href="https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem" rel="nofollow noreferrer">assumptions</a> of &quot;absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market&quot;:</p>
<p>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:</p>
<ol>
<li>Going public, keeping 75% to himself, and selling the remaining 25% to the public thus securing the required funds.</li>
<li>Going public, keeping 87.5% to himslef and selling the remaining 12.5% to the public, and the &quot;rest&quot; 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.</li>
</ol>
<p>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.</p>
<p>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:</p>
<ol>
<li><strong>Value</strong> - 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.</li>
<li><strong>Dividends</strong> (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.</li>
<li><strong>Share buybacks</strong> - The company isn't legally obligated to buy shares back, so again money won't come out of the company's pocket.</li>
<li><strong>Share appreciation</strong> - 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.</li>
</ol>
<p>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.</p>
<p>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)</p>
<p>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.</p>
<p>Where is the flaw in my logic?</p>
<hr />
<p><strong>Remark</strong>: I wanted to ask why is this theorem correct, but as this isn't math, I think the word &quot;logical&quot; is better suited. <em>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 &quot;correct&quot;.</em></p>

CC BY-SA 4.0
2023-11-01T10:29:10.673Z
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
CC BY-SA 4.0
2023-11-01T10:49:03.173Z
@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
snatchysquid
CC BY-SA 4.0
2023-11-01T12:31:55.820Z
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.
Michael Greinecker
CC BY-SA 4.0
2023-11-01T12:38:19.317Z
@MichaelGreinecker Bruh
snatchysquid
CC BY-SA 4.0
2023-11-01T12:40:11.123Z
(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...........................................)
snatchysquid
CC BY-SA 4.0
2023-11-01T12:43:13.290Z
@snatchysquid then you should clarify your question. Even outside formal scientific meaning of logical Marriam-Webster defines logical as: "formally true or valid : analytic, deductive. a logical statement. 2. : capable of reasoning or of using reason in an orderly cogent fashion.". M&M theorem is formally true and valid. M&M theorem is deductive logical theorem. M&M derived their theorem using reason in an orderly cogent fashion. I suggest you edit it to say "is it justified/realistic?" or "how does it held up empirically". I am sorry if it feels like I am nitpicking a single word, but I
1muflon1
CC BY-SA 4.0
2023-11-01T12:43:47.857Z
especially on an international site people will be highly confused by your local slang use of the world 'logical'
1muflon1
CC BY-SA 4.0
2023-11-01T12:43:59.393Z
It's incredible how, while I wrote so much about the topic of M&M Theorem, explained myself in detail, and yet still people really can't let go of a single side comment meant to make sure redundant comments such as those won't come up
snatchysquid
CC BY-SA 4.0
2023-11-01T12:44:28.963Z
My question is well stated, just imagine this little comment at the end isn't written
snatchysquid
CC BY-SA 4.0
2023-11-01T12:46:24.503Z
I am just trying to help you to make your question clear which increases chances it will be upvoted, and answered. If you believe your question is so perfectly posed any improvement is impossible fine, stick with it.
1muflon1
CC BY-SA 4.0
2023-11-03T06:20:04.843Z
Your questions after my original answer made me realize I have to post a much better answer than I did. I will post a better answer or much revised answer if I have time.
H2ONaCl
CC BY-SA 4.0
2023-11-03T06:55:31.530Z
@H2ONaCl Thank you in advance and I appreciate your time and effort :)
snatchysquid
CC BY-SA 4.0
2023-11-03T10:29:52.413Z
Are you missing the basic point that the ‘enterprise value’ of the firm includes both the value of equity and the value of debt ?  It seems you are focused only on the equity.
dm63
CC BY-SA 4.0
2023-11-03T13:23:37.333Z
@dm63 I am aware of both, but I'm saying that the value from debt can be recieved by selling more shares to the public (the original owner will keep less), and so the total amount of money will be the same, but without the downsides of debts, e.g. having to return the money
snatchysquid
CC BY-SA 4.0
2023-11-03T22:39:32.950Z
Right but if you are 100% equity financed the profits need to be shared more widely. If you are 50% equity financed the profits are more concentrated with the shareholders but there is a debt to pay.  It evens out.
dm63
CC BY-SA 4.0
2023-11-04T08:02:05.650Z
@dm63 You always have 100% of shares, it's simply that the original owner will hold more/less. Assuming you give out some Dividend or something, it doesn't matter how much shares the "public" (people besides the original owner) have, you will get X dollars either way.
Also, you say "profits need to be shared..." but they don't even need to be actually shared besides the idea of ownership the shareholders have (they won't get money coming out of the company, if there's no dividend, and if there is then the amount will be constant no matter the percent the public holds as I said)
snatchysquid
CC BY-SA 4.0
2023-11-05T11:29:01.637Z
Can you clarify in your option 1 and 2 whether the proceeds of the public sale are being given to the founder outside the company, or the funds stay inside the company (in the latter case this is a sale of new shares which dilutes the founder while raising money)
dm63
CC BY-SA 4.0
2023-11-10T16:14:53.440Z
@dm63 Stay in the company, as I believe happens in every IPO (there is no real point in giving the money to the founder, besides making him richer)
snatchysquid
<finance><stock-market><corporate-finance><value>
Why is the Modigliani-Miller theorem logical?
snatchysquid
# Why is the Modigliani-Miller theorem logical?

(Asked by: username_0 on 2023-11-01)

Quoting [this](https://economics.stackexchange.com/questions/6927/why-was-modigliani-miller-so-relevant-and-innovative-when-it-came-out) 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](https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theorem) 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".*

**Tags:** finance, stock-market, corporate-finance, value

> **Comments:**
> **username_1**: 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  
> **username_0**: @username_1 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  
> **username_2**: 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.  
> **username_0**: @MichaelGreinecker Bruh  
> **username_0**: (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...........................................)  
> **username_1**: @username_0 then you should clarify your question. Even outside formal scientific meaning of logical Marriam-Webster defines logical as: "formally true or valid : analytic, deductive. a logical statement. 2. : capable of reasoning or of using reason in an orderly cogent fashion.". M&M theorem is formally true and valid. M&M theorem is deductive logical theorem. M&M derived their theorem using reason in an orderly cogent fashion. I suggest you edit it to say "is it justified/realistic?" or "how does it held up empirically". I am sorry if it feels like I am nitpicking a single word, but I  
> **username_1**: especially on an international site people will be highly confused by your local slang use of the world 'logical'  
> **username_0**: It's incredible how, while I wrote so much about the topic of M&M Theorem, explained myself in detail, and yet still people really can't let go of a single side comment meant to make sure redundant comments such as those won't come up  
> **username_0**: My question is well stated, just imagine this little comment at the end isn't written  
> **username_1**: I am just trying to help you to make your question clear which increases chances it will be upvoted, and answered. If you believe your question is so perfectly posed any improvement is impossible fine, stick with it.  
> **username_3**: Your questions after my original answer made me realize I have to post a much better answer than I did. I will post a better answer or much revised answer if I have time.  
> **username_0**: @username_3 Thank you in advance and I appreciate your time and effort :)  
> **username_4**: Are you missing the basic point that the ‘enterprise value’ of the firm includes both the value of equity and the value of debt ?  It seems you are focused only on the equity.  
> **username_0**: @username_4 I am aware of both, but I'm saying that the value from debt can be recieved by selling more shares to the public (the original owner will keep less), and so the total amount of money will be the same, but without the downsides of debts, e.g. having to return the money  
> **username_4**: Right but if you are 100% equity financed the profits need to be shared more widely. If you are 50% equity financed the profits are more concentrated with the shareholders but there is a debt to pay.  It evens out.  
> **username_0**: @username_4 You always have 100% of shares, it's simply that the original owner will hold more/less. Assuming you give out some Dividend or something, it doesn't matter how much shares the "public" (people besides the original owner) have, you will get X dollars either way. Also, you say "profits need to be shared..." but they don't even need to be actually shared besides the idea of ownership the shareholders have (they won't get money coming out of the company, if there's no dividend, and if there is then the amount will be constant no matter the percent the public holds as I said)  
> **username_4**: Can you clarify in your option 1 and 2 whether the proceeds of the public sale are being given to the founder outside the company, or the funds stay inside the company (in the latter case this is a sale of new shares which dilutes the founder while raising money)  
> **username_0**: @username_4 Stay in the company, as I believe happens in every IPO (there is no real point in giving the money to the founder, besides making him richer)  

---

## 1 answers

### Answer by username_4 on 2023-11-11. Score: 0

Putting some hypothetical numbers: pre IPO let’s say the assets are worth 75mm and therefore the founder has equity worth 75mm. Now in option 1 we sell 25mm of new shares to the public so now we have assets = 75mm+25mm cash =100mm, and on the other side we have equity =100mm. In option 2 we sell 12.5mm of equity and 12.5mm of debt, so have again assets =100mm, versus now 87.5mm equity and 12.5mm debt.

The MM theorem says that the value of the company is determined by the assets which are generating the income, which is the same in both Options. However it’s still useful to look at the income statement. Let’s say the EBIT generated by the assets is 15mm. Then in Option 1 you simply have 15mm income versus 100mm equity for a 15% ROE. In Option 2 the income available to the equity holders is 15mm - interest of (at 8% say) 1mm = 14mm, on equity of 87.5mm which is a ROE of 16%. So you have a higher ROE because the company is more levered and therefore the equity is more risky in Option 2. The MM theorem argues that the correct discount rate for the equity cashflow in Option 2 results in the equity being worth 87.5mm, so that the increased ROE is exactly offset by the increased discount rate.

You also make the point that the company is somehow worth more in Option 1 because there’s no debt to be repaid. But think about Option 2 after repayment of the debt. You just have 87.5mm assets (75mm +12.5mm cash) and 87.5mm equity. Ok this company has then issued fewer external shares than option 1 but the founder’s equity is still worth 75mm in both cases.

Hope that provides a clear example.

> **Comments:**
> **username_0**: I'm not sure I agree with the first sentence in the 2nd paragraph - the value of the company should be determined by the assets generating the income minus the debt (and maybe other factors), which is not the same in both options, because in option 1 there is effectively no debt. Also, I don't understand the point you make in the last paragraph - how are they worth the same if they have exactly the same stats but one company also had debt and therefore less money (which means less money to use to invest back in the company so it can grow).  

---

