Capital Structure Theory Explained - Raghavendra Rau

So today, as you know, I'm, this year's series of lectures is about the big ideas of finance, right? The nice part about finance is probably the simplest of all business school topics. And the reason is we only have six ideas, right? So if you understand these six ideas, you understand everything there is to understand in finance. And as Darran pointed out, five of these ideas have won Nobel prizes. So the only idea which didn't win a Nobel Prize is the first concept, net present value. But that is such a basic concept that nobody had the audacity to claim they came up with the idea, right? So today we're gonna talk about the third idea in finance. The Gresham College lecture that you're listening to right now is giving you knowledge and insight from one of the world's leading academic experts making it takes a lot of time. But because we want to encourage a love of learning, we think it's well worth it. We never make you pay for lectures, although donations are needed. All we ask in return is this. Send a link to this lecture to someone you think would benefit. And if you haven't already, click the follow or subscribe button from wherever you are listening right now. Now, let's get back to the lecture. If you want to follow this stuff in more detail after my lecture, I do note that there is two books I've written in Chinese as well as in English. So you're welcome to take a look at them. This is exactly the same thing as a lecture, but in considerably more detail. Okay? So what are these six basic ideas? The first idea, which we covered in the first lecture was that of what we call net present value, right? The idea is very simple. All it says is, if I want to pay for something, if I want to invest in something, I have to get back more than I invest. That's it, right? Very simple idea. If you, if I get back less than what I invest, it's not worth investing in it. The second idea, which we covered in November, was called portfolio theory and the capital asset pricing Model. That idea comes from the fact that when you calculate the net present value of anything, you need a discount rate. You need an interest rate. Where does that interest rate come from? Well, Markowitz and Sharp got a Nobel Prize for coming up with the concept of the capital asset pricing model. Today you're gonna talk about the third big idea of finance that we call capital Structure theory. And again, two people, Ani and Miller got Nobel Prizes in separate years for exactly the same type of idea. Ani got it for a slightly different topic lifecycle theory, but it's very similar. So I'm combining them for this idea.<affirmative>. The fourth big idea is option pricing, which we'll cover next month, and shows on Merton. Got a Nobel Prize for that one. Asymetic information, Olo, Spence and Stakes got a Nobel Prize for that one. And the final idea, market efficiency, where enormous number of people have Nobel Prizes, except that nobody really knows what that means, right? So the last idea is possibly the most controversial. So I'm gonna save that for the final lecture of this series. So at its core, what is finance all about, right? Essentially, finance is about one thing, and that is basically promises. People are basically, you're saying to you, look, I'm going to give you some fantastically large amount in the future if you give me money today, that's it. That's everything in finance is about that, right? Invest in my company, I'll give you returns, invest in my investment project, whatever it is. I'll give you some extraordinary sum of money back. And of course, the question is going to be, what are these promises worth? So to understand that the first big idea of finance, net present value says, as I said, the present value of all these promises today, you have to compare it to the amount you're investing, right? Because the key is some of these cash flows will be five, 10 years in the future. Gimme money today and I'll give you money in the future. But how do you compare money in the future to money today? You can't compare them because they're apples and oranges. So net present value allows you to bring all those cash flows together to one point in time. Today's value. That's why we call it net present value, right? Basic story in finance, it's used everywhere in finance. And the basic formula is the present value of something is the present value of its cash flows in the future. So you've got somebody promising you a hundred dollars one year from now, you do a hundred dollars divided by one plus a discount rate to the power one one year from now, another thousand dollars two years from now, a thousand divided by one plus r squared two years from now, and so on, right? Okay. Now the problem here, of course, is you needed to have an interest rate, right? So where did that interest rate come from? That's the second big idea of finance. What is the right discount rate? So here the problem is you're turning now to the investor side of the picture. The first idea was the firm choosing to invest in something. We are making an investment decision. The second idea is the people who are faced with providing the financing for that investment decision. For example, somebody comes to you and says, please invest in my company. I'm gonna give you fantastic returns. Of course you can compute the cash flows, but the question is, what discount rate do you use? So here the answer is you want to ask yourself, if I don't invest in this company, what am I gonna do with my money? I'm not just gonna keep it under my bed, I have to invest it in something. And so the, what I'm looking for is what's the opportunity cost of investing in this company? If I don't invest in this company, what opportunity am I giving up? Right? So the discount rate is interest rate on the next best available opportunity. That opportunity should have the same level of risk. And the entire lecture on portfolio theory said, risk is measured by looking at what you are already holding. And basically, Marco and Sharp said, every rational investor should hold only two assets. A risk-free asset, a government bond, and a market portfolio, right? Consisting of every asset in the world. So the risk is measured by how much additional risk do you take on by adding your stock to this market portfolio? And of course, the formula there is the standardized Covance is called the beta, and the CAPM just says the discount rate is equal risk free rate plus the beta times RM minus rf. That's a formula we concluded with last time. Okay? So this is, all these ideas are connected. If one of these ideas fails, every idea fails. So finance is kind of, these six topics all have to hold, otherwise finance falls apart. So you need to know this before we actually go to the next point here. So the third question we are gonna ask is, well, going back now to the firm, so I'm now a firm manager, and as a manager, I'm asking, okay, where should I get the money? Right? I need to invest in this opportunity, but I have all these investors to approach which investor do I ask for to give me money? And the reason is, it's not about which investor in particular. It's which contract I offer them. For example, I can have one choice, I can borrow, I can issue debt, okay? So if I borrow money, basically I'm promising somebody a steady stream of interest, cash flows and maybe the money back at the end, and in return I get their money upfront. Okay? What are the cons of this? Well, the big coin is I have to pay interest every year, right? I can't get away from that. It's a legal obligation. But what's the pro here? The pro is I don't give up control of my company. I still own my company completely. Okay? What about the second choice? The second choice is issue equity, right? Rather than issuing, uh, interest. And you have to, uh, issuing debt and you have to pay the same interest every year. You say, I'll give you a share in my profits. So if I make a lot of money, you make a lot of money, I lose money, you lose money, right? I can't guarantee you anything. So what's the coin here? Well, the coin here is you lose, might lose control of the company, right? So you issue too much equity, you don't control that. Equity people can say, we don't need you as a manager in the company anymore. You get fired even though it is your company. This is what happened, for example, to Steve Jobs in 1990s when, you know, apple kicked came out, he later came back in and also happened to Sam Altman had opened AI last year, even though that wasn't, you know, commercial company in that, in that sense. Anyway, the pro of course is flexible. You don't have to pay dividends every year. Sometimes, you know, if you choose, you can pay dividends. If you don't choose, you need not pay dividends. So that's, these are the major choices. The two big choices you have. You have a whole, whole bunch of different types of subsidiary choices. You can issue particular types of debt. You can say, okay, this is a contingent form of debt. If I do really well, you can convert the debt to equity. That could be like a convertible bond, things like that, right? But in essence, these are the two big choices. Companies have choice number one issue, debt, steady stream of cash flow, but you have to pay those cash flows. You cannot get away from them. Choice two, issue equity, which can fluctuate depending on where they, how much money you're making. But you know, you might lose control of a company, right? So how do you choose what to finance a company with? That's a question we are facing. Now, one way to look at this, let's just say, let's see what companies actually do, right? So what I have here is sort of like an aggregate balance sheet for manufacturing companies in America. And on the left hand side, we see current assets. We see fixed assets. On the right hand side, we see liabilities, both short term and long term and equity. Those are the major parts of a balance sheet. They equate each other. Now, if you look at this and say, Hmm, how much debt and how much equity do firms issue on average, one might say, okay, well you can see that the total amount of debt, both short and long term, is given by this number here and this number here, right? That's a total amount of debt you've issued. This is the total value of the company. So one way of looking at this is to say, debt over total assets is about 60%. Another way of looking at it is to say, well, you know, the current liabilities, they're sort of offset by the current assets. So what are current liabilities? They're short term stuff. So for example, if you're running a restaurant, accounts receivable, accounts payable, accounts receivable, current assets, accounts payable, current liabilities. So you can say, okay, people owe me money, and when they owe me money, when they pay me, I can pay the people I owe. So they sort of cancel each other, account receivable, cancel the account payable and so on. So another way of looking at it is the only thing that matters, you take this out, you take this out, these two cancel each other. The only thing that matters is looking at the long-term liabilities of the company and taking the sum of those two. So what you have here is long-term liabilities divided by long-term liabilities plus equity. Another way of looking at the debt equity ratio, okay? So on average you can say in American companies, 60% total debt, maybe 45 to 50% long-term debt. Okay? But that's not the whole story, right? So if you actually go and in detail and look at what the pattern is by industry, what we find is the numbers are all over the place. So for example, you can have internet information providers, almost no debt at all. We have, um, semiconductors, almost no debt, all the way down to hotels, significant amounts of debt and airlines, 96% of debt. So different industries seem to finance themselves in different ways, okay? So that's one problem. You have to explain the cross-sectional structure of debt within the firm, okay? But the numbers also change over time. So that same number, the aggregate number I showed you, changes every year. What we have here is on the top part, we have the investments within the firm. These investments need to be financed in some way or the other. Most of it comes from internal expenditure, right? So basically you're looking at capital expenditure is much more significant than anything else. So big things the company does obviously uses up a lot more money than the working capital. There's short term small stuff, but where is that financed? Well, if you look at where it is financed, most of it comes from internally generated cash, right? So the company generate profits and they use the profit to plow it back into the company, and they finance the investments that way. Okay? But what about the remaining amount? Well, do they issue debt? Do they issue equity? The answer is it depends on the year. So for example, if you look at this in 1992, what do we see? We see that the companies issued a lot of debt and they bought back shares. Okay? Okay, fine. What about 1993? Well, they bought back debt and they issued shares. What about 1992? Well, they issued both debt and equity. There's no pattern. And every year the numbers change. So what we have is cross-sectionally. The patterns are different in different industries in a time series. The numbers are different over time and gets worse. It changes according across countries as well. Different countries use different levels of debt. These were the problems that Mulani and Miller were faced with when they were trying to come up with one idea. What explains the structure of capital within the company? This is the problem they had. Now, if you went before moving, Glenn Miller came along, you went to a consultant for advice, right? You are a CEO of a company. So you go to your consultant and you say, look, I need to raise money for my internal investment. What should I do? Should I issue debt? Should I issue equity? One group of guys would say, borrow. And you say, why? They say, well, I've done this study. There are 3000 companies in my sample and I've checked every time they issue debt. What happened? The share price went up, the value increase. So this is a good thing to do. Issuing debt, the market seems to like it. Fine, you say, but you want a second opinion. So you go to a different consultant. The second consultant says, no, no, no, that's not a good idea. Issue equity. Why? Because I've looked at a different batch of 3000 companies and whenever they issue debt, the value went down. So you have different consultants all coming up with different pieces of advice. Nobody could tell what's the right thing to do, right? So the issuing equity, people say, well, you know, if you borrow, you could go bankrupt, you could lose everything. Don't borrow too much. But how much is too much? 20%, 40%, 80%, nobody knew. So this is where Molar Miller came in. Now, how do you think they approach that problem? Right? One would imagine they would go and talk to a whole bunch of companies and ask them how they issue debt and equity, right? Yeah, I see a bunch of nodding heads. Nope. They didn't do that. What they did was to lock themselves into their office and think, so this is entirely a thought experiment. There was nothing there, which actually involved talking to a manager. They didn't do that, right? They said in principle, how can we come up with this from first principles? So what was their major insight, which got the, the Nobel Prize? Well, what they said was very simple. When you issue debt or equity, the companies don't just keep the money, right? It's not like, you know, remember the Uncle Scrooge comics where Uncle Scrooge takes a whole bunch of money, uh, you know, coins and puts it in a swimming pool and tries to swim in the money. They don't do that, right? They actually invest the money. They do something with the money. So a company issues, debt does something with the money and the value goes up. Why? One reason. The debt itself is valuable. Second reason, the stuff they invested in that was valuable. The debt was bad, but they invested in something which was so good, it counteracted the negative impact on the debt. So the problem is by actually investing, you are using up, you're creating or destroying value by investing in a positive or a negative NPV project, okay? That's the issue they had. So, but the NPV of the project is the investment side. It has nothing to do with the financing side. The financing side is about the choice between debt and equity. The investment side is NPV, which you already talked about. So Morgan Miller said, what we need to do is not look at a typical company situation. What we need to do is study what are called leverage recaps. So what is a leverage recapitalization? The answer is very simple. Let's take a typical company. So you have assets and a mixture of debt and equity financing the assets, right? So that's the, it's a balance sheet. So the assets are equal to the liabilities, fine. Now the company starts to do a recap. What it is does is it issues debt, but what does it do with the money? It doesn't invest in anything. What it does is takes the money and buy shares back. That means it adjusts the equity side of the balance sheet, right? It never goes to the left hand side. It never touches the assets. So if it issues debt, it buys back shares. If it issues shares, it buys back debt. So essentially what's happening is that it is changing the right hand side of the balance sheet without touching the left hand side. So now if this happens and the value goes down, why is it going down? It can only be because of the debt. It can't be because the company's investing, because the company is not investing, right? We have fixed that part. So everything that's happening is done on the right hand side. So one possibility could be you issue debt and the value goes down. The other possibility could be you issue debt and the value goes up. But all of this will be due entirely to that mixture of debt and equity, which you have within the firm, right? So that's what they did. That was the entire insight they had. They said, let's look at a world where all the firm is doing issues. Debt buys, back, shares, issue shares, buys back debt. I'm not going to invest. I'm not touching that side. There's no NPV involved. If there's a change in value, it must be because of capital structure. Okay? So we need a little bit of notation here. I'll explain that notation too. The notation is gonna be a little complex. So I'll show you what the notation means in a pictorial format in a bit. So at the moment, I'm gonna call a firm, which has no debt at all. We start with a completely unlevered firm. The firm has no debt. That's why it's called unlevered. Okay? So the value of that firm must be equal to the value of equity because it has no debt, it's unlevered. So the assets must be equal to equity. That's it. Balance sheet. Second thing, we have a levered firm, which is identical in the asset side to the unlevered firm. What does that mean? It means they have similar growth opportunities, they have similar investment projects. They, the CEOs are clones of each other, right? Identical among all lines, except firm two is partly financial debt and partly financial with equity. Alright? Third thing, the company can choose to borrow, and if it borrows, it pays a cost of rd, cost of debt on it. Borrowing rate, right? Fourth thing is the cost of equity, and that's derived by the capital asset pricing model, which we did last time. The cost of equity is how much do shareholders want if you choose to invest in that company. Finally, we have the cost of assets of the firm, which is the same as the cost of equity for a firm which has zero debt, because the assets for that firm is equal to the equity in that firm. I'll show you this a little bit. The weighted average cost of capital is our final number, and that's a weighted average of every form of financing the firm has. For example, it's paying RD on his debt, but this is the level of debt within the firm. So that's the weight which you put on the debt, and similarly, the weight you put on the equity, that's an overall weighted average cost of capital on the firm. Now, let's ex, let's explain this a little better. So what we have here is straightforward. You have an unlevered firm firm with no debt at all. Okay? So the assets are generating returns, right? I mean, they are assets. So you're investing in them, they're generating returns. So those returns are called ra, the cost, the return on the assets of the firm. But because the firm has no debt, it's the same as writing the cost of equity when the firm has no debt, or E, when debt is zero. Okay, fine. What about firm Levi firm? The asset side is still the asset side. It's ra, but it's just generating the same assets. So generating the same returns. But on the right hand side, we've got debt and we've got equity. The debt is, has an interest rate of rd. The equity has an interest rate of re. So that's what we have is the weighted average cost of capital is a weighted average of the RD and the re, right? And what are the weights? How much debt is there in the firm? How much equity is there in the firm? Okay? So very straightforward formula. And if that's the overall cost of capital for the firm, weighted average with the debt and the equity, there's only two forms of debt here. Only two forms of financing here. If you had more firms, you would add them on preferred shares, convertible debt, whatever cost of each take the weighted average of all those costs together. That's a relevant cost of capital for this firm. Fine. So what are the questions we wanna answer? The value of the endeavored firm is vu. The value of the levered firm is vl. So the first question you wanna answer is, the value of the levered firm different from the value of the unlevered firm. That means in some way, has issuing debt changed the value of the firm? Second question, what happens to the cost of equity? If you issue debt? Does the cost of equity change? And a third question is, what happens to the firm's overall cost of capital as you add debt to the capital structure? Right? So three big questions. Is the value of the levered firm equal to the value of the unlevered firm? Or is it different in some way? Second question, what happens to the cost of equity? Do shareholders care about this? Third question, what happens to the firm's overall cost of capital? Okay? And the answers to these three questions was what got Ani and Miller the Nobel Prize? So let's see what they did. Let's start with a perfect world. Now, remember, Moland and Miller were both economists from the University of Chicago, right? For those of you who are familiar with economists from the University of Chicago, their idea of a perfect world is very different from our idea of perfect world. So what do Chicago economists think makes a perfect world? First thing they say is, there should be no government, right? Of course, that means no taxes, right? That means no lawyers, no bankruptcy costs, no transaction costs, and of course, efficient markets, right? So this is the ideal world for an economist from the University of Chicago. So let's start with this world. Perfect, fine in this world, the proposition one, which they came up with, let's just say, and by the way, the perfect world doesn't exist, right? So that's why they, it was a thought experiment. The beauty of their approach was that they said, let's start with this perfect world and then relax one assumption at a time to see how far we can get with what's the optimal structure of the firm. Okay? So initially, all these assumptions, perfect world, and they said in that world, the value of the firm doesn't change. That means, in other words, the value of the levered firm is equal to the value of the unlevered firm. Second thing they said was, shareholders think it's riskier now. So what do shareholders do? They ask for higher returns, otherwise they won't invest in the company, right? So the rate of return to demand by equity holders goes up and it's given by the cost of assets, plus cost of assets minus the cost of debt, times the debt equity ratio of the company. I'll come back to this, the third one says, but even then, even though the shareholders are asking for more money, the weighted average cost of capital of the firm stays the same. It never changes. So let's prove this. Okay? So we are now coming up on proving three Nobel prize winning formula. So you have to dust off all the mathematics we did in our high school. Ready? Everybody, right? Excellent. Let's do it. So proposition one and the proof is actually very simple. We'll call it the pizza proof. Okay? So you have here a pizza which cost 10 pounds. Alright? So you decide to sell one fourth of that pizza. Okay? So the question for you, and I'm gonna start over here, is how much would you start for selling that one fourth slice to the pizza? You can use that QR code and slide on on your phone to try to figure out exactly how much you would pay for one quarter of the pizza, right? You can charge any price you want, what price would you charge? Excellent. I can say that a lot of you would be charging about four pounds for a slice of pizza. Excellent. That's totally fine. Of course, remember, this is University of Chicago, and remember the first assumption we made perfect competition. The moment you charge four pounds for one quarter of the pizza, what is the immediate thing which will happen? If the market is perfect, somebody else will jump in and undercut you, right? So you charge four pound, they'll charge 3 99, you charge 3 99, they'll charge 3 98. And so literally the only price at which you cannot, you know, uh, make a profit or a loss is 2.5, which you can't charge less than 2.5, but then you're giving up money, you're leaving money on the table. So literally what they said was, you want to sell a quarter of the pizza, you have to sell it for 2.5. You cannot sell it for more than that 'cause of competition. You can't sell it for less than that because you're not stupid, right? So that's the basic story here. So the only price is 2.5. So what that means is, now what do you have? You sold your pizza originally, 10 pound sold a quarter, you ended up with 2.5, and you end up with three quarters of a pizza worth 7.5. The question is, are you wealthier than before? Hmm, not really, right? One pizza worth 10 pounds, three quarters of pizza worth two, 7.5 plus 2.5 in cash. Exactly the same thing. So really you're not better off than before, and that's the proof. Now, I can see a lot of faces say, wait, what kind of proof was that, right? I mean, they got a Nobel Prize for that. So let me get a little more sophisticated here. Okay? So by the way, that's how they actually explained their thing to the, um, so when Miller got the prize, a whole bunch of journalists went to him and they said, professor, can you explain your why you got the prize? You know, in ways that our readers can understand. And he used the pizza proof. It was not in the paper. This is how he described to the journalist. And the journalist said, oh, interesting. Um, can we talk to someone else? Because they're like, what the hell? Right? They didn't understand this proof. So let's talk about a different way of doing it. Okay? So imagine that you have an unleavened firm and this is what you have, right? So the firm has no debt at all. So it makes a hundred dollars in earnings every year pays zero interest because it's unlevered. And that money goes to the net income of the firm. What does the firm do with it? Gives it out in the form of dividends. Okay? This is an unlevered firm, no interest done, okay? You own 10% of the shares. So that means your income every year is $10 and you are happy, okay? Maybe not ecstatic, but you are happy. Alright? Now, the firm says, I'm going to issue $200 of debt paying 10%. Okay? So what happens to the balance sheet of the firm? Well, earnings are still the same, but interest goes up from zero to 20. That means the net income drops to 80 and reform pays that out. So you have $80 of dividends, which you're getting. Remember, you own 10% of the shares. So your income is now $8. Okay? The question I'm gonna ask you is, would you be happy? Somebody is happy? Oh, that's nice, <laugh> two people, okay, I, I really want to speak to these people off the cliff seminar, right? Okay, so we see it's a sort of even thing would mean I'm angry and it doesn't matter to me. But the actual answer is correct, it shouldn't matter. I'll tell you why. And this seems obvious, right? I mean, as you can see over here, um, the angry part overwhelms the, it doesn't matter, right? This is again why they got a Nobel prize and because it's not intuitive, okay, let's go back in here. Remember the key part is if your firm is issuing debt, the money has to go somewhere. It cannot invest this money. So what does it do with this money? It has to give it to the shareholders that she gives it to the shareholders as a special dividend, okay? It can't touch the asset side because remember, it's a leverage recap with a firm issues debt. It has to do something with that money. So you assume it either buys back shares, or it gives the money to the shareholders. So if I give the money to you as a shareholder, you own 10% of the company, how much do you get? 210% of the company. You get $20. Now what do you do with this $20? You put it into the bank. How much is the bank paying? 10% perfectly competitive. So you get $2 of interest now and $8 of income. Are you happy? It's the same as before. It hasn't changed, okay? That was the intuition Mother, Glen and Miller said the firm decides to take on leverage. You can undo whatever the firm does by doing exactly the opposite. The firm issues that you say, fine, I lend exactly that amount. Okay, let's go to a slightly different scenario here. There's a levered firm, which is giving you $120 of interest.$80 is your net income, and the dividend is $80. So you're going along and you own 10% a share. You getting an income of $8 a share, okay? It's pretty good. And now the firm says, you know what? I don't like bond holders. I don't like debt. I think debt is bad. I'm gonna buy back all my debt. Fine. So what happens? Your earnings now is still a hundred. That hasn't changed. The interest is going to zero. Your dividends is a hundred and your own 10% of the shares. So your income is now $10 higher than before. Question is Brilliant. Everybody got the story right? So the answer is, again, it shouldn't matter. Why? Because the firm is buying back debt. This person here is still a little angry, but <laugh> I would say don't worry too much about it because the key part is the firm needs the money from somewhere, right? It's buying back debt. So where does it get that money from? It has to be from the shareholders. You own 10% of the company. So it's going to put you on the hook for 20 bill dollars. So you give the firm $20, right? Where do you get the money from? You have to borrow it. If you borrow it, you pay 10%. So yes, you get $10 of dividends, but you pay $2 of interest. So you still end up with the same $8 as before. Okay? So the income never changes here. The firm has reduced its debt. So you take on debt, you undone whatever the firm has done. That was the essence of Molan Miller proposition one, it shouldn't matter in a perfect world what the firm does because the money has to come from somewhere, right? You can't create money, it has to come from somewhere. Okay? The proposition two said the shareholders are asking for more money, right? The shareholders in some way, their risk has gone up and it's given by this formula here. So why is that happening? Why are they asking for more money? Remember, it's a perfect word, which means no bankruptcy costs. It's not about bankruptcy. There's something else. Let's imagine that you have an investment opportunity that costs you a hundred dollars and it can either give you $101 or $99. That means essentially your returns are either 1% or minus 1%. You make one or you lose one. But suppose you don't actually put in the entire a hundred dollars yourself. What you do is you go to your mother and you borrow $99 from your mother, Okay? Why your mother? Because your mother's a nice person and she will not charge you any interest, okay? So making putting interest in makes it a little more difficult. So I'm gonna assume mother because nice people, right? Okay, so now you own 101. So you have to, only thing you have to do is give your mom her money back. She's not asking for interest, she just wants some money back. So 101, you return 99, your profit is two. Here you own 99, return 99, your profit is zero. But how much money had you put in $1?$1 becomes two. That's the return of 100%.$1 becomes zero. That's the return of minus 100%. Same investment opportunity. But leverage boosts the positive and the negative. That's why leverage is risky. Makes returns much more volatile than before. Okay? What happens to the firm's overall cost of capital? Well, let's say you are the CFO of an all equity finance firm. Uh, your CEO comes to you and says, our cost of equity, which is the cost of assets, because the firm has no debt, it's 12%. Okay? The cost of debt is 6%. Why don't we borrow the shareholder's asking for 12. The bond holders are asking for six, let's issue 50% debt. What do you say? This is a great idea, a terrible idea. It doesn't matter. Remember, the cost of debt is 6%, the cost of equity is 12%. You guys are very, very good. Okay? It does look like it's a great idea because the cost of debt is lower than the cost of equity. The key point, of course, is the moment you issue the debt, the shareholders ask for more money. They say, look, it's riskier for us. How much more money? Let's take proposition two. It says that's a 12% plus 12% minus 6% times one. Because 50% debt, 50% equity, the shareholders are going to immediately ask for 18%. The more orders are still asking for six, but the average of six and 18 is still 12%. So what does the CEO say? Well, the CEO might say what stupid shareholders, they keep so greedy they're asking for more and more. Fine, I'm gonna get rid of more of them. I'm going to get rid of all except for one guy. That means I'm gonna go for 99.99999% debt. What happens to the cost of Capital One shareholder? Everybody else a bond holder who's asking for 6%, but that one shareholder now ask for a million and a half percent, the average of a million and a half and 6% is still 12%. So then the CEO says, let's get rid of the last guy. All buy back all the shares. What do the bond holders ask for? Well, one might say 6%, but remember the definition of an equity holder is somebody who's paid after everybody else is paid off. So if there are no bond, if there are no shareholders in the firm who's lost in line the bond holders, which means the bond holders become the equity holders, which means they ask for 12%, right? So the cost of capital never changes. So the traditional view of the cost of capital was as you issue more debt, the cost of equity goes up, but the cost of debt goes up too. So the weighted average cost of capital kind of goes down a little bit in the beginning and then goes up in the end. What Molan Miller said, in a perfect world, cost of equity does go up, but the cost of debt stays the same. So the weighted average cost of capital never changes. Alright, now let's add the first imperfection taxes. If you remember this from the first lecture this year, what I said was this is the flow of finance within the firm. And what I have here is a leakage, right? From the point of view. Again, going back to Chicago, the point of view is if I pay money here, that means I have less money to pay here. If I pay less money here, these guys will give me less money. So this is a problem, right? I wanna minimize the amount I pay. So basically, how do they do that? So they're gonna relax. Assumption one. Now there's a government and there are taxes, but only corporate taxes. And the corporate taxes is a tax rate of Tao C. Okay? So again, we have a weighted average cost of capital, but now I've added one minus tax rate because now I'm looking at the after tax cost of debt. Debt cost me 10%, but I'm saving 40% of taxes. So it actually only costs me 6%. That's the idea. Fine. Same three questions. Is VL different from vu? How do the cost of equity change and what happens to the firm's overall cost of capital? And in this corporate tax world proposition one says, debt is good, take as much debt as you can. More debt the better. Why? Because it reduces your taxes. The second one says the, the formula is the value of the levered form, value of the unlevered form, plus the tax shield in the debt proposition two says the cost of equity goes up, but not as much as before because the shareholders are protected by a tax sheet. They're getting money back from the government. And the third one says that the firm's overall cost of capital goes down is given by that formula. There are variance for this formula, depending on the assumptions you make about the type of debt, but we will ignore that for now. Okay, so how do we prove it? Well assume you have an all equity firm and you have a levered firm on here. So you come in, let's say it's again the pizza proof. You go in every day to your school and you're carrying this big pizza with you. And this is giant bully at the door who stops you and takes away half your pizza. The bullies, of course, the government, right? So, but you realize that the bully only checks for pizza. Doesn't actually check for cash. So what you do is before the bully gets in, right, you sell half the pizza to your teacher and then you keep the money in your shoe and walk through the pizza, sees only half the bully, only sees half the pizza and takes half of that. So the bully only takes a quarter of the pizza, not the half of the pizza. You are left with cash, plus the quarter of the pizza you have left, which means you're better off than before. Essentially. That's the scenario here. That's the scenario here. And that's the idea. The what's left over for the shareholder, the bond holder is bigger. You pay less taxes to prove that. Very straightforward. You've got same thing unlevered firm. But the key difference here is the taxes are 40% and the firm is paying that. You own 10% of the shares, your income is $6. The firm issues $200 of debt paying 10%. What happens? Well, you pay the debt, but your taxes go down from 40 to 32. Your net income is 48. Dividends are therefore 48. And so your income is 4.8. If you ask the question, are you happy? The answer is yes. Why? Because you get $2 of interest from that debt. Remember the form has to issue the debt and gives you the 20 bucks. So you use that to invest and you got 4.8. So you end up with 8 cents more than 80 cents more than before. So every year you get 80 cents more. Where's the 80 cents coming from? Well look at the taxes, right?$20 of interest saves you 20 times 40% of taxes on 10% of the share. So you save 80 cents every year. So you wanna find out every year you're saving 80 cents. What is the present value of that stream? Infinite stream of 80 cents a year. How do you find the present value of an infinite stream of cash flows? Basically you're looking for a formula that goes on like the same NPV formula, but goes on forever. How do you solve that? Well, it's very straightforward. You say the present value is that number multiply both sides by one plus R, that first one becomes C. So this cancels, this becomes one, this becomes two, and so on. So what you see is the second formula, but this whole bit here is the famous, the first top formula. So PV times one plus C plus pv, and you can solve that to just say present value CR. Now you're getting 80 cents every year. So that's the cashflow you're getting every year. So what is the value of that? 80 cents? Well, 80 cents divided by R, 200 times 10% times 40% divided by R. But what's cr? Well, you only get the tax shield if you can pay your interest. So the risk of the tax shield is exactly the risk of the interest. That means the R must be 10%. So putting that in the formula, you get the 10% cancels, the RD cancels, and that was Ani Miller proposition one. Okay, fine. So what can we conclude so far? Well, in a perfect world, capital structure doesn't matter. But in a world where taxes, debt is good, borrow as much as you can, right? Okay, are they really important in corporate policy? Well, let's take an example. A Belgian tax reform in 1982. What happened here was, for some reason, I'm not quite sure why the Belgian government decided that debt has a cost. Equity will give you a cost of 13%, and every firm can deduct that cost from its income statement. So what happened? Turns out more equity was issued in those two years than the previous 13 years. The entire Belgian stock market went up by 40% in one month. Why? Because everybody said, whoa, tax shield and shock. Every time an equity announcement happened, the share price went up because they said, oh, these guys are taking advantage of a tax shield. Right? So what about personal taxes? Remember, you're getting $2 a winter, but you're paying taxes on that, right? So shouldn't it affect the value of the form? Well, unfortunately, now it starts getting complicated. The problem is we don't know what the shareholders are paying. So for example, if you have, if you are paying heavy personal taxes, you may want the firm to pay taxes, not you. But if you're a pension fund or an endowment, you're tax exempt. So you don't really care that much about what the firm is doing. You're happy to take the interest upfront. Or it can be, well, the firms can balance some shareholders pay taxes, some don't. But this requires you to know who your shareholders are. So really, Ani Miller didn't have an answer to this. Their basic story was, if you have a big enough pool and you the shareholders have to pay taxes, they will go away from your company, but somebody else will replace them. So in effect, you can treat it like a certain thing holds in the presence of taxes. Alright, so what is the optimal amount of debt? What if we con, can we conclude? Well, Mo Miller one says, take as much debt as you can, but we don't see this. We don't see companies with a hundred percent debt or even 99% debt. So why not? Well, we have to relax assumption too, right? No lawyers, no bankruptcy costs. Now we have lawyers and bankruptcy costs. So what do these guys do? Well, the first thing it does is it reduces your flexibility, right? Imagine a company has a lot of debt, you think it's gonna go bankrupt. Are you gonna buy the products of this firm? Let's, let's say it's making laptops, right? Are you gonna buy a laptop from a company which has a severe amount of debt? No, because you don't know what the after sale service can be. You don't even know the company will exist one year from now. So even the presence of too much debt means that people will back away from the company people. You will not be able to hire a good employees because nobody wants to join a company which might go bankrupt. Okay? Alright. Second problem is excessive risk taking companies going bankrupt. What they will do is take all sorts of risks. Why? Because the costs are born by the bond holders or they might underinvest. So that means basically, if a good opportunity arises, they won't take it because the benefits will go to the bond holders. The company will be safer. Why should they choose to invest in that project? These are called the agency costs of debt. So this leads to what we call the trade off theory of capital structure. The trade off theory of capital structure says the value of firm is the value unlevered firm plus the present value of the interest tax sheet, plus the incentive benefits of debt. Some debt is good because managers know that they have to service that debt. Otherwise the company goes bankrupt. They all lose their jobs. If you have too much cash, you attempted to spend it on yourself, right? Think about all of us, when we have our annual budgets and you don't use your budget before the end of the year, what happens? The budget disappears. So a lot of us, towards the end of the year, we buy a lot of stuff. We don't need new laptops, new whatever, right?'cause otherwise the money goes and next year they say, oh, you didn't use it last year. We cut your budget this year. Sound familiar? Right? A lot of people. Okay. So that's the incentive. Benefits of debt, financial distress costs, and the agency costs of debt, reduce that value. So who has high debt? If you have high fee cash flow, you need the tax shield. If you have stable cash flow, there's a low property of financial distress. If you have lots of tangible capital, financial distress, less costly. So you might choose to have that level of debt. Few growth opportunities, you don't need fundraising. So debt overhang is not a problem. So these are the companies which has high levels of debt. Okay? So this theory of capital structure basically says that if you go with Molan Miller proposition one, you end up here, right? In the perfect in the world with taxes, if you are thinking about agency costs and the value of distress costs, firms balance the two together in the trade off. One was the other. Every firm has an optimal level of debt. Okay? So how to form the established capital structure in reality. Well, there's some people that, there's a survey being done by Graham and Harvey at Duke, and they say that most companies do actually have a target capital structure in mind. How much to borrow. They know what is good for them and what is not. And you ask them what effects that policy. They will tell you things like credit rating, insufficient internal forms, level of interest rate. These are all things which work with Mo Grani Miller, right? But the second, so most corporations in general have low debt asset ratios, changes in financial leverage have been shown to affect form value. And they seem to be differences in capital structure across industries, which we can now explain, right? For example, airlines. The assets are leased, uh, uh, assets, they can easily be taken away. It's stable things. Internet information providers, the assets are the engineers. You can't handcuff them to their desks. They won't want debt because if they take too much debt, the engineers will leave if they think the form is gonna go bankrupt and the form will definitely go bankrupt. So that's it, right? And there's evidence that firms behave as if they had a target debt equity ratio, but it doesn't explain everything. For example, lots of profitable firms have no leverage at all. For example, from 1962 to 2009, about 10% had zero debt, no debt at all. Um, zero leverage firm, and they stay year after year. They never take that, right? And they pay higher, higher dividends. They have the money, they pay higher taxes. Why are they paying higher taxes? That's called, that was a paper called the Mystery of Zero Leverage Firms, which is a very American thing. Why are these guys paying taxes when they don't have to? So what can we conclude about capital structure? In a perfect world, capital structure doesn't matter. So what's a perfect world? Capital structure shouldn't affect a fee cash flow. The asset side of the balance sheet is completely independent of the liability side of the balance sheet. Capital structure decision doesn't reveal any new information, right? Third thing, investors and firms can trade the same set of securities at the same price. No taxes, no transaction costs, no issuance costs. But even in perfect capital markets, capital structure does affect something. The risk of equity increases when you shoot debt. So in a world with taxes, it pays to borrow. So borrow as much as you can, but of course, companies do not borrow as much as they can. They trade off the tax benefits of debt from the financial distress, cost of too much debt, and they end up with an optimal capital structure. Unfortunately, this doesn't explain everything. Some firms don't even appear to think about this tax benefit they can borrow even when they can easily pay their debts. So that last example is a different theory of capital structure, which I'm not gonna talk about today. That will be in the topic of asymmetric information. So the informational effects when you start issuing debt, we'll spend some time talking about it, I believe in May, right? But for now, this is what we can conclude about capital structure. And that's it. What I'm gonna do is take a couple of the questions online first, and then our colleague will, um, will bring the mic to before. So Professor Rao, a couple of questions. You spoke about promises and, um, the perfect world, and it's something that resonated with myself. And one of the questions online. First question. How do you account for such poor returns in the real world versus the assumptions in the perfect world? Well, the perfect world is a pure thought experiment, right? There's nothing, I mean, it's not like, um, it's not like we are expected to believe it exists. It's the thing about this is this mythical paradise, which we are supposed to live in. And in a mythical paradise, nothing matters. Capital structure doesn't matter. In the real world, our returns are very different. It's not just taxes, it's bankruptcy costs, it's informational effects. In this class, in this session, I haven't talked about information because moment you issue something that reveals information to the market and the market reacts to that information. So returns in the real world have very little connection with returns in the perfect modig gani, Miller world, and they just tap the beginning. But it was a good way to think about how do you separate the investment issue of the firm from the capital structure decision of the firm. What you present tonight is very rational. How do you account for irrational behavior and decisions? That's a very good question, and in fact, I'm going to address those in my final lecture on market efficiency. So we'll hold off on that there. And there are a lot of factors. For example, there's a paper by Ricki mal menier, and there's another paper by me. We show that CEOs, as we know, are humans. They are not Chicago rational economists. So there are lots of things that affect their choice to do something or not based on purely behavioral factors such as they were born during the Great Depression, or even that they're married. Married CEOs take less risk than, you know, unmarried CEOs. Maybe one reason for that is they've used up their quota of risk when they got married, right? Or maybe they're more risk averse, who knows? But that those are things, those are, those are behavioral factors that affect capital structure. We look forward to the, the sick lecture in the series for that. Uh, my questions is about the, yeah, you mentioned, uh, earlier about the, uh, principle agent of the problem of the CEO. Uh, it's lead, uh, open to the offer financialization while, uh, what society expect from the firm is the value that, uh, they created, not just earned. So how, how to like balance, uh, the value that firm created, uh, uh, versus the offer financial decision. Thank you. Okay. So the, as I mentioned in my first lecture, the idea of what firms are for has changed a lot since the 1920s, right? In the 1920s, there were a lot of people who believed that the reason people were firms were there were also to help society. But as I pointed out over the last, from 20 19, 20 to 1970, when Friedman was, uh, was the culmination of all this, they basically said, it's not our business to talk about, you know, whether to help society or not, which our business is to do what's good for our shareholders. If the shareholders want to do what's good for the society, that's their issue. But they were, you're right, focus principally on principle agent problems. You let the managers do whatever they want, they will help themselves, rather help anybody else. So that was the overriding focus of those guys. You can't trust anybody literally. Okay. Okay. So can, um, mo Glan and Miller's principles be expanded into other forms of issuing finance other than issuing debt and just equity and used by real life companies? Okay. Molan and Miller actually followed in a long tradition of what we call separation principles, right? So everything in finance involves separating one decision from another. So for example, last time when we talked about portfolio theory and the capital asset pricing model, we were, oh, we talked about, start with our first lecture and pv. We separated the investment decision of the firm from the consumption decision of the shareholders. The shareholders want something they can borrow and land in the capital market to where they want to go be, be. This is exactly the same idea. It's a separation. I can separate the investment decision of the firm from the financing decision of the firm, like independent of each other. Everything in finance, and we see this in the next class as well, is about showing that each decision is independent of every other decision. So we don't need to worry about all the other ramifications, we can just focus on one particular area. Um, uh, your models earlier about the difference between debt and equity did not take account of the behavior of shareholders who buy and sell quite quickly. So a company that borrowed to buy its own shares to increase the share values, some people will be in there quick, get their 10% 'cause of the share value's gone up and then sell again <affirmative>. And so you are not taking account of what shareholders do. They don't stay for a very long time in many cases. Um, as somebody like me who's bought in Nvidia and sold and bought again has made lots of money. Yeah, that is an excellent point. This is a question about fairness and those kind of issues here. Unfortunately, finance doesn't concern itself very much about fairness. So for example, if the company, you know, a company issue shares or whatever, or makes a tender offer to buy back shares, and some shareholders are on holiday, some shareholders haven't, you know, kept up with the stuff, they will lose off. Some people will take advantage of that. They will make money, other people will lose money. So it's a wealth transfer between shareholders. So there is a technical term for shareholders like this and that is suckers, right? So finance calls them, you know, you don't, you don't do, you're not alert all the time. Tough luck your problem, not mine, right? So this is again, as I said, a very peculiarly, heartless way to believe, right? But that's finance for you. There are no nice people in finance, I'm afraid. Okay. Well, I think we're running short of time, so I'm just gonna take one question online, um, which may, maybe I'll train this in a good way, which is, are there any real world economies that come close to the perfect world you've described? No, I can't think of a single one. Well, I really can't think of a single one that fits exactly all the criteria we have. It is a, but as I, most models start with that world because then you can see by relaxing each assumption, how do we get closer to the real world? And what is the impact of each assumption? Half, I think the questionnaire here is probably asking to find a country which didn't have a government, I'm sorry, close. Sorry. The, the questionnaire is probably trying to find a country that didn't have a government and came close to happiness for them. Ah, okay.<laugh>.<laugh>. Yeah. But on that note, I think press out many thanks again for your rich insights. Thank you, Ian, and for, for simplifying the, the complex world of capital structures. Professor Rao, thank you. Thank you.