Today, we will talk about capital structure theory and before I start, I will show you the same thing again. What is the objective of the firm? It is to maximize shareholder value. And for that, we talked about capital budgeting decision last time, very briefly. Today, I will start talking about financing decision. And in the financing decision, do you remember what we're doing? We're trying to find money for taking projects. Because in this part, we know which projects to take. Now we need capital source to take those projects. So we will try to find optimal capital structure if there is one. And this optimal capital structure should maximize the firm value. We will see whether we will be able to do that. And when I say optimal capital structure, I'm talking about optimal mix of equity and debt. When I say equity, I'm talking about issuing stocks. And debt, we talked about debt before. It can be public debt, like bonds, or it can be private debt, like bank loans. And in this sense, we will try to find the right kind of equity and right kind of debt to issue. Okay, this is another thing you remember from Tuesday. What is the value of the firm? The value of the firm is the summation of debt and equity. So we have some part of equity and some part of debt, or just vice versa. So what we will try to do is we will try to maximize this pie, the value of the firm as much as possible. And we will try to increase the size of the pie, because this is how you increase the value. And when I say capital structure, again, we're talking about how to finance the projects, where the money comes from. It can be in the form of debt. It can be in the form of common stock or preferred stock. There was one more source that companies use for financing. Do you remember what it was? The biggest source, actually, it's not debt or equity. It was something else. Which is internal funds. Exactly, 80% of the money comes from internal funds. And if the money the company has is not enough to cover the cost of the projects the company wants to undertake, then the company will be in financial deficit. In this case, companies will use debt or stock. Do you remember which was more common? Was it stock or debt? It was debt, right? Perfect. So the question we're going to ask ourselves all the time is, does capital structure really matter? And some people say yes, it matters. Why? Do you remember the advantages of debt? We talk about a few things. One was cost of debt is lower than cost of equity. Do you remember that graph? I have it somewhere. I will show it again. Cost of equity is really high. Cost of issuing equity compared to cost of debt. And there was the tax advantage. Do you remember the tax advantage of debt? Where it comes from? Let's remember income statements where basically it was revenue minus cost minus depreciation. So this was EBITZ. And from EBITZ we reduce what? Interests. So we end up with taxable income. And from taxable income you pay tax to the government and you end up with net income. So if you have debts you will have interest payments which will reduce taxable income, which will reduce the tax you pay to the government. So that's a tax advantage for instance. So people focus on those advantages of debt and they say of course using the right kind of financing is important. But some people say, why does it matter? You're thinking about the same pie. You can slice the pie in four or in eight. It doesn't matter. It doesn't matter whether the slices come from debt or it could. It's the same slice of cake, people say. And the article that I assigned to you, which was given the talk by Professor Miller, he says the same thing. I think a pizza delivery guy goes to Yogi Bear. And the Yogi Bear says, the pizza delivery guy says do you want four slices or eight? Do you want me to slice the cake in four or eight? And Yogi Bear says slice it in eight. I'm hungry. So it's the same pizza. So this is what Modigliani and Miller will say. Actually we're going to start talking about in like 10 minutes maximum. Okay. So why are we spending two weeks on capital structure? Why are CEOs thinking about what kind of source they're going to use? Probably capital structure will matter. At least in real life we're going to see it matters. So now let me show you a couple of very simple examples on how that can affect return to shareholders. Remember, we're trying to maximize the value of the firm. So in this first case, here we have good performance of a company. I'm going to show you three different versions of this table. Let's try to understand this one well, and then we're going to move very quickly in the next two. So suppose that this company has $10 worth of a cutie or $7.5 worth of a cutie or $5 worth of a cutie. So three different cases. And this company has some debts with 5% interest rates. So this is the interest rate on the debt. So the company can have zero debt, $2.5 worth of debt, or $5 worth of debt. In all cases, the asset value is the same, right? It is 10. It is 10. It is 10. The asset value doesn't change. So when we calculate debt to a cutie ratio, it's going to change, of course, because we're using more and more debts. So debt to a cutie ratio will be zero, which is zero over 10, or it will be 2.5 over 7.5, 0.33, or it will be 5 over 5, which is one. Clear? Okay. If it's, I'm giving it to you. It comes from, I mean, it comes from the sky, let's say. Abit is $2 in each case, earnings before interest in Texas. Interest payment depends on how much debt you have. It's always 5% of what you have as debt. So 5% of zero is zero. 5% of 2.5 is 0.125. 5% of 5 is 0.25. So these are the interest payments for the debt you have. So earnings before Texas, taxable income will be 2, 1.8, or 1.75. This is simple, right? Is there anything that's not clear? No? Okay. The tax rate in the economy is 40%. So 40% of 2 is 0.8. 40% of 1.8 is 0.75. 40% of 1.75 is 0.7. So you end up with net income. And these are the net income in all those three cases, which is taxable income minus tax. Again, simple. So you end up with net income. And in each case, we're going to calculate return on equity. What is return on equity? Do you remember return on equity? Income over equity, right? Net income over equity. So this is 1.2 over 10, 12%. This is 1.125 over 7.5, 15%. 1.05 over 5, 21%. So as you can see, the more debt you use, you increase your return on equity, which is a good thing. So you see that when the company has good performance, this is a good performance case, because EBIT is $2. In the other cases, I'm going to reduce EBIT. When a company has good performance, increased leverage is a good thing. It increases return on equity. And you all see this, right? Okay. The other examples, I will move fast, I promise. So in this case, I put average performance. Everything is the same. I'm just changing EBIT. So this time, instead of giving you $2 EBIT, I'm giving you $0.5 EBIT. In this case, again, I'm doing everything the same. I'm not going to go over them. And I calculate return on equity in each case. And it is 3%, 3%, 3%. So increasing debt had no effect on return on equity when you had average performance. What about the decimal one? Oh, it's the same. It should be the same. Okay. So good performance, leverage increases return on equity, average performance, leverage doesn't affect return on equity. Let's look at the bad performance. In this case, I'm giving EBIT to be equal to 1, minus 1. So there's a loss for this company, really bad performance. In this case, if you calculate return on equity, it's going to be minus 6%, minus 9%, minus 15%. So this time, when you increase leverage, what happens to return on equity? Return on equity decreased. So when the company has bad performance, we see increasing leverage actually affects return on equity in a bad way. What is the bottom line? Leverage amplifies the effect of good or bad operating performance on return on equity. That's what's called leverage. So in good times, that makes everything better. In bad times, that makes everything worse. Okay. Let's look at another example if you don't have any questions. Yes, Alija? Why did you pay the tax? Why there is a tax? There are negative earnings. Okay. Minus $1, minus 1.25. But there is also tax. Why there are... Why are we paying taxes even if we are... Why there is a tax? Okay. Why it's the case? Okay. Your homework is create the same table. Okay. But instead of using a bit as minus, use it as a positive thing. It can be 0.01. It doesn't matter. And try to create return on equity. And think that why taxes is negative here. One more thing. Last time... Bar 2. Bar 2. This is RF bank. You asked about Ishpenk and whether they have different stocks. I couldn't find anything on it. So, again, your homework will be to look for it. I don't really know because... No, no. When I say homework, this is not... You don't even have to submit it. It's just something that you can share with us. Remember, the purpose of this class is all learning together. Okay. So, I look for... Remember, I said Google has different types of stocks. Type A or type B. And it has different voting rights. Type A stock says one vote right. Or type B has 10 vote rights. So, but to say, I think Ishpenk has more than one type of stock. I look... I search for it. I couldn't find it. So, if you can look for it and share the information with us, I will really appreciate it. Don't do it now. Don't do it during the class time. Okay. Okay. I think in television, there is still a text part. I think here it has some different stocks. I look at balance sheet for the information. I couldn't find it. It's different. Okay. Just send me the link with it. Okay. I trust you, but I'm in academia, so we have to show everything with references. Even in every graph, you will see my references. I pay a lot of attention to that. Okay. Very good. So, let's look at another example. So, consider that we have an old equity firm, and this firm wants to have some kind of debt. The firm borrows $8,000, which is debt, and buys back 160 shares at $50 per share. So, they are repurchasing stocks, actually. So, in the current form, the assets of the company is worth $20,000. The company doesn't have any debt. It's an old equity firm. So, everything is in the form of equity. That to equity ratio is zero, because that is zero. Interest rate is not applicable, because the company doesn't have any debt. Share is outstanding. Suppose that this company has 400 shares outstanding. This is the current case, no debt case. The share price is given at $50. In the proposed project, let's say, the company will still have $20,000 worth of assets, but it will have $8,000 debt. This time, the remaining part will be equity, which will be $12,000. That's an equity ratio will be $8,000 over $12,000, which is $2,000 over $3,000. Interest rate is given. It is 8% given. Share is outstanding. What's going to happen to share is outstanding? So, we had 400 shares. We're going to buy back $110,000 often. It's going to decrease to $240, and share price is supposed to let $50,000. Forget about the market reaction. What's going to happen to stock price? We're going in very basic steps. In this case, let's look at what's going to happen to earnings per share and return on equity. Under the current structure, all the equity case, we're going to look at three different forms of economy. We might have recession. We might have normal times, or we might have expansion. EBIT will be $1,000, $2,000 or $3,000, depending on where we are in the economy. In the current structure, we don't have any debt. Interest will be $0,0,0. Net income will be $1,000, $2,000 or $3,000. How do we calculate earnings per share? I put it in the slide. It says net income over share is outstanding. We have 400 shares in each case, and income changes in each case. You can calculate return on equity. It's going to be 5%, 10%, 15%. This is the current case. Let's look at what happens under proposed structure. In the proposed structure, EBIT will be the same in each case, in recession expected and expansion cases, same with the current structure. We're going to pay 8% interest on how much debt we have. Do you remember? 8,000. Thank you. We're paying 8% interest on $8,000 debt. This is what's going to happen to our net income. Again, you calculate earnings per share, but this time, the number of shares outstanding is equal to 240. You're dividing net income with 240 in each case. This is what happens to your earnings per share. This is what happens to your return on equity. If you compare return on equity with the previous case, in the previous case, it was 5%, 10%, 5%, 10% and 15%. The current structure is good in which time? Being on the equity is good in which case? Recession, expected or expansion case? In the recession. If you're a risk averse CEO, what are you going to go with? Are you going to go with the current structure or are you going to have some debt? You're risk averse. You're going to go with current structure because return on equity is better when you don't have any debt. When you look at expansion or normal times case, though, leverage makes things better. If you're a less risk averse or risk-neutral, then you would be okay with taking some debt. The same idea, the similar intuition, just a more numerical example, let's say. Basically, when we're thinking about debt, this is what we see. If you draw a graph with EBITs and with earnings per share, we thought any debt, this is what you're going to see with the numbers we just used. With debt, we're going to have something like this. As you can see, we're going to have a steeper relationship between earnings per share and EBIT when you have some debt. What this shows is you have some break-even points on the left-hand side. Which one is better? Is having that good or not that good? Which one? Not that case is better because you're having more earnings per share per EBIT, that's a good thing. After the break-even point, though, you have more advantage if you have some debt. Clear? I have only one minor question here. Why do you think this line is steeper when the company has some debt? It's not very easy to see, but think about it. Basically, this means as you increase EBIT, earnings per share will increase more if you have debt. Think about the example. What is earnings per share? It is income over what? Shares? When you have that case in the proposed structure, do you have less or more shares outstanding? Less. Less. That's the case, right? When EBIT increases, you're distributing it into less numbers of shares. Earnings per share will increase more. That's why it's steeper. In that case, because you buy back securities. Okay, it was just a minor question. Now we can finally start capital structure theories. I'm going to start with trade-off theory. We're not going to have time for packing order and market timing. I'm going to actually cut kind of in the middle of Modigliani and Miller today. And next week, next Thursday, we're going to talk about packing order and market timing. I will actually upload another set of slides, which will give you the evidence on capital structure theories. So I will give you real-life examples of everything we see next week, next Thursday, after finishing all the theories. Okay, so again, what are we trying to do? We are trying to maximize the value of the firm. Do you remember this little guy from Tuesday? So the value of the firm depends on cash flows the company generates. And of course, since we are interested in the value of the firm today, we are discounting all those cash flows with the appropriate discount rate, which is weighted-average cost-off capital. Do you remember what weighted-average cost-off capital was? You don't have to give me the formula, just the idea. It's cost-off financing, right? Exactly, weighted-average cost-off capital. And you will take projects if weighted-average cost-off capital is less than the return that project will generate to you. What kind of financing, what kind of cost we can have? What kind of financing can we have? So this is weighted-average cost-off capital. What is the weighted-average part? It's debtor-ecuci. So we have cost-off ecuci and cost-off debt. So together we're going to solve examples on this today. So don't worry. So this is weighted-average cost-off capital. And this is the basic present value formula, if you remember. So you discount all those cash flows, you bring the values to today. And as I said last time, if your capital structure doesn't affect this part, what is the only way to maximize the value of the firm? To decrease weighted-average cost-off capital as much as possible, right? If you make this smaller, when this is fixed, you're going to increase the value of the firm. So today this is what we're going to see. We're going to assume that capital structure doesn't affect cash flows. And we will try to see whether changing capital structure will really change weighted-average cost-off capital. Okay, this is what we will try to do. So we said we are trying to maximize firm value by minimizing WEK, assuming that we cannot affect cash flows. We know that that is cheaper than ecuci. There's tax advantages with it as well. But we also know that there's a problem with that. If you increase that a lot, you increase the possibility of bankruptcy. So basically what we will try to do is choose the debt-to-ecucer ratio, which will minimize weighted-average cost-off capital. It sounds very simple. It's, of course, not very easy in real life. And what we are going to see is we will be aware that capital structure indeed affects the cash flows. So we cannot say that there is a purpose. As all ecom people say all the time and holding everything out constant. It's never constant. So this part will complicate everything. But in general, this is the picture we will have in our minds. So we know that cost-off debt is lower than cost-off ecuci. And we know that weighted-average cost-off capital is the weighted-average of those two costs. So it has to lie in between. So what we will try to find is, if there is one, we will try to find this point, the optimal debt-to-ecucer ratio, which will minimize weighted-average cost-off capital, which will maximize the firm value. So for this one, Modigliani and Miller came up with a very interesting theory. They actually got a Nobel Prize with it. And you know, this year, finance people got Nobel Prize. Probably like first time ever. Generally, ecom people take stock. And when the camera is off, I will give you like gossips about those people. Modigliani and Miller came up in 1956 with a new idea. So they said, forget about the traditional wheel. And they say, capital structure is irrelevant. Why are we spending time on it? It's irrelevant, they said. So this was a big thing at that time. But they made very, very simplifying assumptions. Even in this stage, like as almost, I mean, as university students, you will be aware how basic those assumptions are. So they assume there are no taxes in the economy. They assume there's no bankruptcy. They assume there's no transaction cost, so you can easily exchange stocks and debt and everything. And they assume financing doesn't impact operations. Very simplifying assumptions. And they actually prove those by arbitrage and low of one price. And I'm going to show you the proofs as well. It's not very complicated. Later on, Miller wrote another paper and he relaxed a couple of assumptions. So he included the taxes, for instance. But he concluded the same thing. He said, capital structure is irrelevant. So today I'm going to spend most of the class proving you capital structure is irrelevant. Then I'm going to relax some assumptions and we're going to see how things will change when we relax assumptions. First, I'm going to introduce taxes. Then actually I will stop. Next week I'm going to introduce bankruptcy and we will see how things will change. Okay, so as a starter, the simplest world with no taxes, no bankruptcy. So in this world, we're going to assume there are two firms. They have the same operating cash flow. Company U, it is unlevered, all-equity firm. And Company L, it has debt and equity both. So it's the levered firm. And we're going to assume that we're going to buy 10% of the unlevered firm and 10% of the levered firm. So my investment will be 10% of the unlevered firm. And from the investment, what am I going to make? My return will be 10% of the profit the company generates. Very simple case. Okay, forget about dividends and everything. In the other case, you're buying 10% of the levered firm. So since it is levered, you own 10% of the equity and 10% of the debt because the company has both. So in this case, you own 10% of the debt, 10% of the equity. So together, you own 10% of the entire firm, which is VL, levered firm. What is my return? As a debt holder, I'm going to get 10% of the interest payment and I'm going to get 10% of what is left out after interest payment was done, profit minus interest. So total, 10% of the profits. So from here, if your return is same, you're getting 10% of profits in both cases. If there are two investments with the same return, what do you expect from the investment? Values? Should they be the same difference? If you get the same return from two investments, what does low form price say? What does no arbitrage say? Thank you, Yeet. If there are two things with the same return, their prices will be the same. So in this case, 10% of VU will be equal to 10% of VL because they have the same return. We're assuming that capital structure doesn't affect profits. Those profits are the same. So what is the conclusion of the proof? VL should be equal to VU. So whether the company has debt or not, it's irrelevant. The value of a levered firm should be equal to value of the unlevered firm. If we assume that capital structure doesn't affect profits. This is Modiglia-Miller proposition one, actually. So can you understand what you read in the article now a little bit better? Okay, that's the idea. Okay. But remember we're in the no bankruptcy, no tax case. In that case, the value of a levered firm should be equal to value of unlevered firm. Very important assumption is that... Very important assumption is that capital structure doesn't affect cash flows of the firm. That's our simplest assumption. And firm value is determined entirely by the cash flows. That's it, not the capital structure. So no matter how the ratio of debt to equity you use, there is no optimal debt to equity ratio because no matter what you do, you cannot increase the value of the firm. So this is Modiglia-Miller proposition one. You kept the structure is irrevolent. When we think about debt, if capital structure is irrevolent, what kind of debt you're using is irrevolent, long-term, short-term, senior, subordinated, whatever you can think of, it's all irrevolent. What kind of stock you're issuing is all irrevolent, common stock, preferred stock, type A, type B, it doesn't matter. None of those decisions will affect the value of the firm. So if value of the firm doesn't change based on the capital structure, let's go one step further. We're going to move to proposition two. So the value of the unlevered firm will be this, right? Cash flows over one plus WEC. For the levered firm, it's going to be the same. Remember our assumptions, cash flows were the same for those firms. But for the levered firm, you're using WEC-L. So if these two things are same, when cash flows are same, what do you see here? For WECs. WECs should be the same, exactly. So Modiglia-Miller proposition two says what? It says the firm's cost of capital is unaffected by capital structure. So you cannot minimize WEC by changing your capital structure. Are you tired? Are you doing okay? I'm going very slowly, I know, but I think this is good for now, because I'm going to show you something very ugly now. Ready? Yes. So we said weighted average cost of capital is same. It is irrevolent of capital structure. Now let's focus on cost of equity. Okay, so cost of assets, or return on assets, is weighted average of return on debt and equity. Same with WEC idea. So this is weight of debt, cost of debt. Remember there are no taxes. That's why we don't have one minus t here. Plus weight of equity, cost of equity. So together they're going to give you the cost of assets, or return on assets, which is equal to WEC of an unleveraged firm, by definition. Here some magic happens, okay, simple things, and you come up with this. So cost of equity is equal to, or return on equity is equal to return on assets, which is basically the risk of a company, or return on a company if the company doesn't have any leverage. Plus you're introducing some additional risks due to leverage. So as you can see from here, if this part is positive, return on assets minus return on debt if it's positive, increasing debt will increase cost of equity. So now we are moving into something like this, and try to be awake for a while because this part gets confusing for some students, okay? Just wake up, wake up, okay? So cost of equity is increasing in debt, and I'm going to show you where it comes from in data and CAPAMs and stuff, okay? But cost of equity increases as you increase debt. Cost of debt is fixed, it doesn't change with debt, and it is lower than cost of equity. And weighted average cost of capital is going to be fixed. The idea is same, remember we said weighted average cost of capital doesn't change when you change the debt to equity ratio. It should be a straight line. But my question to you, I mean the answer is written here, but I want you to give me an answer understanding this. If cost of equity is increasing in debt, how come weighted average cost of capital stays constant as you increase debt? I mean this is fixed, this is increasing. When you take the average of those costs, it's a flat line, why? Let's wait like five more seconds for someone new. One Mississippi, two Mississippi, three Mississippi, four Mississippi, five. Because as we're increasing debt, we're increasing the debt to equity ratio, so the weights of the costs are changing. So the weighted average stays constant. That's exactly one thing. Remember weighted average cost of capital is what? Weight of equity times cost of equity plus, do you want me to write it? Okay, this is of course no tax case. Weight of equity times cost of equity plus weight of debt, cost of debt. So as you increase, as you use more debt, what happens? You're increasing weight of debt. You're decreasing weight of equity. But you know that cost of debt is less than cost of equity. So just stay with me. One sentence, you can get it. When you increase debt, cost of equity will increase. But at the same time, you're using more of the cheaper financing source. So they're going to offset each other. And weighted average cost of capital will be the same. This is what this note says. Was it clear? I want someone else to try to explain it to me back. Who wants to explain it? This time I'm going to wait till eight. Let's go step by step together, okay? So you start with the first sentence and then I will continue. It's very important. So you're increasing debts. So what happens to the weight? What happens to the weight of debt when you increase debt? Okay, and it increases, right? You use more debt. So weight of debt will increase, okay? Weight of equity will decrease, right? Because it's slicing the pie. If you cut the slice bigger for debt, the slice for equity will be smaller. You're going very well, okay? And then is there anyone who wants to step in? So when you use more debt, what happens to cost of equity? If you increase debt, what happens to cost of equity? It's going to increase exactly. But as you're using more debt, which one is cheaper, debt or equity? Debt. Debt is cheaper, so you're using more of the cheaper financing source. So those two effects will offset each other. I think it was perfect Olga, very, very well. Okay, he is right. I just said, okay. Perfect. And I thought you were going to ask me why cost of debt is smaller than cost of equity. So I put the slide, which was from the previous slides. It's not in the slides you printed. So we already know that cost of stock is very high. This is cost of IPOs. Then we have cost of seasoned equity offering, which is also equity, cost of equity. Then we have convertible bonds, which is form of debt. And then we have normal bonds. So cost of equity is always higher than cost of debt. So nobody asked this, but it's there if you're interested. Or you already remember it. Okay, I thought this part wasn't going to be very clear. So I put this mathematical example. It's going to show you the same thing, changing debt to equity ratio is not going to change work. So this example shows that thing just in mathematical numbers. So I use different debt and equity numbers here. I have 1,000 equity, zero debt, 800 equity, 200 debt, 500, 500, 100, and 900. So I have $1,000 worth of assets. I'm just slicing it differently. So in each case, you can calculate weight of equity and weight of debt. Let's just do this for this part. So if I have $800 worth of equity and $200 of debt, what is my weight of equity? How do I calculate this? It's 800 over 200? One thousand. Thank you. Okay, so it should be equity over assets. Do you want me to write it as V or A part? It doesn't matter. Okay, so it's going to be 0.8. And weight of debt will be equal to $200 over 1,000, which is the remaining part. So together, it should be equal to 1. Okay, so in each case, I have different cost of equities and kind of different cost of debts. So when you calculate WEK, this is weight of equity times return on equity, weight of debt times return on debt. So if you do that, you're going to calculate the WEKs in each case, WEK will be equal to 15%. So if you're interested in where this intuition comes from in numbers, this is an example you can find in your slides. So basically, we said cost of equity is increasing in debt when we have no bankruptcy and no taxes. And the rate of increase depends on this difference. And if a company doesn't have any debt, this is going to be equal to 0 and cost of equity will be equal to cost of assets because there's no debt. All the cost or return should come from equity. Very straightforward, right? Now I want to link it to some risk, but I want to take a break and then we can continue. Let's take a 10 minute break and don't be late.