Session 4 (Val MBA): DCF Structure and Risk free Rates!

Here's the thing, okay? Hey, I'm going to get started. Um Reminder again, if you haven't picked a group, find one. Haven't picked a company, pick one. Haven't collected data on your company, get started. The sooner you get that process started, the better it is for you, right? Um Today, we have a lot of stuff to cover. And today, we're going to actually start to get into the mechanics of the inputs that we take for granted when we estimate discount rates, cash flows, right? I mean, things that look pretty simple when you see them in a textbook as risk-free rate, beta, risk premium. We're going to dig deeper, and we're going to discover there are layers there that often get misunderstood. So, today, one of the things we're going to focus on is risk-free rates. So, here's my start-of-the-class test on risk-free rates. Go with your gut. Don't try to, you know, second-guess yourself. Go with what you think the answer is based on what your understanding is right now. So, let's say you're valuing a Brazilian company. And you can value it either in nominal reais or in US dollars. Risk-free rate in reais is 7 and 1/2%. The risk-free rate in US dollars is 2 and 1/2%. In which of these currencies, if either, will you get a higher value for your company? Anybody want to give that a try? Manish? So, what I was Beyond you, you say you you were saying you were seemed to be saying no when you said same. So, give me the logic. I'm setting you up. So, give me the logic on why you think the values would be different. Okay, that's what my setup said. Discount rate is lower, value should be higher, right? Turns out that Manish is right because it turns out that the discount rate changes when you switch currencies. But, what else changes to offset it? Your growth rates, your cash flows. It turns out that if you do things right, your valuation should be currency invariant. What's the temperature today in New York? 40 something? If I convert it to Celsius, does it feel colder? Right. I mean, currency is a conversion mechanism. You can't take a good company and make it a bad company by switching currencies. We'll talk But, it gets violated all the time. And we talk about what causes mistakes. But, if you do it right, you should get the same value for any company, which is incredibly convenient because you know what I've given you license to do, right? You have a Russian company to value. You don't feel like doing it in rubles, I don't blame you. You can do it in euros, you can do it in dollars, and if you do it right, you should get the same value for the company. An extension of the same idea, and by now you kind of get the answer. You can do your analysis in nominal terms or real terms. What does that mean? I mean, I hear people say, "I did a real valuation." Now, Shruti, what does it mean when you say I did things in real terms? Um which one? Right. So, you take inflation out. Because when we think Let's face it, our normal thing is to think about nominal numbers, right? So, when I ask you, "How much will you make next year?" You adjust for the fact that inflation's 5%, you raise No, but when you do real numbers, you have to take that inflation out. It's a It's more work. That's why, you know, people prefer to do normal things. We'll talk about the kinds of countries where you end up doing things in real terms. So, let's say you take a company, you take nominal cash flows with whatever currency you pick, nominal discount rate, you value the company. You take that same company, and you do everything in real terms. You take inflation out of the numerator, you take inflation out of the denominator. You kind of know where the answer's going, right? What should you get as value? Exactly the same value. Again, there are lots of ways you can screw up. We'll talk about those. But one of the things we're going to talk about currency is how inflation is the central actor, and how you have to be consistent in how you deal with inflation. Yesterday, I was I was on CNBC. I was supposed to come on at 3:20, and the 10 minutes before They ask you to log in 10 minutes. I never go in anymore, I just do it on Zoom. So, I'm sitting there on Zoom watching the previous panel go through. I mean, they're you know, they're from different investment banks, market strat. And for the entire 10 minutes, they're talking about the Fed, the Fed, the Fed, the will raise rates, the Fed will lower rates. And this has become a bit of an obsession in markets that the Fed sets interest rates and it drives all narratives. Today we're going to talk about the delusion of believing that the Fed sets any interest rate and why it gets us into a lot of trouble. But it's been used as the reason why rates were low for the last decade. Quantitative easing. Across the world, central banks have been viewed as the reason rates were low. Again, go with your gut. Right now, if you think about where you are, what you think about central banks, do you think it was central banks that kept rates low over the last decade? Sounds like it, right? Everybody seems to think so. Today I will show you a graph that I think explains why rates were low for the last decade. Did central banks affect rates? At the margin, they do. But I've called the Fed the wizard the you know, I I wrote a piece on the Fed. I called him the Wizard of Oz. You remember the movie The Wizard of Oz? The Wizard of Oz has mystical powers. That's why everybody, you know, Dorothy wants to get there, the straw I mean, every person in that movie wants to get because they think the wiz and you've seen the movie, right? It's like a 4-hour movie. You wait all the way to the end. The climactic moment comes about and guess how much power the the wizard really had the wizard really has. Nothing. The Fed really has no power. I know it sounds absurd. It goes against everything we're told about the power of central banks. The power of the Fed comes from the perception that it has power. We'll talk about what allows them to set that perception. But ultimately at the margin, the Fed doesn't set your mortgage rate. It doesn't set treasury rates. They're set by demand and supply. And we'll talk about going back to fundamentals, a much healthier place to think about what's going to happen to interest rates this year? So again and the next question you can see the FOMC said, you know what they in fact let's start the discussion going. When the Fed talks about raising or lowering rates, what's the only rate the Fed actually controls? The federal funds rate. The Fed funds rate. When was the last time any of you borrowed at the Fed funds rate? You know the Fed funds rate, right? Rate is, right? What is the Fed funds rate measure? The rate at which banks can lend and borrow overnight. It's an overnight bank borrowing and lending rate. None of us ever gets to see the Fed funds rate. What's the fixation of the Fed funds rate? It's a number. It influences treasury rates at least at the very short end because people say the Fed funds rate is going up, it must mean that something happened. We talk about the the direction of that because we act like the Fed drives interest rates and I'm going to argue that rates actually drive the Fed. That's where the perception of power comes from. But the Fed doesn't set long-term rates. Last year if you think about the narrative for markets, what was happening to interest rates at least if you were watching the Fed? What did the Fed do to rates last year? They raised them four times. The T-bond rate started the year at 3.88% and ended the year at 3.88%. So where was all the interest rate raise? So if nothing else I wanted to dissociate this discussion from the Fed. Take the Fed out and talk about the fundamentals that drive interest rates. It's a much much healthier place to be. I still remember the days where you knew the Fed chair's name, but the rest of the Federal Open Market Committee nobody cared about. Now they're celebrities. They have social media accounts, they talk all the time. A good fit Fed chair is like you remember the old days with children they would say, good children should be seen not heard." I know that's that sounds terrible in hindsight. Good Fed chairmen should be seen and not heard. You don't want to keep because and that's the problem we're in is we act as if the Fed is the driver of all things interest rates. Last thing is is this notion of negative interest rates. I'll tell you it's mind-boggling when you think about negative interest rates. When you took your econ class, whatever class what that was, remember interest rates came from preferences in real interest rates and the rates were always positive. Nowhere in a textbook do you see negative rates. So, when the phenomenon of negative interest rates hit the market in the last decade, people were just completely thrown off. So, what do we do now? And I'll tell you why it's unnatural when you think about negative interest rates. When you borrow money, what do you normally think about? How much you have to pay to the bank. When you have negative interest rates, you borrow money and the bank will actually mail you a check. It's mind-boggling. And before you start celebrating, I'm going to argue that when you see negative interest rates in an economy, it is never a good sign. Um we'll talk about what it is that allows economies to have negative interest rates, but you can have negative interest rates. And from a valuation perspective, it puts you in a bad starting point, right? And your starting point is minus 0.5%. You're saying, "So, what?" You're saying, "Well, that's going to give me a really low discount rate. That's going to cause my valuations to blow up." And that's exactly what a lot of analysts in euros and Swiss francs and Japanese yen started worrying about. So, when you start worrying about negative numbers causing a problem, it's easiest way to fix a negative fix a negative number. Just take your pencil and make it draw the other direction. Minus becomes plus. They would normalize numbers. It is a horrifically bad practice. And we'll talk about when normalizing interest rates is not a good practice, but you could see what drove it. They were worried that if we use negative risk-free rates, the valuations would all would all all start imploding. But if you do things right again, it's all going to be okay. Leave the negative interest rates as is. So, we'll come back. Lots of different issues with risk-free rates. We'll come back and address them, but I am going to start off by going back to where I left you on the main lecture note packet. And at least I set the table last session talking about the different ways you could put a number on a company, right? Intrinsic valuation, there's pricing, there's option pricing. And we started on this exercise of what is intrinsic valuation. So, let's step back. In intrinsic valuation, usually you do a discounted cash flow valuation. At the risk of sounding incredibly stupid, what are the ingredients that you need for discount? Let's take the D C F and break it down. You need cash flows, need a discount rate, right? Stating the obvious, but there's one more thing I want to point out. Usually, you need cash flows for the life of an asset. So, if I give you a 10-year asset, you project cash flows next 10 years, you take the present value, you're done. 15 years, next 15 years. One of the challenges in valuing a publicly traded company is at least in theory, a publicly traded company can go on and on and on forever, right? A corporate charter tells you when a company is founded, it doesn't give you a specific point in time. There are a few royalty trusts which have finite lives, but usually companies can at least in theory go on forever. Help me out here. Starting an Excel spreadsheet, you're going to do a discounted cash flow valuation of a company with a potentially infinite life. You've decided, you're one of those people that type papers, I'm going to estimate cash flows for the life of this company. You do year one, then you do year two, then you do year three, then you do your four. You see where this is going, right? You're going to end up with an Excel spreadsheet that never ends. 16,935 years from now, you're still estimating cash flows. Now, when will this end? This is my vision of hell. You show up in hell, you don't want to be there. The devil walks up to you, and he gives you a PC. I'm a Mac user. To me, vision of hell always has PCs. He gives you a company to value, GE, and he says, "Estimate cash flows forever in an Excel spreadsheet that never ends." Can't do that. It just not doable. So, what do we do in valuation? We look for closure. What does that mean? We stop at a point in time, sometimes arbitrary, sometimes chosen, and we can't you know, ignore what happens after that point in time. We try to capture what will happen after that point in time with a number. It's called a terminal value, but don't let the words kind of get in the way of the intuition. You're You're putting closure because you basically say I can't do cash flows forever. The terminal value is supposed to capture what the present value of cash flows will be beyond that point in time. It sounds almost intractable, but we'll talk about the assumptions you can make that allow you to get there. It's one of those I think one of the components of valuation that people often mess up, and we'll talk about how do you But that's why we do a terminal value. So, let's break it down. We do a dis- DCF model. You have cash flows for the life of your estimation, a terminal value that captures the present value of the cash flows beyond that, a discount rate that is matched up to the cash flows, and a present value. Every discounted cash flow model is a variant on this generic approach. In fact, we're going to talk about three different discounted cash flow models. The first is a model which focuses on a particular cash flow to equity that you can observe, which is dividend. Why do we do it? Cuz we just don't want to estimate cash flows. It's so much work. You have the number right in front. You have dividends. You estimate dividends for 5 years, 10 years, and the end of the fifth or 10th year you stop. You estimate the value of dividends beyond the 10th year and capture it in a terminal value. And because these a dividend is a cashflow to equity, you discount it back at a cost of equity. What you get is a present value will be the value of equity in the company. Dividend discount model. 1937 John Williams book from which discounted cashflow valuation was born. That was a dividend discount model. The Ben Graham security analysis book built around a dividend discount model. When I took my MBA uh I did my MBA in 1979 to '81, we spent 20 minutes of the two-hour two-year MBA program talking about valuation and all I got was what they call the Gordon growth model, a stable growth dividend discount model. There are still people who think this is the only way to do discounted cashflow valuation and still use the Gordon growth model. Now, the way I describe the Gordon growth model in valuation, it's like doing surgery with a with a hammer. You try doing surgery with a hammer, it's going to be bloody and it's not going to end well. But people keep trying. So, that's one one set of cashflows, dividends cost of equity present value. The problem with dividends is we know conclusively that companies don't pay out what they can afford to in dividends. How do we know that? I I can prove that Google doesn't pay out what what can afford in dividends. The proof is actually on the balance sheet. What's the item that gives them away? Cash. You know how much cash Google has? 110 billion. How did they end up with 110 billion cash? It's not mana from heaven. It showed up as a direct consequence of not paying out Again, I'm not saying this is a good thing or a bad thing, but companies don't always pay out what they can afford to. And that creates a problem for dividend discount models. You do a dividend discount model valuation of Google, what are you going to get? Zero, right? If you tell me Google's worth zero, I think you're definitely wrong. We can talk about whether Google's worth a trillion or a trillion and a half, it's definitely not worth zero. So, here's the second model. Instead of looking at the actual dividends, what if I can estimate potential dividends? Sounds fancy, but what's a potential dividend? How much can companies afford to pay out as dividends? Anybody want to give that a try? Yeah, man. How much should can companies afford to pay out as dividends? They could pay out their earnings, right? They can pay out whatever they want. Net income. If they paid out net income, they can They can even pay out more than net income. It'd be a liquidating dividend. But, to the extent that they want to continue as businesses, they have to hold back some cash to make reinvestments. They have debt payments coming due that they have You know, potential dividend is whatever cash is left in the till at the end of the year after you met every conceivable need. Every investment you got to take, every payment you got to make. Can we get that out of a company's financial statements? Yes. And which financial statement would I find that in? The cash flow statement. The statement of cash flows. You go to the statement of cash flows, you can estimate potential dividend in a couple of minutes. And for Google last year, that number was $22 billion. They paid no dividend, but they could have paid $22 billion. You see how it changes the frame of reference? Instead of using dividends, I estimate these potential dividends. Let's give it a fancy name. Let's call it free cash flow to equity, but that's basically potential dividends. It's still a cash flow to equity, so I discount it the cost of equity. I still have to put closure when I get to year 5 or 10. And what I get as a present value will be the value of equity in a company. It's a comparative to the dividend discount model. In companies like Google, it'll give you a more realistic estimate of value. You can argue maybe with any company. Because companies can pay out more than they can afford to dividends as well, right? And if I use a dividend discount model, I will overvalue those companies. The free cash flow to equity model, I'm coming back to reality. I'm going to get a more realistic estimate of equity valuation. So, you got dividends, free cash flow to equity, both equity valuation model. The third model is cash flows to all claimants. For the moment, don't worry too much about the definitions. We're going to come back and talk about how exactly you can use the statement of cash flows to get cash flows to equity. But the free cash flow of the firm is a pre-debt cash flow. Because it's a pre-debt cash flow, you have you can't start with net income. Net income is after interest expenses. You start with operating income. You have to act like you pay taxes on that operating income. Let me repeat that again. Not the actual taxes paid, you have to act like you pay taxes. And again, we'll talk about why we have to act like we pay taxes. And then you subtract out what you have to reinvest. But you stop there. No debt payments. So, there'll be no cash flows from debt, cash flows to debt because debt is viewed as part of capital provided. Free cash flow of the firm is a pre-debt cash flow. The discount rate I will use will be a weighted average cost of capital. We talked about why it's so because you're matching up. As with the dividend model and the free cash flow to model, I need closure. And what I get as a present value will not be the value of equity. It'll be the value of the business. You can always get to value of equity by subtracting out debt. So, if you look at these pictures and and again, for the moment, just look at the pictures in in in a big picture sense. They will look very similar with the only difference being what's the cash flow, what's the discount rate, and the closure. The dividend discount model, my job is to forecast dividends. How am I going to forecast dividends? I can either just take the existing dividends and put a growth rate in, or I can take existing earnings, project them out, and put a payout ratio. Remember, payout ratio is the percentage of your earnings you pay out in dividends. Either way, my end game is to estimate dividends for the future. At some point in time in the future, I stop and I say, "I want closure." I take the value of dividends beyond that, that becomes my terminal value. I discount them all back to today at the cost of equity. I get the value of equity today. The present value is the value of equity. So, dividend discount model, essentially, my focus is on forecasting future dividends, putting closure in a terminal value, discounting it today. Now, if I replace this with a free cash flow to equity model, all I'm doing is taking that dividend number, which I can observe with this potential dividend. As I said, don't worry about the mechanics now. We'll talk about estimating potential dividends. But, if you compare dividends to potential dividends, you can already see some significant differences. What's the lowest number a dividend can be? Zero. Zero. Can a free cash flow to equity be negative? Yes. Yes. And that's again an opening you get with free cash flow to equity that you don't get with dividends. You value a young growth company, you might say, "No dividends, I'm done." But, really, your hole is much deeper because you got to come up with cash flows to keep the company going. It's a more flexible, more tangible way of estimating equity. But, ultimately, all I've done is replace wherever I had dividends, I estimate free cash flow to equity. More work estimating because now I've to estimate how much you're reinvesting and what your debt payments are. But, the end game is I get a more realistic number for what the equity investors can get. Discount back at the cost of equity, I get the value of equity in the company. And we'll talk about whether that equity, you know, includes cash or not. You can do a free cash flow to equity either way, but ultimately, the closure is equal to equity. And finally, if you look at the third model, again, it looks very similar to the previous picture. The only difference here is, instead of looking at post-debt cash flows, free cash flow to equity, I look at pre-debt Cashflow to the firm. When I look at growth, my growth will be in operating income, not in net income. Because again, once you decide to go down the route, you got to basically stay disciplined and stay with that same way of thinking about things. So, with equity income, I can think about growth in earnings per share, growth in net income. When I'm talking about free cashflow to the firm, I'm looking at growth in operating income. Now, you might wonder, why are they going to be different? A little later, when we talk about growth rates, I'm going to show you a typical balance sheet. And as you go down the I'm sorry, typical income statement. Starting with revenues, ending with earnings per share. And we're going to see what happens to growth rates as you move down the income statement. You can start thinking about why would growth rates vary, but they will vary. The discount rate will be a cost of capital. And here, what I've valued are the operating assets of the company. Why? Because I start with operating income. At the risk of sounding stupid, I haven't valued any assets whose earnings are not part of operating income. The case of Google, what have I not valued yet? The 110 billion in cash. The income from that cash is not part of operating income. So, I have to add cash. If you're a company with a cross-holding in Microsoft, what percentage of that OpenAI joint venture do they have? I'm not sure whether it's 51 or 49%. It might be a minority holding. If it's a minority holding, that is not going to show up as part of your operating income. You're saying, how much can it be? What are people estimating that OpenAI to be worth? 60 60, 80 billion. That's a lot of money. Pet- petty cash you're leaving on the ground. So, there's a lot of mopping up to do with free cashflow to the firm. We're going to spend some time on that mopping up process. But at this point, what I want to think about is, ultimately, they're all variants of the same theme, right? Cashflows, discount rates, closure, present value. The key is to stay consistent with whatever choice you've made up front in how you're going to approach the valuation. Today, let's say you know, you picked your company. I didn't ask you whether you picked a company because by now you're tired of that, but let's say you picked your company. What's the first step? You're going to go collect historical data. Why aren't you collecting future data? There is no future data, right? So, let's accept that up front. And so, don't complain to me that all your data is in the past. It is going to be in the past because that's all we know. And let's remember, when you get past data, you're not assuming things will extrapolate from past data because if you assume that, I really don't need you, right? ChatGPT can do the valuation. You're going to use the past data to make your best estimates for the future. So, again for the moment, I want you to think process. When I look at past data, you know, the three questions I'm trying to get answers to to help me make my forecast for the future. First is, I want to get a sense of is this company growing? How quickly is it growing? You know, the the metric where you get the most honest measure of growth, don't look at earnings. Can a company with very little growth report increasing earnings? Yes, by cutting costs, by moving things around. Look at revenue growth, right? When you have a company which is growing revenue, Unilever, it's growing revenues by 1% a year for the last 15 years. That's going to frame my story for Unilever. Which is, when I look at the future, I'm going to build a 15% growth rate unless I tell you a really good reason why I'm breaking the story. So, I'm looking at revenue growth. The second question I'm trying to address is, how profitable are you as a company? So, there I'm going to look at margins. Again, dollar profits are a starting point, but I look at margins. Are you making 10% margins or 40% margins? I was just looking at the they call the Mag 7. I think that's what they told me on CNBC. Now the seven stocks that carry the market. You know collectively what those seven companies are worth? I'm just writing a piece on it on my blog. 12 trillion dollars, 12.2 trillion. You know what the collective market cap of the Chinese equity market is today? Second largest equity market. It's now 11.8 trillion. Seven companies have a greater market cap. I don't even want to tell you what the collective market cap of Latin America, Africa, and the rest of Asia is, but it's less than 12. This is kind of a scary moment. Seven companies have as much market cap as the next biggest region of the world. And I was looking at the margins, and maybe you have a sense of it, but which of the seven companies do you think has the highest margins? Meta does. Because online advertising is almost effortless. Right? There's no production needed. Which of the seven seven companies do you think has the lowest margins? Amazon's margins are about 6%. Doesn't make it a bad company. It also happens to have the highest revenue. So all those things factor in. So when I look at the past, I'm trying to get a sense of are you in a business where you can make 40% margins? And it's not that good companies make high margins and bad companies don't. A manufacturing company will always have lower margins than a software company because the unit economics work against you. Sounds like a fancy word, but how much does it cost you to sell the next unit you sell? So I'm looking at the past and are you a company that has profit? And how do the margins fit? And maybe you're a company with very stable margins. You look at regulated utilities, they have low margins, extremely stable. Why? Because people consume the same amount of power, the cost of power doesn't vary that much. It's cost plus pricing. But you could have a company with on average 30% margins where the margins swing around. Commodity companies in 2023 were among the most profitable companies in the world in terms of margins, 26% margins. But before you start celebrating there, the sector with the lowest margins in 2020, cuz as oil prices go up and down, now you're going to see the margin shift. So, you're looking at the past to see both profitability and swings in profitability over time. And third, if the company's been growing, the question you're asking is how much did they invest to grow? What did they invest in? Key question, don't skip that. If you're a manufacturing company, that'll mean building more capacity. So, you'll see plant and equipment. You might have to go back in time to see when did they build the last plant. If it's a technology company or loosely what accountants would call companies with intangible assets, it gets messy, right? It's technology company, it might be R&D. An oil company might be exploration cost. What are you trying to find out there? Is this a company that's delivering growth efficiently? What does that mean? Are you getting a lot of revenues for every dollar you capital invest? So, when I look when you look at the past, don't make it about computing ratios or DuPont, whatever the pictures that they draw, 17 different ratios. It's nice exercise, but the questions you're asking are to set the platform for you to tell a story. What does the growth look like? What does the profitability look like? How much is this business reinvesting in? What is it reinvesting in to get future growth? So, as we go through valuations, I'll show you some of the things tools you can use to look at past data and make the judgments. But that's what you're looking for when you look at the past. Cuz once you've done that, comes that uncomfortable moment where I ask you to forecast the future. It's uncomfortable because when you're looking at the past, when I ask you why is your margin 17.3%? What do you do? You point to the accounting numbers and say that's why. But now I'm asking you what will the margins be in the future? What will growth be in the future? And that's where I say don't just extrapolate the past because if you do that, for some companies it might work hard, but for a lot of companies you're going to see breaks from the past in good ways or bad ways. Your job is to assess those breaks. So as you look at the future, you're trying to forecast growth and margins and reinvestment. The full version of the model, that's what you'll do. You'll project revenue growth, you'll project margins, you're going to project the reinvestment you want to deliver the growth. And we'll go into the specifics of doing that, but your end game is what will the free cash flow of the firm be? And I want to do it with as little detail as I can get away with. Do you see why? Because you want to keep your focus on the big questions. If you start breaking down your costs into 25 line items, you very quickly start to lose control of the narrative. There is one special case where your job can get a little easier. If you have a company with stable margins, you'll say how do I know? You know, remember you got 15 years of the past. You have a company's margins have been between 4% and 5% last 15 years, you just got lucky. Why? Because you margins are stable, you don't have to project revenues, right? Because your margins your operating income and your revenues are going to grow at the same rate. And your growth can actually be simplified to be a product of two things. How much are you reinvesting as a percentage of your earnings? It's called a reinvestment rate. And how well are you reinvesting? We'll have to debate how to measure that. But as a generic, let's assume you're reinvesting 60% of your earnings and you're making a 20% return on the projects you invest those earnings in. Your expected growth rate is going to be 12%. You can do that only when margins are stable. So we'll talk about those special cases, but the end game is you're trying to estimate cash flows of the future. Keep that in mind. Your focus should always be in the future. Whenever you look at data, whenever you look at information, it's not about what that information is for the past, it's what can I learn from it to forecast the future. And to discount these cash flows, you need a discount rate. Generically, let me set up what you need. There are two ways you can raise money for a company, right? You can borrow the money use your own money. Generically, I need a cost of debt, and I'll set the table on what a cost of debt is supposed to be. It's a rate at which this company can borrow long-term today. Keywords are long-term and today. You can have 3-month loans. I don't care. I'm going to act like it's 10-year loans. Sounds unrealistic, but it's because you have to have roll over those 3-month loans. What's the significance of today? I see people computing costs of debt for companies by looking at everything the company has on its book, every loan taken. Never ever don't go down that route. That is not the cost of debt you need in valuation. It's a rate at which you can borrow money today. And might not seem like it, but I've made your life a lot simpler. Cuz you get that cost of debt, I'm going to start with the risk-free rate. That's why the risk-free rate becomes such a significant part of the conversation. Then we're going to add a default spread, a credit spread. We'll debate how to estimate it, but that's your cost of debt. The cost of equity is a nightmare. Why? Because it's a number you have in your heads. I can't read your mind. We'll talk about how in finance, and that's where we're going to start with is that question of risk. We try to estimate a cost of equity. The keyword is try. But ultimately, your cost of capital is a weighted average of those numbers. That's where we're going, and we want to focus then on how we get there. So, in terms of sequence here in valuation, you start the sequence by looking at the past. You look at And I would suggest looking not just at the past, but also looking at the rest of the your peer group. What do you learn from that? By looking at So, let's say you're looking at uh at a chemical company, and you look at 100 other chemical companies. What do we learn by looking at the cross section? Manish? It's uh comparative value actually worth? You're not pricing it. At this point, you're just trying to learn business fundamentals. What do we say? Revenue growth, margin, free investment, right? You did that for your company, wouldn't you also want to know what the growth looks like for the sector? I you know, I I'd like to know, if I'm a 15% steel company and the growth in the sector is 3%, I know I'm going to be moving towards 3% as I scale up. If your margin is 11%, I want to know whether that's typical for the sector, higher, lower. This again is to get perspective, right? Because you're going to sit there saying, "Can I increase the margin?" I'm going to say, "Yes, but you have to make a judgment to how much." And to do that, look across. You start by looking at the past, that's your first step. That's where I'd like you to be as soon as you pick your company is to download that data so you could start looking at those. Second step, assess risk. We'll talk about what risks we're talking about, how to bring it into discount rates. I think it's a good step to stop. Don't spend too much time on I in discount cash flow evaluation, I think people spend far too much time financing discount rates and not enough time thinking about growth and future cash flows. Because that's where valuations are made or broke. If you truly want to screw up a valuation, it's not going to happen because you got the discount rate wrong. It's because you got the margins hopelessly wrong. So, step three is where you make or break valuations. And that's where stories come into play because that story is going to drive those numbers. Yes. I'm thinking about estimating growth and crafting that story versus Craft the story first and then estimate growth. The sequence is better than going the other way. How How often are you taking into account like outside factors of the company, things like financial All the time. All the time. The question is, how much? Like how how much does that weigh into your Depends on the company. I'll tell you what, if you have a mature company, I can say focus on the company, not care about the outside. If you have a young company, there's not much there. Almost everything is going to come from outside. I'm going to show you my Uber valuation in 2013. There was no ride-sharing business. I was basically making up stuff on the fly. Looking at car service generally, looking at So, the less there is in your company, the more you have to look outward. A Coca-Cola, you can say focus on the company and say, "I don't even have to look out." But, the younger a company, the more the sector is evolving, the more you need to look outside the company. What's that? Apply closure. That And we'll we'll we'll spend some time on how to do it right. And last step, tie up loose ends. Deal with cash, cross-holdings, all those things that we got treated as garnishing at the end. So, let's get started. Let's start by looking at the D in the DCF. As you think about discounted cash flow valuations, you say discount rates matter. Yes, they do. How much they matter, we'll come back and address it, but less than you think. But, I'm going to lay out the consistency principle that's going to drive how we think about discount rates. The first we've talked about already. Cash flow stack, equity cost of equity, cash flow to the firm, cost of capital should be good. Currencies matter. If you decide to do your cash flows in reais, your discount rate has to be reais. Cash flows in dollars, discount rate has to be in dollars. And if you choose to do things in real terms, take inflation out, everything has to be in real, both cash flows and discount rates. You tell me how you estimate discount rates, I'll tell you what the right discount rate is, because I can't do that until I know what you put into your cash flows. So, with that long lead-in, let's talk about what the D does in the DCF. What is the load No, we talked about risk adjusting the value. The job of risk adjusting the value, we do a discounted cash flow valuation the traditional way, entirely rests with the discount rate. Cash flows don't do anything. They're just expected cashflows. So, the discount rate carries the entire burden for S. And if I were to set up a template for coming up with this country, it would start with the risk-free rate in whatever currency of choice. And that's what we're going to spend the bulk of today talking about is how do we come up with the risk-free rate? A risk premium that measures what investors demand for investing in equities as a class. This has nothing to do with your company. So, already you can see two items in that equation have nothing to do with your company. Risk-free rate, equity risk premium. And then, at least on an intuitive basis, I'm going to ask you, is your company riskier than average, safer? And I want a relative risk measure. Do you know Do you see what I mean by that? I don't want you to say the standard deviation is 35%. What do I do with that? Is that high? Is that low? I'd like you to convert your risk measure into something that tells me whether your company is riskier than average, about average, or below average. Notice I've studiously avoided saying the word beta. Because beta carries all kinds of luggage with it. But what is a beta? A beta is a measure of relative risk, right? Average risk company beta is one. Well, you know, riskier company beta is So, in a sense, a beta is a measure of relative risk. So, let's start this process off by asking, what's supposed to show up where? Now, one of the exercises I find cathartic is when I sit down to value company, especially if there's a lot of uncertainty, is I start making a list of everything I'm uncertain about. And you you're very quickly going to discover there's almost nothing in your evaluation that you feel certain about. Even the risk-free rate. And I don't know, maybe it's So, make that list. It'll be three pages long. And then imagine making this list for Tesla. You're uncertain about The Elon Musk page alone will be, you know, 50 items long. And if you just look at that list, it's overwhelming. What the heck do I do with 150 items of risk? What do I do? So, here's what I would suggest to kind of organize your thinking. Take those risks and put them into buckets. Here's your first set of buckets. Is it economic risk or estimation risk? Let me draw the the distinction. Economic risk comes from outside, from macro forces, things you don't control. Estimation risk is risk you can make go away by going out and collecting more data. Economic risk versus estimation risk. The reason I make that distinction is estimation risk, I told you you can reduce by doing more work, collecting more data. I have some bad news for those of you who want to tie every loose end up, dot every I, cross every T. 90% of the risk in evaluation is economic risk. There's nothing you're going to be able to do, no matter how many iterations you run and how much data you collect and how many what-ifs you run. Recognizing that is healthy because it means you're not beating yourself up saying, "I feel uncertain." Economic uncertainty, estimation uncertainty. The second grouping is micro versus macro uncertainty. Micro uncertainty is uncertainty I feel about the company, its management, its products, its competition. Macro uncertainty is uncertainty I feel about interest rates and inflation and GDP growth. You're saying, "Who cares?" Micro uncertainty can cut in both directions. In other words, some companies can help you, some it can hurt you. Trust me, there's a lead lead in here. Because it can cut in both directions, as you hold a portfolio, let's say you have 30, 40 companies, if you've done your assessment without bias, what should happen to micro uncertainty? In some of your companies, management should do better than expected. In other companies, they they'll do worse than expected. Micro uncertainty will get averaged out in a portfolio. And that is really the insight that has driven all of finance as we know it for the last 8 years. Because if you're a diversified investor, what have I just said? Micro uncertainty should not show up in your discount rate, it gets averaged out. The only uncertainty that should be showing up in your discount rate is macro uncertainty. That's what a beta measures. Beta doesn't measure volatility, it doesn't measure risk, it measures the portion of the risk that is driven by macro forces. And the third grouping, friends, is discrete versus continuous uncertainty. What is discrete Let's start with the easy one, continuous uncertainty. You're a US company with European operations. Every minute of every day, your value changes. Every time the exchange rate changes, right? Euro strengthens, weakens. I It can go up, it can go up, but that's continuous uncertainty. In contrast, if you're a company with operations in a country with fixed exchange rates, there's no risk, there's no risk, there's no risk, and one day you wake up, there's a lot of risk, devaluation. It's discrete. Yes, Jared. Um I was curious in this, like how do you consider uh the tax rate that you use when you're doing the discount rate? More so, like do you Do you normally use the effective tax rate the company pays or what they actually Why do you have to do When you say tax rate, you you act like you get only one shot at the Can you have a tax rate for next year that's different from a tax rate in year two? Yeah, and that's I guess that's what I'm asking too. It's like Every number Is that all the time? Exactly, right? So, if you start with let's say in the US, you start with a 25% tax rate, there's a problem. In 2026, that tax law basically goes away. You go back to 40% tax rates, right? If this something is not done. So, you might say, "Look, you know, we're going to go back to 40% tax rates, for the next 2 years, I'm going to use 25%." The choice of effective versus marginal come back to because the answer is different depending on whether you're looking at cash flows and computing after-tax cash flows or doing a cost of debt. But your tax rates can be your specific. In fact, every single input can be your specific, which is both a blessing and a curse. It's a blessing because it gives you flexibility. It's a curse because it gives you flexibility. Right? Because you don't get this one shot. I got the tax rate. I'm done. It's a number that you might have fooled with. So, discrete versus continuous risk. Let me ask you a question. If you run a business, if you're an investor, which of those risks do you think is easier to deal with? Discrete risk or continuous risk? Discrete. Dis- Discrete risk is easier to deal with? Why? I think continuous risk is easier to deal with. Discrete risk, you don't think there's risk there, and the whole thing hits you on the head, 70% off. Right? We're terrible at dealing with discrete risk in finance. What are examples of discrete risk? Now, somebody from Iceland emailed me last week and about this Icelandic It's a private company. But it's actually There's a There's a volcano in Iceland that has become more active. And this company has a significant portion of its operations at the foot of the volcano. He said, "How do I bring that into my valuation? Is that discrete risk or continuous risk?" Discrete. The whole thing could blow. Terrorism risk, discrete risk. Default risk, where a company goes out of business. We're terrible at bringing those into valuation. And I'm going to talk about how you can use probabilistic tools to kind of deal with them. You know what I'm talking about? Decision trees, scenario analysis. No. Discrete was I mean, I I I was valuing EasyJet. This is a UK-based airline in 2019 when Brexit was still up in the air. And the value EasyJet is very It was very much a function of what happened with Brexit. Because as a UK airline that got almost all of its revenues from flying British tourists to Greece or some part of the EU. Depending on what happened with the Brexit, their entire business could blow up. Or it could be okay. I actually did different scenarios, so it's discrete risk for no Brexit, weak Brexit, strong Brexit. I mean, because the value would be different. So, first step with risk is understanding that risk can be put into the buckets. So, let's say you've done that. Here's the follow up. Recognizing that not all risk is created equal. Not all risk is going to get rewarded. And I've laid the foundations for that. If your risk is risk that is company specific and your investors are diversified, they will treat that risk very differently than the risk that you're exposed to from interest rates, inflation, GDP growth through the macros. In fact, when you look at valuing a company, and this is very tough to do, but you got to try it. Rather than ask, "What do I want to make on this company? What is my cost of equity?" Recognize that in this case at least, you got to be a price taker. You have 100,000 or 500,000 dollars to bring to the game. You're not setting the price of risk. You got to look at risk in your company through the eyes of the marginal investors in the company. You say, "Well, who the heck are the marginal investors?" They own a lot of shares and trade those shares, usually institutional investors. What BlackRock or Fidelity think about the risk in your company is what's driving how you think about risk and attaching a cost of equity. Risk through who whose eyes? And finally, we will talk about the diversification effect because it is lurking in the background in every risk and return model in finance, and I've listed out, you know, at least four generic versions. The CAPM, the original risk and return model, risk-free rate plus beta times equity risk premium. And then you got the arbitrage pricing model, you have multiple betas and multiple factors, usually unspecified. More generically, a multi-factor model. Or even what Fama and French came up with is called proxy models. Tell me your market cap, tell me your price-to-book ratio, I'll give you They're all built on the premise that investors are diversified. Is that a safe assumption you think to make? If I'm valuing Facebook, is it safe to assume investors are diversified? The marginal investors are diversified. There's one very big investor in Facebook who's not. But he's not the marginal investor. I'm talking about Mark Zuckerberg. While he owns a lot of shares, but he doesn't trade those shares. You print out the top 17 investors in in Meta. 16 of the 17 are big institutions. Isn't safe, yeah? Come in safe ground. In fact, with almost all US companies, until you get to really small cap companies, take a look at who who the top 15, 20 investors are in your company. You're going to see institutions in there driving the game. But if you're valuing a company in the Ivory Coast, that has 10% float. You know what float is? The percentage of shares that actually are traded. A lot of, you know, it's amazing. There are portions of the world, Australia and Canada have a lot of these what are called junior miners. These are companies that are publicly listed, float of 5%, 10%, 15%. The marginal investors individuals who might not be diversified. You're in dangerous ground using any risk and return model in finance. You're valuing a privately owned business for sale to another individual. You're definitely on dangerous ground assuming that person is diversified. We're going to come back and talk about how to adjust these models for the fact that investors are not diversified. But in the bulk of public companies, we start with that premise. Investors are diversified. The only risk they care about is the risk that they cannot diversify away. So, in every single one of these models, the build-up is the same. You start with the risk-free rate, and then you adjust for that extra risk by estimating betas and risk premiums. So, our task is kind of laid out for us. We need a risk premium in every one of these models, it doesn't matter which. We need a beta or betas depending on whether you're using a CAPM where you have one beta or multi-factor model where you have multiple betas. And we need an equity risk premium, single one in the CAPM for the entire market or ones for each factor in multi-factor models. At least we know what we need to do. Risk-free rate, beta or betas, risk premiums. Let's start with what should be the easiest of those three numbers, which is the risk-free rate, right? So, here's what I'm going to do with the risk-free rate. I'm going to state what makes an investment risk-free. And then I want you to think about how would I get an investment like that in whatever currency I'm looking So, when you're looking at something being risk-free, you basically know exactly what you're going to make on that investment over the period of your investment. Let's say to take an example. This morning I was checking out one-year T-bills. Right? You You You I don't know whether you know this, but if you have cash in your account or your brokerage if you have an online brokerage account, you can directly buy US Treasuries. The advantage is you don't have to worry to worry about the things you worry about with a bank fixed deposit no over 250,000 is insured or not. You just buy Treasuries. So, I tried and I wanted to buy, you know, one-year T-bills. Yeah, and the rate right now is like 5.12%. So, this morning if you bought a one-year T-bill, the rate on it is 5.12%. Let's say you have a one-year time horizon. So, a year from now, so you buy the T-bill, a year from now I knock on your door and say, "What did you make on the T-bill?" What's your answer going to be? 5.12%. Assuming the US Treasury doesn't default. Always add that caveat, right? Assuming the US Treasury is default-free, you know exactly what you're going You think, "This is good. I'm going to use the US Treasury." If you bought a 10-year T-bond by mistake, it's on the list, you just hit the wrong one. You bought a 10-year T-bond, you still have a one-year time horizon. Is your return still guaranteed? What portion of it is guaranteed? Coupon. The coupon portion, which right now is about 4.05%. What's not guaranteed? Price. The price. And what causes a Treasury price to change a 10-year Treasury? When interest rates move, they go up, prices go down. In fact, you're saying how much can they earn? 2022, the 10 US 10-year Treasury bond lost 20% of its value during the course of the year. Why? Because rates went from 1.5% to 3.9%. So already you can see when you talk about risk-free rates, your time horizon matters. So if somebody says, "What's the risk-free rate?" you can't answer it unless you say is it over a year, 5 years, 10 years? And in valuation and corporate finance, I'm going to lead you to one end of the spectrum. When you do valuation, you saw all those pictures I had, dividend discount model, free cash. How long am I estimating cash flows for? Five. Five. Am I doing it for 5 years? What happens at the end of 5 years? Terminal I put a closure, and what goes in the closure? Cash flows beyond that. In effect, I'm assuming cash flows forever. Right? So I'm going to ask you what what which maturity do you care about? But time horizon matters. Second, when you say, "What's the risk-free rate over the next 10 years?" You're not still completing the story, right? You didn't tell me whether you wanted it in Turkish lira, in which case I'm going to give you a really high number, or Swiss francs, in which case I'm going to give you a little Currency matters. Risk-free rates without a currency attached are kind of meaningless. There's no such thing as a global risk-free rate. That's Anytime you hear somebody say, "What's a global risk-free rate?" they have no idea what they're talking about. Risk-free rates don't go with countries, they go with currencies. And third, I was taught to estimate a risk-free rate, all you need to do is find a government bond. Implicit there is the assumption that governments don't default in the local currency. I'll come back and address that. But in theory, they shouldn't default, right? Because what can they do? Print more money, pay the debt off. We'll talk about why that assumption is flawed in a few minutes. But the assumption is you got a government bond rate. What are you looking for trouble? Just take that rate, that's your risk rate. So let's do let's address the question of risk free rates by dealing with a series of I'm going to give you a bunch of choices. And with each one, we're going to kind of go to We'll start easy and then we'll go to more and more difficult currencies. So first one, I want to do a valuation in US dollars. How many of you I know if you picked a US company, many of you might choose to do your valuation in US dollars. You don't have to. You can value US company in euros or pesos if you want. Let's see if this You want a US dollar risk free rate for your valuation. And I'm going to give you a bunch of choices. You tell me whether that choice will work for you and if it doesn't, tell me why not. Can you use a three-month T-bill rate? Right? Why not? Term is too short. Because three months, you know, if you have a 10-year time horizon, a three-month T-bill is not risk free, right? Because you know exactly what you'll make for the next three months and then you go There is reinvestment risk. Reinvestment risk means you don't know what you make. A three-month T-bill is not risk free if you're looking at long-term cash flows. How about a 10-year T-bond rate? We're getting closer, right? Why closer? Because your cash flows last forever. In fact, if I pick purely based on maturity, a 30-year T-bond is actually better than a 10-year T-bond, right? Yeah. I mean, I guess it depends on in your model, when do you call the terminal? That doesn't matter. What goes into your terminal value? Cash flows beyond that. Terminal value is just an artificial stop, right? When you do terminal value, it's cash flows in perpetuity that drive it. Your terminal value is not the ending point for your cash flows. It's just an artificial ending point that you apply because you're assuming cash flows beyond that point in time will grow at a constant rate forever. So, it's got nothing to do with whether you have a 3-year time horizon or a 5-year or a 10-year, you should go as long-term as you can. So, if I had to pick just risk-free rates, I'd pick the 30-year rate. It's better. But, almost every valuation you see me do, I stop at the 10-year rate and I'll tell you why. First, the 10-year rate is the the you know, the the way the rates get set is you get a fresh auction every Monday. The 10-year, every time there's an auction in 10-year will show. 30-year, in fact, there was a brief period in history where there was no 30-year bond nine between '98 and 2000 and they took it out. And the 30-year rate is really quirky rate. It's a rate that the 30-year bond is held by Japanese insurance companies for something that they do. The rate can be varied. So, I take the 10-year rate because I think it's more reliable. It's most liquid of the bonds. I can get the rate. And by the time you get to that point of the term structure of the yield curve, it's pretty flat. You're not going to get a huge difference between the 10 30-year rate. But, there's another more pragmatic reason. The risk-free rate is just the start of my estimation problem, right? What do I do to get a cost of debt? I add a default spread. If I pick a 10-year T-bond, I have to find a 10-year default spread that I get by looking at 10-year corporate bonds. If I pick a 30-year T-bond rate, you know what I need to find? 30-year corporate bonds. Good luck with that. Right? They're like a dozen you'll find. I have to remember that I have a lot more work coming and a 10-year rate makes it. So, if anybody makes a big deal about the 10 versus the 30, I just concede. There are some things on valuation where you say, "Okay, you can have that." If that is the the the the hill they want to die on, go ahead, let them have it. But, be prepared to explain why you're going to go with the 10-year rate. What about the TIPS rate? You've heard of the TIPS rate is an inflation protected rate was about 1.53% On a TIPS rate here's how it works. You buy a TIPS bond. I guarantee you 1.53%. You're saying, "Why would I take that?" But I give you whatever inflation you get that year. So if inflation is 5%, you actually get 1.53 plus 5. If inflation is 1%, you get to You see what that 1.53% becomes? We talked about real valuation. You want a real risk-free rate. This is about as close to a real risk-free rate as you're going to get is the US TIPS rate. Don't play stupid games. I want to pick the lowest, the highest. I've heard people say, "I want to be conservative." I've actually seen people use a T-bill rate now because it's higher than the T-bond rate. That's not the way intrinsic valuation works. You just pick and choose whatever makes you come up with something that makes you comfortable. So long-term rates and in the case of the US, be clear about the implicit assumption you make. That there is no default risk in the US Treasury. Is that a safe assumption? Now 2005 I would have said, "Oh, of course." But if you remember just a few months ago, we had another incident where where There are three ratings agencies, S&P, Fitch, and Moody's. S&P lowered the US rating from AAA, which is they view as default free, to AA+ in 2012. Fitch and Moody's had left it at AAA. Last summer Fitch lowered the rating to So which leaves just Moody's as the only ratings agency And that Pandora's Box has been opened, which is now there is a question of can the US government default? We'll talk about what to do if if you that door gets opened, it's not the end of the world. It's just you you got to have one more layer of estimation. When you use the US Treasury rate, you're implicitly assuming that there's no default risk. Any questions on the risk-free rate in US dollars? Let's talk about the risk free rate in euros. I don't know how many of you are choosing a anybody picked a European company to value? Who you value? Mondelez, the chocolate maker. Is it a French company? Swiss company? Swiss company. Okay, that can't be it because Swiss it's not euros, it's Swiss francs. I want somebody with the European company in euros. No? Who are you doing? Ferrari. Italian company, right? So, you need a but you're doing evaluation in euros and the financials are probably all in euros. I would think that'd be the easiest currency to pick. You want a euro risk free rate. So, what did I do? I would did what I was trying to do. Go look up government bond rates in euros and I found a dozen European governments with 10-year bonds all denominated in euros. Entire EU zone, right? There's Italy. Should I use the Italian euro bond rate as my risk free rate in euros in valuing Ferrari? Tell me why. I want a risk free rate in euros, right? These are all 10-year bond rates in euros. So, why are This is a 90 98, you could see why the rates were different. Deutschmarks, French francs, lira, these are all in euros. What's the only reason the rates vary across these governments if they're all in euros? Inflation. Not inflation. It's your all euros, same inflation. Default risk. Greece used to be off the charts 10 years ago, right? Why? Because there was default risk. Which already means that you cannot use any of those higher rates because the definition of risk free is you can't have default risk, you can't be using a default. So, if you're valuing in euros, I'll come back to you. Which of these rates is probably a safest number? German. Not because it's German, but because it's the lowest. Don't get too fixated on the German part. In 5 years from now, in fact, the German 10-year euro bond has historically been the lowest of the 10-year Euro rates. But it's getting all The Netherlands is actually getting really close because Germany, as you might have been reading, is having some budget issues and problems with fit. So, there might be a very real possibility that a year from now, when we look at this, the the Dutch 10-year Euro bond rate could be the lowest rate, in which case I'd use that rate. The lowest of the 10-year Euro bond rates becomes my risk-free rate. Cuz it's the most likely to be default free. In fact, there are some who argue that I should use the ECB, which is European Central Bank's 10-year rate. The only problem is not that liquid, not that traded. So, I stick with the German Euro bond rate, whether I'm valuing a Greek company. I know you want to punish a company for being Greek or Italian. I'll give you plenty of chances to do it. Don't do it in the risk-free rate. Right? The risk-free rate is basically a risk-free rate in the currency in which you've chosen to do the valuation. Now, let's make things difficult. Let's suppose I'm looking at an Indian company. And I want to do my valuation in Indian rupees. I want an Indian rupee risk-free rate. So, I looked up a 10-year Indian rupee government bond. Rate on January 1st, 2024, was 7.18%. Good, right? I've got my risk-free rate. But before I use it as a risk-free rate, what do I need to do? I need to stop and check that it's default free. So, I cheated. Here's how I tried to answer the question. I went to the Moody's website. You can go to the S&P website. I clicked on sovereign ratings. You know what sovereign ratings are? These are ratings that these agencies attach to countries. And I saw two ratings for every country. A foreign currency rating and a local currency rating. The foreign currency rating is the risk that Moody's sees in India when it borrows in dollars or euros, some currency other than rupees. And I didn't care about that. But I looked in the local currency rating and I hoped and prayed that I would I would see a triple-A rating. If I had, you know what I'd have done, right? I would have used this 7.18% as my risk-free rate and blamed Moody's if something went wrong. But I didn't have that luxury. Moody's claimed that the the local currency rate rating for India was BAA3. Much higher than it was, a better rating than 10 years ago, but it's not AAA. So, if I trust Moody's, what is Moody's telling me? There is default risk in India and it's in that 7.18%. It's an algebra problem, right? The 7.18% is a government bond rate. It has some default risk. I want to take out the default risk. I'll tell you ways in which you can estimate that default spread, but in the case of India, the default spread was 2.39% at the start of 2024. 7.18% is my government bond rate. My default risk is 2.39%. So, I'll give you the choices in what to use as a risk-free rate. Maybe you can stick with the government bond. It's always risk-free, 7.18%. That's one choice. In which case, you probably are using a rate that includes default risk in it and double counting risk as you go along. The second is you grab the 2.49. Basically, you have two choices. Do I add the number or subtract the number? Which do you Which you think I should do? I should subtract the number because that government bond rate includes default risk. I'm trying to take it out. The risk-free rate in Indian rupees at the start of 2024 was 4.78%. I've been doing this risk adjustment to government bonds now for 15 years. And every time I do it in a country where I do, you know, and I do it and I always get the same pushback. Why are you doing a default spread on a local currency bond? Government shouldn't default in local currency. They can print the money. To which my pushback is actually an empirical one. You know that half of all sovereign defaults in the last 50 years have been local currency defaults. Governments choose to default rather than print more money. Why would they do that? Is there a There must be some cost to printing money, right? What do you think the cost of printing more money and paying off your debt is? Inflation. Inflation. You debase your currency. Basically, governments have They're between a rock and a hard place. Do I default or I debase my currency? And here's the lesson that Latin America has taught us about Let's face it, Latin America has mastered sovereign default. I mean, this is a continent that I think 80% of sovereign default somehow find their way to Latin America. So, they know every aspect of it. And here's what Latin America has learned from this conundrum. I mean, I went to Brazil for the first time in 1997. I did 20 years in a row, every year I'd go to Brazil. And when I went to Brazil in '97, it was 5 years after they had hyperinflation, 5,000% inflation. And the only question I got asked during 2 days of evaluation, only question was about inflation. Everything was about inflation. The world revolved around inflation. Who can blame them, right? But it left scars. And here's how the scars manifested themselves. Nobody in Brazil could issue long-term bonds, including the Brazilian government in reais. Cuz nobody wanted to buy a long-term bond in reais. They'd seen what in hyperinflation It wasn't until 2006 that the Brazilian government was able to issue 10-year bonds in reais, 14 years after debasement. As a contrast, think of Argentina. In any just world, should anybody lend to this country ever again? Probably not. It's what defaulted like five times in the last 24 years. But amazingly, 2 years after every default, they're back again. You know, we now have a new government. I guarantee you, 2024, 2025, Argentina is going to become the Latin American market to go. It's almost like formal never learn. And governments have learned from this. Which means governments do default in the local currency, which also means that I would have to clean up for that default. Now, the key question here is the government bond you can observe is how do I get that default spread for a country? Yes. I have a quick question. Yeah. So, India is risky, right? So, where does that show up in the valuation that What is that? Are they ingredients in your discount rate? You got your risk-free rate. Beta and equity risk premium. So, it's got to show up in one of those two places. Which do you think it's going to show up in beta or equity risk premium? Then why not in beta? Is that the systematic Beta, the average beta for all Indian stocks has to be one. There's only one place to show risk, and it's good. You know exactly where the risk should show up. And the reason I do this is to prevent double counting. You need to see where the double counting shows up. If I use 7.18% as my rupee risk-free rate, and I adjust my equity risk premium because it's an Indian company, I'm going to double count it. So, let's talk about how to get this default rate. I'm going to give you three pathways. When I first started 30 years ago, there was only one way to get a default spread. If a government issued a sovereign bond in it in dollars or euros, and 30 years ago it was only dollars, you could estimate the default spread by looking at the bond. Take an example. Much of Latin America, Brazil, Peru, Colombia, Mexico even, issued 10-year bonds in dollars. It's tradition that they raise money in dollars. If I told you that the Brazilian 10-year key bond rate, now let me look at the number, 5.75% at the start of the year. That's a 10-year dollar bond issued by Brazil, 5.75%. Can you estimate a default spread from that? It's a dollar bond. Um the American You can't Usually you can't compare bonds in different currencies, you can't. But these are in the same currency. I I get a difference of 1.87%. What's that for? That is my default spread for Brazil. That's pretty convenient, right? Unfortunately, there are only about 15 to 20 countries where you can pull this off. 10 are in Latin America in dollars. There are five in Europe where they issue in euros. Wait, so what you're saying is that these countries emits in dollars. No, no, no. They borrow money in dollars. When you say emit, I don't I'm not sure what it is. They look Yeah, they borrow money in dollars. They issue 10-year bonds, dollar denominated bonds. Yeah. Right. And then You take the rate on that bond and compare it to the T-bond rate. Right. That's that's the country default That's the default spread, exactly. That's one way to do it, but as I said, it works for about 15 or 20 countries cuz you need a sovereign bond in dollars or euros where I can compare to risk credit. Yeah. I'm wondering if that spread is there an associated probability of default? Yeah. All spreads go with an associated likelihood of default, right? You give me the default spread, I can estimate a probability of default. It's just basic algebra. Set up the price of the bond, you back out what the chance is. So, it's They both come from the same source. I'm just attaching it as a spread rather than as a probability of default. Yes. Oh, I just looked at it. Did you say the the rate at which they issued the bonds and the difference between the T-bond rate? It's not the rate at which they issue the bonds, the rate at which those bonds trade at right now. It's a current market rate. So, Brazil has something bad happened in the last week, the rate will shoot up on the on the Brazilian dollar bond. So, the default spread is a dynamic number. It'll change as the country risk changes. Difference between that and the US Yeah, T-bond rate. Yeah, but if you if I'd given you a Polish 10-year euro bond rate to get a default spread, what would you do? What did you subtract? You obviously don't want to subtract out a T-bond rate, right? It's in euros. You take the German euro bond rate, subtract it out. So, you need a sovereign bond in a currency in which there's something default free. Yes. If you know that's going to change though, then how do you factor that into the life? You said like the the default risk is Let's say, when you value your company today, what are you using as your T-bond rate? 4.08% Do you think that's going to change tomorrow and wait next week? Everything changes, right? That's neither here nor there. Unless you have a direction of change, the fact that things change is part of life, right? Everything in valuation is subject to change. So, you make your best estimate and you make your cash flows consistent with that estimate and then if everything changes, you revisit the valuation. And guess what? The price will also get adjusted. So, everything is in motion all the time and trying to nail things down almost never works. Yes. When you compare the same country and issue in dollars and an issue in the local currency, the difference in rate is the currency exposure. It's got nothing to do. The their inflation is going to come into play. Don't ever compare bonds in different currencies. They tell you absolutely nothing. Right? So, comparing a Brazilian 10-year dollar bond rate to a Brazilian real bond rate, I don't even know what that begins to tell me. But, the first rule is never compare things in different currencies. So, 15 countries. There are 175 countries, right? This is not going to help me enough. So, this is second way and this is relatively recent. About 15 years ago, there was a market that got created called the sovereign CDS market. What is the sovereign CDS market? It's an insurance market. We want to insure against default risk. So, remember that Brazilian dollar denominated bond 5.75%? Let's say you bought that bond and now you're lying awake at night worrying about default risk. You want to insure yourself. You can go to the sovereign CDS market and you can buy insurance against default. The insurance takes a form of an annual number. Let's Let's say it's 2.3%. You're saying, "What do I do with that?" You buy the Brazilian bond, you collect 5.75% in coupons. You pay out 2.3%. You're saying, "That reduces what you make." Of course it reduces what you make. But now if you default, you get insured. The nice thing about the sovereign CDS market is it's a market estimate of the default spread in your country. You say, "What's nice about a market estimate?" You get constant updates, right? And there are 80 countries with sovereign CDS spreads. You've gone from 15 to 80, that's a move in the right direction. Now I have default spreads for 80 countries. And there's a third way that I can answer. You're saying, "Why are you coming up with three ways?" There are lots of countries that don't have sovereign dollar bonds. And there are 90 countries without sovereign CDS spreads. So with those countries, you know, "What do I do?" Most of those countries have a sovereign rating, like I showed you for India. If you can tell me what your sovereign rating is as a country, I can estimate what default spread goes with that rating. I will look up to it. It looks magical, but here's how I come up with the lookup table. I take the 80 countries for which I have CDS spreads. Those 80 countries all have ratings, and based on the level of the CDS spreads, I say, "If you're triple B rated, here's what your default spread should be." So let's try this out at the start of 2024 for the Brazilian real. There's a government bond, dollar denominated bond minus the risk-free rate. Default spread based on the government bond is 1.87%. That's one estimate. Here's the second estimate. CDS spread, start of 2024, 2.39%. But the sovereign CDS market is an insurance market with one flaw. There's a counterparty risk in it. You know what a counterparty risk is? You buy insurance, your insurance is only as good as the person who sold you the insurance. In fact, this market almost collapsed after because Lehman was one of the biggest sellers of insurance. Would you want to buy insurance from Lehman after No, that insurance is useless. It almost fell apart, they put it together, but it still has that friction. Let's call it market frictions. What does that mean? That 2.39% might not be a pure default spread. And I clean up with it for it very simplistically. Are there some countries where there's close no default risk? There must be, right? I mean, Switzerland, you know, nobody's debating it. Maybe I should change the way I do this. I I've generally taken the US CDS spread and subtracted from every other default rate, but maybe I should take the Swiss the or the lowest sovereign CDS spread and say that is a CDS spread for a country with no default risk. That must be just pure friction. Uh there's no other reason to have a number there. Subtract it out. If you feel uncomfortable doing it, just stay with the 2.39%. Now, I subtracted out the US CDS spread, the 1.81% is my my cleaned up estimate of the default spread. So, at this point I have 1.87% of the government bond, 2.39% from the sovereign CDS, 1.81% from this cleaned-up sovereign CDS, and here's the third approach. Brazil has a BA2 rating. It's a country that slid in the ratings. It's gone in the opposite direction from India. It was BAA3 a decade ago, it's now down to BA2. This is my lookup table based on rated countries and spreads I can observe. A typical BA2 rated country has a default spread of 3.28%. With Brazil, I can get all three approaches to work for me, and that is a problem cuz I can pick only one. Because the numbers are going to be very different depending on which one I pick. Remember, I'm using this to clean up my risk-free rate. It started 2024, the 10-year government bond rate in reais, the Brazilian 10-year government bond rate in reais was 10.35%. Remember what I do with the default spread? I subtracted that out from the 10.35%. So, I use the rating-based spread from the lookup table, I get a much lower risk-free rate in riyals than if I use one of the other two approaches. If this was all you were doing, it looks like I'm going to get my I'm going to bias the discount rate too low if I use the 3.28%. But, here's my advice to you. Pick one approach and stay consistent. Everything's going to be okay. And here's why. If I pick the 3.28% as my default spread, I'm going to lower my risk-free rate. That's good news, right? But, remember what I said about the number where your risk shows up in the equity risk premium? One of the ways you adjust the equity risk premium is based on a default spread, and if I take out the 3.28% here, the 3.28% is going to come back as So, whatever you gain by having a lower risk-free rate So, just pick one. Just stay consistent. Don't play Hamlet. Should I use this? Should I use that? Should I Just pick one. Move on. Right? Because as long as you stay consistent, you're going to be okay. Yes. Is there a reason you can't just average them? Like, if you have three methods, you can just average them to say, "Okay, this is like You could. So, that makes it If it makes you feel more Because ultimately, it's consistency, right? The only reason is one is a market-based approach, the other is a rating agency-based approach. There are advantages to each that you might lose both those advantages. The advantage of a rating-based approach is more measured. Ratings agencies don't overreact. The disadvantage of rating-based approach is it's measured. It takes for forever. It took them like 2 years to bring down the rating for Greece after Greece got into trouble. And by the time they decide to do it, it's too late. So, there are advantages and disadvantages. So, you have to pick your poison. Which one do you feel more comfortable in this? Run with it. Let's talk about real risk-free rates. I've kind of given away the answer. But, to get a real risk free rate, need to know exactly what you will make guaranteed after inflation. The very it's a much more difficult standard to me. And until about 20 years ago, there were no securities in the US that offered a real guaranteed rate. That's when TIPS were created. So in a TIPS bond, you're actually getting an a rate that you effectively are guaranteed no matter what the inflation is because the inflation is on par. Or if you have deflation, you can actually end up with lower than 1.8%. It's basic I think it but the inflation is actually specified in the contract. I think it's based on the CPI. It will tell you what measure of inflation. So you know exactly what you get. So if I were doing a real analysis in the US and you wanted a real risk free rate, it is 1.8% or whatever it is today. But here's the challenge. Nobody in the US does things in real terms. As I said, it's unnatural to do things in real terms. Your taxes are in nominal terms. The kinds of countries where you see real analysis tend to be countries with high inflation. Lots of Latin America, they would do things in real terms because they didn't want to deal with inflation. He's saying, I need a real risk free rate in Brazil. And I have some good news. If you can get the real risk free rate in the US, there is it's not Remember, it's currency free. It's a real risk free rate. That should be the real risk free rate across the globe if capital can flow freely. You see why if capital Cuz if capital can flow, basically real No, of course capital doesn't flow freely. There are some countries with higher real risk free rates. But I think if you're if you wanted to do a real valuation, my advice is use the TIPS rate. Wave your hands around about the assumptions you need you need to make. Move on. This isn't the fight you want to have. No, because it's just not worth it. So I did what I just described for the Indian rupee for every currency in which I could find a government bond. Let's remember qualifier, you need a government bond to start. There are about 40 governments which have government bonds. This is my risk-free rate in those 40 currencies. The way to read this is that the height of the column entirely is the government bond rate. The red portion is the default spread. So, you take the Turkish lira, the Turkish lira government bond rate was 23%. You clean out for default spread, the Turkish lira's risk-free rate is 16 and 1/2%. Mind-bogglingly high number to get started, right? And if you look across currencies, I'll state the obvious, risk-free rates vary across currencies. Why? Why do risk-free rates vary across currencies? Inflation. See, only reason You can't say it's risk, right? Because I've cleaned up for the risk, it's not default, it's inflation. High inflation currencies have high risk-free rates, low inflation currencies have low risk-free rates, and deflationary currencies can have what? Negative risk-free rates. And I wrote about negative risk-free rates, I said they're uncommon, but they're not unnatural. They can happen. They've very seldom have happened in history, but basically, that's what you get. To close the session, couple of things that I don't shouldn't have to tell you, but I'm going to do it anyway. One is No, this isn't response to Jared's point about things can change, they can change in a heart. 2020 when I started this class, the T-bond rate was 1.7%. People were complaining about how low it was. By March of 2020, the T-bond rate was down to 0.7%. COVID hit. You say, "Why do risk-free rates vary across time?" Here's the answer, I don't want you to say it's because the Fed does it. No, it's got nothing to do with the Fed. Rates collapsed because COVID hit, the economy shut down, you went into deflation, negative real growth. Rates change. Why did rates jump in 2022? Again, nothing to do with the Fed. Because inflation came back, rates had to go up. Rates can change over time, and even in currencies that we think of as stable currencies, it can sometimes happen. And if you're working with currencies like the Turkish lira, expect this to be the normal, not the exception. Your rates can and will change, which means when you do evaluation in May 6, leave your risk-free rate as an input that you can adjust at the last moment, right? Just make an input into your evaluation. Update it to your most recent one. And finally, there are governments where you either don't have a government bond, right? Or you don't trust them. There are two currencies with negative risk-free rates on the graph I showed. The Swiss franc, which I get it, that you know, deflation. The other one was a Vietnamese dong. I seriously doubt that the Vietnamese dong has a negative risk-free rate. You know how I get it, I start with the government bond, right? So, I checked to see how liquid and widely traded the Vietnamese 10-year government bond was. I couldn't find a single trade on it. So, rate seems to be a bond that the government issues. It makes Vietnamese banks hold it at a rate that they specify, which means that rate is really not an interest rate set by demand and supply. So, next session when we start, we're going to talk about how to get risk-free rates in currencies where either you don't have a government bond or you don't trust the government bond, and we'll start with that on Monday. Thank you.