[NOISE] [MUSIC] Now we have to talk a little bit more about risk, okay? We've just done our sensitivity analysis, right? And it might seem to some of you that the example we just solved suggests that risk is actually not changing the NPV, right? We laid down the risk in the sales of the company, but in the end we decided that the NVP is still the same, right? So it might seem a bit strange, you know? Where did risk go? Right? Of course this is wrong, okay? Risk is going to affect the value of a project. We like safety, right? We want projects to be safe, so the higher the risk of the project, the lower the value should be, right? This idea has to be true, right? So what we're gonna learn now is how do we incorporate risk into the evaluation. The reason why risks is hidden is because we have been taking the discount rate as given, okay? That's really the main reason why we haven't found out risk yet in this course, okay? I've always been telling you the discount rate is 10%, is 8%, is 7%, right? So the idea, and this is the key idea in finance, is that the discount rate should reflect the risk of the project. That is the number that is going to capture risk for us, okay? So what we're gonna talk about now is how do we use, I mean how do we implement this concept, okay? To understand this better, let's go back to model three, and think about the internal rate of return again, right? What we learned in model three is that if the IRR is bigger than the discount rate, then the NPV is positive, okay? So you have to compare the IRR of a project with the discount rate. If you're thinking about risk, right? What we're learning now is that the discount rate captures risk. So another way you can think about this statement is that the higher the risk of a project. If a project is more risky, right? Then it's going to take a higher rate of return to turn this project into a good project, okay? So to make a project positive NPV, if risk is high, you're going to need a high rate of return, okay? So that's an intuitive way for you to think about this relationship, right? It turns out that measuring the risk of a project, measuring the risk of a company, measuring the risk of an investment is one of the key topics in finance. In fact, you spend a lot of your time in an investments course when you're studying investments rather than corporate finance. A lot of the course is typically devoted to this topic, okay? What we will do in the next few slides is to do a review so our course is self-contained and you know how to incorporate risk into corporate finance valuation, okay? But if you would like a more in-depth discussion, what I recommend is that you have a look at Scott Weisbenner's investments course, okay? Which is also available, and it does have a much more in-depth discussion of how we measure risk in finance, which really is the same idea as we're gonna use here to incorporate risk into corporate finance valuation, okay? Let me give you the bottom line first, which you might remember if you took Scott's class already, okay? The way that we're going to measure risk, for a company project, for a company, is by using the weighted average cost of capital formula, okay? If you haven't seen this, it's going to look foreign. If you have, it's going to look familiar. That's why I want to do a review of this anyway. Even if you took Scott's class, I think it might be useful to do a review and think about the weighted average cost of capital from a corporate finance point of view, okay? The name says it all. The weighted average cost of capital is a weighted average, right? You have the required return on that. And then you're multiplying this by the fraction of the value of the company that comes from that, okay? It's debt over value where value is defined as debt plus equity, okay? And then you have the required return on the equity multiplied by the fraction of the value of the company that comes from equity, okay? So the E here is going to be the market value of equity. So it's just a weighted average. What I want to do in the next few slides is to do an example with you, okay? And I'm gonna use this example to review the key concepts and as we've been doing in this course so far, I want to use data from a real world company to do this, okay? Specifically, what we are going to do is we're going to computer the WACC for Pepsico as of June 2015. We need to do this for a certain period of time because, as you just saw the formula, the WACC depends on the value of the company, so we have to measure the value of the company and some of the market data for a specific period of time. But the ideas are the same. You can use the same principle, the same calculation to compute weighted average of capital for any company in any period of time, okay? Let's start with the required return on debt. The data that we're going to use here is expressed here in this graph, okay? It's the data on yield-to-maturity of Pepsico bonds, okay? So debt holders, in this case, they own bonds, right? Pepsico has issued bonds, so debt holders now own these bonds. And what bond holders get is the yield-to-maturity, okay? So this graph shows the yield-to-maturity on Pepsico bonds of different maturity. So you can see here the x axis tells you the years, so here at the end we will see that Pepsico has issued long term bonds that mature only in 2040, those bonds have a yield of approximately 4%, okay? So before we use this data we have to understand a little bit more about what the yield to maturity actually measure, right? And it turns out that the yield-to-maturity is just the expected return on the bond, okay? So you can think of the yield-to-maturity on a bond as the return, the percentage return, right? As we discussed in module three, the IRR is the percentage return. You can think of the YTM, the yield-to-maturity, as the percentage return that an investor would hold by holding a Pepsico bond to maturity, okay? So if you buy the bonds today and the bond does not default, you expect to make 4.2% a year. And default is an important word here. Okay? This calculation only works exactly if the company is far away from bankruptcy, okay? We're not gonna have much time to discuss this in this course, but remember that you can only approximate the required return on that with the yield-to-maturity for a company that's far away from bankruptcy. So for Pepsico, this would be a reasonable assumption, it might not be that reasonable for a company that has a really, really high leverage ratio that is approaching bankruptcy. As we discussed in module one, the leverage ratio gets too high, the company is gonna go bankrupt, okay? So really what happens is that if the bond defaults, you're not going to get 4.2%, so the true expected return for a company like that is lower than the yield to maturity, okay? So here's a question for you. We just figured out that the IRR of the long-term bond is 4.2%, okay? So if you buy the 2040 Pepsico bond and hold until maturity your expected return is 4.2%. Let's think about NPV, right? That's the question. What should be the NPV of these investments? The NPV should be 0. Okay? The zero NPV idea, as we discussed in module three, will turn out to be a very powerful, a very important idea, in corporate finance, or in finance in general, okay? It might seem strange, right? Why is the NPV zero? We haven't done any calculation. I just showed you how to do calculations, spreadsheets, formula. How do I know the NPV is zero, right? It seems like I'm a, that I have a crystal ball here, okay? Really, what I'm using is a market equilibrium argument, okay? Think about the formula. Suppose the NPV was positive, okay? The NPV of, you know, picking up and think about what would it take for you to buy a Pepsico bond, okay? If you had the money, all you need to do is to pick up a phone, call a trader, or go to your computer and buy a Pepsico bond, okay? You should not be making money by that, right? It's very easy to do that, so if the NPV is positive, many investors would be picking up the phone. All the traders would be buying Pepsico bonds, right? They would be calling their brokers, they would be just buying and buying and buying, right? And we learn, we know from economics, basic economics, that if there is a lot of demand for a product, if there is a lot of demand for a financial asset, the price should go up, okay? And if a price of an asset goes up, future return should be lower, right? If pay more for a Pepsico bond today, your return is gonna be lower, right? So if the NPV is positive, everybody would be buying the bond. Same thing, if NPV is negative, everybody would be selling the bond, okay? So the only possible equilibrium in the market for Pepsico bond is one where the net present value is zero, okay? For a financial asset like a bond that is very simple to understand, that everybody can buy and sell, NPV = 0 is a very reasonable assumption, okay? Why are we going over this? Why is this an important idea? Because we are going to use this to estimate returns, okay? This really is a beautiful idea in finance. We just learned that zero NPV is a reasonable condition for many markets. What this means is that, remember model three, if the NPV is zero, the actual return, the expected return should be the same as the discount rate, the required return, okay? So if the Pepsico bond NPV is zero, what this means it that we can use the yeild-to-maturity to approximate the required return on that. The return that we measure in the market is just the return that investors demand to invest in a Pepsico bond. It's the required return, okay? Right? So that's a very useful idea because we can use that data to input in our evaluation and figure out what the required return on that is, okay? One more point here I prefer to use a long term yield to maturity for corporate finance, and we know already why. Since we started this course, I've been pushing this idea that corporate finance application have a long horizon, okay? We're always thinking about the long term, right? So my suggestion is that we always take, try to estimate, the long term cost of that, the long term required return on that. What this means for Pepsico is that we are going to use the 4.2% number, which is the yield to maturity on the long term bonds. So rather than use 2, 3, 4, 5 year maturities, we're gonna take the longest possible maturity that we have available in our data, okay? But really, the key idea is the zero NPV idea, and how we can use that to estimate required returns using expected returns, using actual expected returns.