[MUSIC] Let's go back to the company now. Our original goal was to estimate the cost of capital for PepsiCo. So the first step is going to be to figure out what the required return on equity is? Before we can go back to the cost of capital formula, we have to figure out what we do for the cost of equity when we move from the market, which we just did to a company like PepsiCo? The new feature, of course is the beta in the formula. It's the same formula we just used for the market, except that now we have a beta. So what we need to think about now is what does beta measure? Again, this is a very important concept in finance that you talk about in an investment course in greater detail, but here's the key idea. Really, what it means is that beta measures risk for the company. That's the idea to remember, high beta means high risk. Why? Because if you think about beta and in the next few slides, I'm going to give you an example of how we estimate beta using real world data. If you think about data, what data is going to measure is how the stock returns of the company correlate with the stock returns of the market. So let me give you an example. If the market goes down by 10% and PepsiCo goes down by 15%, then the investors are gonna dislike that a lot. It's a time when they are losing money. It's a time when investors are becoming less wealthy. The overall market is going down. All your investments are decreasing in value. PepsiCo is going down even more, so that means PepsiCo is a very risky stock. So 10%, 15%. In this case, if you think of PepsiCo stock return, it would be an amplified version of the fluctuation of market return. The other example also works. If beta is less than one, then that's a situation when PepsiCo does not fluctuate as much as the market. Maybe if the market goes down by 10%, PepsiCo goes down only be 3%. In that case, PepsiCo is going to be less risky. It's providing almost like a hedge to investors. They're losing 10% on most of their investments, but PepsiCo turns out to be a relatively safe 1. So this is the concept behind beta. So what I want to show you is how we actually estimate beta for a company like PepsiCo using beta. I'm going to use beta for the period of 2000 to 2009 and then I'm going to show you a beta that is computed by Capital IQ using more recent data. So I'm gonna do this for three different periods of time, because when analysts compute data, they typically use five years of monthly data. We wanna have sufficient numbers of data points to figure out how the stock moves with the market. At the same time, you perhaps don't want to use too many years in the past, because the company can change over time. So the compromise in this case is to use 5 years monthly data, so you have 60 data points. Here is an example. This calculation is using a statistical analysis too called a regression. But really, it's very intuitive what the regression is measuring is the relationship between PepsiCo stock return and the market return. So here, you have all the data plotted. On the y-axis, you have the PepsiCo return. In the x-axis, you have the return on the market, which here proxied as the S and P 500. And just by looking at this plot, what seems to be the case is that PepsiCo stock is not that highly correlated with the market. If you look at these points, there are many cases here where the market goes down by more than PepsiCo and there are cases where the market goes up, but PepsiCo doesn't really follow. What this means is that the correlation between PepsiCo and the market is not that high. The regression for those of you who understand the regression, what this is doing here. These tables, this table and this table, what they are doing for you is reporting the summary statistics from a regression of PepsiCo's stock return on the market return. And here's the beta is the intercept on the market stock return, which here in this case is 0.35. So this is significantly below one. Consistent with our intuition and our visual intuition that these returns are not very highly correlated, that's what we found for the earlier period. We can also do this for the later period of 2005 to 2009. If you look at the plot, now it seems that the correlation increased. This line became more positive, that's the regression line here. It became more positive, the slope went up. You actually see here in the regression, the beta. In this case, went up to 0.5. It still not a very high beta, but it's higher than it was between 2000 and 2004. So this is what we find out doing our regressions. Remember that beta is a statistical estimate. Every time we do this, we are estimating a beta using statistics using a regression. You can see for PepsiCo, we came up with two different betas. Of course, they refer to two different time periods, but you have to remember that there is uncertainty in this estimate as well. If you look at that regression for those of you who understand confidence intervals, that gives you the range for which we are 95% sure that the beta is in that range. So the 95% confidence interval for PepsiCo beta ranges from 0 to 0.75. So this means that if you wanna be almost sure that you know the beta, you have to give yourself a very large range. So that's the problem we have to deal with. Before we do that, let me give you more recent data. We're not doing the regression in this case, we could do it. This comes from Capital IQ or Yahoo Finance would give you similar data. As it turns out, beta is such an important number for corporate finance applications that the same sources that will give you financial data, that will give you balance sheets, accounting statements, cash flow statements, market values will typically also give you an estimate of data. As I just discussed, the beta from Capital IQ, you take it for June 2015. For example, it's going to reflect data for the last five years. So, it's starting in June 2011 to June 2015. This will be the relevant data to compute this specific beta. So you can get beta from the internet. So how do we use this data? We have three different estimates, we have this confidence interval. For sure, our data suggests that PepsiCo has a fairly low beta. Remember, our initial discussion. If beta is below one, that means the stock return of the company is dampening the movement in the market. This is definitely the case for a company like PepsiCo. All of our estimates came close to 0.5. What I recommend that we do in practice is that we use a range for our betas. To recognize the fact that beta's a statistical estimate and that we are very uncertain about what the natural number is rather than using a number, we end up using a range and my other recommendation is to shrink the data towards one. So what do I mean by that? Let me give you the meaning first and then we'll talk about why we are doing this. So for example, for PepsiCo, I suggest that we use a value of 0.05, which is in the range of the beta that we got, but the range between 0.4 and 0.7. So you can see that the range is getting closer to one. If the range was a symmetric range around 0.5, we would be using 0.3 to 0.7. So we always use a range that is shrunk, that approaches one. Why? Remember that the beta is what's going to measure how risky the company is relative to the market. So if the beta deviates a lot from one, if its close to zero, if it's very large, then your cost of capital for the company is going to be very different from the market. Since we are estimating beta using statistical analysis, I think it's a good idea not to give that much weight to beta and use this shrinkage idea to do that. So what I suggest is we use a range, but a range that is shrunk towards one. In the case of Pepsico, we are using 0.4 to 0.7. So what does this mean? That if you use 0.5, which is our best guess. What you're going to get is a cost of capital of 5.5%. So it's the same thing we use for the market, except we are multiplying the market risk premium by the beta, which we estimated to be 0.5. And if you use a range, you're going to get cost of capital between 5% and 6.5%. And by the way, there is no correct way to do a range. This uses a combination of our statistical analysis with common sense and really this idea of shrinking the beta towards one is a common sense idea. So, use the formulation of your regressions of the standard deviations with common sense to figure out what a reasonable range for the beta is. In this case, it would imply a range of 5% to 6.5% for the cost of value. So think about the following question to make sure that you understand how we use beta in finance. So the estimate that we got, suppose now that the market return ends up being 8%. As we learned, that's just right on our expectations. The market does just as we expect, but PepsiCo returns 7%. Market, eight. PepsiCo, seven. Should the PepsiCo investor be happy or not? First reaction you might have is no. The market return eight. PepsiCo returns seven, so the investor is losing money. That would turn out to be the wrong answer. Remember, high risk, high return. We are pretty sure that PepsiCo's data is lower than one. So Pepsico does not have to return 8%. PepsiCo has less risk than the market. That's what we just learned, even taking that range into account. We're going to find out that PepsiCo is less risky in the market. So when we estimated, the reasonable range for PepsiCo required return on equity would be 5 to 6.5. So what that means is that an investor should be happy? Even if the beta is 0.7, which is on the high end of our estimate, the investor is still making more, the actual return is still higher than the required return. So the investor should be happy not sad. [LAUGH]