[SOUND] [MUSIC] So now let's move on and try to estimate the required return on equity. We just did the required return on debt. And what we learned is that we can use yield-to-maturity to approximate the required return on debt. As long as the company is sufficiently far away from bankruptcy. That's the idea that we just learned. The first thing to notice though, is that we're not gonna be able to do the same thing for equity. We do not have yield-to-maturity on equity. Why? Because equity really has no promised cash flows. When we invest in an equity security. Unless it is preferred equity, which is really more like a bond. What you're getting is the residual cash flows. After the company pays interest to bond holders. Then, it's going to pay cash flows to equity holders. There is no notion of promised cash flow, equity holders get whatever is left. And, of course, the hope is that even after you pay interest, there is gonna be a large cash flow to equity holders. In some cases it could be zero, if the company becomes bankrupt. But anyway, the point is that there is no notion of promised cash flows to equity. Which stop us from estimating a yield-to-maturity on equity. This concept does not exist. What we are going to use is a very important finance model. Which we call the capital asset pricing model. This is a model that you study in detail in an investments course. Like Scott Weisbender's course, that we just talked about. Here we are going to have a quick and intuitive discussion of how to apply the capital asset pricing model to a corporate finance application. So here's the model. It is the sum of a risk free rate, which we're going to take as the yield-to-maturity on a government bond. The security in the economy that has the least risk is the, is a bond that is issued by the government. Why? Because the government can always use taxes. The government can always tax people, can tax companies to make sure that it has enough funds to repay the bond. That argument doesn't always work, but if you're thinking about markets like the US, which are established, mature. Then it's reasonable, and there is some evidence on that, that the security that probably have the least risk. Are bonds issued by the government, in this case the US government. That's why we use that as the risk free rate, and then there's going to be a risk premium. For a company, the risk premium's going to be the beta times the risk premium of the stock market. If you remember the CAPM and this sounds familiar, great. If you don't, we're gonna have, like I said, a quick and intuitive discussion of why the CAPM works. And how we use it In corporate finance. The most valuable thing is intuition. Really what you should take from our finance courses is an intuition of how the CAPM works. Let's start with the market. We're actually going to start by figuring out what is the required return on the market. The way we do that is by ignoring data. As we're going learn to next, the data is going to capture the relationship between stock returns for the company and stock returns for the market. If you do that then the data goes away from this formula. The yield-to-maturity plus the risk premium on the market are going to give you directly the required return on equity. We just have to estimate two things. Let's start with the yield-to-maturity on government bonds. I told you that we're going to use securities issued by the US government in the case of PepsiCo. And here is the data for June 2015. It's another reason why we always have to think about cost of capital for a given time period. Because yield-to-maturity are going to change. The risk free rate on the economy, the return that you get from buying a government bond, is going to vary over time. In June 2015, it turned out that the 30 year government bond was returning 3%. And as I said, my recommendation is to always take the longest possible maturity. What I'm going to do here in the formula is use 3% as our risk free rate, for this calculation. If the risk free rate, if the yield on the 30 year bond, goes down to 2%, we would turn, change that 2%. If it goes up to 4%, we change that to 4%, that should be easy. All that this requires is for you to open the newspaper, and get a table like that. Or go to Yahoo Finance, Wall Street Journal there are many sources where you can get this data. The risk premium is a lot more complicated. This is a huge topic. Measuring the risk premium on the stock market's a huge topic. It has already given a Nobel prize to economists who studied this, and discovered some of the most important facts. It's one of the key objects that we study in economics. I mean, not only finance, more broadly it's one of the key topics we study in economics. Here we're gonna have a very intuitive and practical discussion on the risk premium. The concept is that, the risk premium on the stock market, is the additional return. That an investor would demand to put your money in the stock market, rather than putting in a government bond which is safe. The government bond will very likely give you that 3% return, unless something really unexpected happens. Which we believe it's not, but investing in the stock market is obviously risky. The stock market can give you a very high return, can give you a very low return. How do we estimate the risk premium on the stock market? Let's think about that. Going back to what we already discussed, let's think about this question. What should be the net present value of investing in the market? Suppose you take your money and put it in a the stock market, what should be the NPV? A reasonable guess is that the NPV should be close to zero. We can use the same argument that we use before. If the NPV is positive, then a lot of people would start buying stocks. The price of stocks might go up. If the NPV is negative, people would sell. Stock prices would go down, stock returns would go up. Again, we can think of this as a market equilibrium story. But with the stock market, your intuition is probably telling you, it's the right intuition. Your intuition is telling you that the NPV in the stock market is less likely to be zero than the NPV on a bond. The bond is a simpler asset, it's easier to value. If the NPV deviates from zero, it's very easy for participants, for investors, for analysts to figure this out. And bring the market back to equilibrium. For the stock market, it's more complicated. If the stock market thinks, for example, there is a big crisis in the world. Stock prices go down, people naturally become afraid. They might take the money out of the market instead of perhaps investing more. Risk is going to complicate this calculation. We're gonna talk more about that in a second. For now, remember the idea we discussed. If the NPV is zero, we can use actual returns. We can use realized returns to estimate required returns. That is the idea that financial economists use when they look at historical data. Historical returns on the stock market to measure expected returns, to measure required return. Here, what you have is the average return on stocks and bonds between 1928 and 2012. Treasury bonds in that period returned on average 5.38%. You can see that this number is larger than the 3% yield that they are returning now. Common stocks returned 11.26%. I stopped these in 2012, but the number wouldn't change much if we add two or three more years. What we find from the historical analysis is that the risk premium, the difference between the stock market and the treasury bonds, is approximately 6%. Let's go back to the NPV equals zero idea. How can we use this 6% to estimate the risk premium? The assumption we have to make, to use the 6%, is that the NPV of investing in the stock market during that period was zero. If investors were on average getting a zero NPV, by putting their money in the stock market. If the IRR is the same as the discount rate, then that 6% is exactly the compensation that investors demand to put their money in the stock market. Again we can take realized returns and use them to estimate required returns. But, as we just discussed, this assumption is less likely to be reasonable for the stock market. And it's very interesting, when you look at what practitioners and academics are doing these days. Most of the evidence that I see suggests that we are not actually using a risk premium of 6%. Most academics and practitioners are using a lower risk premium, when estimating future expected returns on the market. Why? Because the idea behind this is really that the 20th century was probably a great period for the U.S. economy. There was a time when US economy grew a lot. The US really became the dominant country in the world, so perhaps the NPV was not zero. Even if we take an entire century of stock market returns, investors might have derived a positive NPV. In that case, the 6% might be too high. If you use 6% as the risk premium, you assume that that gives investors a zero NPV. If the NPV was positive, that means the 6% was an excess return. What I suggest, the bottom line, that we use a number lower than 6%. I actually see many practitioners using 4% as the market risk premium. I suggest we use 5%, mostly for conservativeness. You don't want to lower the risk premium too much. Because that is going to reduce the cost of capital,. It mirrors for corporate finance applications. I suggest we use 5% as our risk premium on the stock market. Now comes the question for you, It should be simple to do this. Suppose we are doing this calculation in June 2015. What would be the expected return on the market? How much do you expect the market to return next year? Suppose we are in June 2015, how much should the market return between June 2015 and May 2016? Very simply, all you need to do is to add the 3% yield on the government bond, with the 5% risk premium and you would get an 8% return. So that is our zero NPV return. If things go, on average, as we expect, the market should return 8% and that should give investors exactly a zero NPV. That's why we can use that as a discount rate, it's a required return. Notice that here, in this formula, we are using 3%. You always start from the current T-bond yield. Don't take the historical ones. For bonds, as we just learned, we have great data on current yield-to-maturity. We know we have a good estimate of what the bond is likely to return in the next 30 years. We should always use that, instead of historical bond yields. We do 3%, plus our assumption for the risk premium, and we get 8%. That is our estimate for future market returns if we do this in June 2015.