Now, in terms of valuation, if you think about the standard coupon bonds, there's something interesting about the valuation. Here, you have to remember from our previous course or from your previous knowledge, remember the idea of present value. Present value is, you're going to receive amounts of money as time goes by. But because the 100 you'll receive in a year in two, in three, in four, or in 10, they come at different points in time. They have different value for you. The further away they are in the future then the lower is the present value or the current value of that amount. Therefore, what we do is discounting. We try to forecast what this asset is going to pay and we bring them back to the present. That's the idea of present value. Now, what is interesting about bonds is that these coupons that the bond is going to pay are completely fixed. There are exceptions to this, but again, the typical coupon bond, this installments that the bond is going to pay and the face value at maturity, all of them are completely fixed. Unlike a DCF, discounted cash flow valuation for a company, where you're trying to guess what the company is going to generate in terms of cashflows here, the cashflows are completely known. So there's no uncertainty in the numerators of the expression that you see there. Then there's a discount rate because again, not only the coupons that you're going to get as time goes by, they would be coming at different points in time, but also you have to adjust by the risk. We'll talk about the risk of bonds in a little bit. Basically, how much you're willing to pay today for a bond. That's why you put a V to indicate value, not necessarily price, because again, going back to our discussion of market efficiency, stocks can be mispriced. Bonds can be mispriced too. The intrinsic value of the bond that you will pay today, that's the zero that you're seeing there is the present value of the cashflows that the bond is going to pay discounted at a rate that has to do with the risk of a bond. That's the way, the relatively simple, of course, the deficit in the details sometimes. But they're relatively simple way in which we value a coupon bond. Now, of course, we talked about zeros, and zeros, as we said before, they have no coupons. What you would pay for that is basically the present value of the principal you're going to get in the future because there's nothing to discount in-between today and the end of that bond. When you do that calculation, we go back to what we mentioned in passing before. That is if you're going to get 1,000, five years from now, the valuation of that bond today, how much you'd be willing to pay has to be less than 1,000, simply because 1,000, five years from now will buy a lot less than they can buy today. Therefore, you never pay face value for a zero coupon bond. You always pay less than face value for a zero coupon bond. Finally, you get the consols. Consols have a little bit of a mathematical complexity in a sense, because remember, these are strictly speaking, bonds that will never stop paying cashflows. However weird that idea might be this is the ideal of a consol, but it's not that strange if you think about it. Because when you think about the discounted cashflow to value a company, companies don't end either. In principle, you're always discounting an infinite amount of cashflows. Well, this is even a simpler version of that because the cashflow that is repeated over and over and over again never changes over time. You see the present value calculation and then you see that this thing continues over time. If you're not familiar with mathematics, just believe me, if you're familiar with mathematics, you know that this is something that collapses into a very simple expression, which is the coupon divided by the discount rate, I should say. If you divide the coupon by the discount rate, that should give you the present value of those coupons that will come over and over and over and yet over again in the far future. That's in terms of valuation. Today we will not really talk about valuation, we'll talk about how to come up with a discount rate of a bond. I'll save the details for a minute from now. But it's important that you keep in mind that in a way up to a point, valuing a bond is simpler than valuing stocks, simply because we don't have any uncertainty about the cashflows. We know what the cashflows are going to be. Now, you might be thinking, well, but there may be companies or countries that issue a bond and then they don't pay all the cashflows. That is of course true, and that is what we call default risk. In a way, there's a probability that the cash flows will be paid. We're going to get back to that in just a second. Of course, if you promise to pay a series of cashflows, but the market doesn't quite believe that you're going to do that. That is going to be reflected in the market price. Again, we'll get back to that in just a minute. What can we say about the discount rate? Well, we need to go back for a second to the previous course and we say all discount rates have two parts. One part is what we call the risk-free rate and the other part we call the risk premium. The risk-free rate is the same for all assets. It doesn't matter whether you're valuing stock or whether you value a bond, or whether you value in real estate, the risk-free rate is the same as the starting point of the calculation. That essentially is what you would actually require as a compensation for the expected loss of purchasing power. This has nothing to do with risk, and it's got to do with expected loss of purchasing power. In other words, if you know that they're going to pay you back, if you bear no risk whatsoever, at least you wouldn't want to lose purchasing power. When the bond expires, you would want to buy pretty much the same things that you're buying today. That's the idea of the risk-free rate. But again, this doesn't apply only to bonds. It applies to bonds, it applies to stocks, it applies to real estate. It applies to alternative assets. It applies to all the other assets. So it's the same regardless of the asset, what changes from asset to asset, and the way we calculate it is what is called the risk premium. The risk premium is how much more you want in terms of return because now you're bearing some risk. This is where the CAPM when it comes to stocks, comes in, the CAPM says, look, there's a way to calculate that risk premium and it's by multiplying the market risk premium times the Beta. Then you add to the risk-free rate, and then you come up with a required return on equity. Well, there's also a way to calculate different one, although some people use the CAPM for bonds, but it's not very widely used. But there's a way to at least think about the risk premium of bonds, and is to think about the sources of risk. We'll talk about those in a few minutes. But at least let me introduce the idea of default risk which we mentioned before. This is related to the probability that the issuer is going to pay or not the cashflows that he promises to pay. Then there's interest rate risk, which has to do with the variability of bond prices and returns over time. Then there's liquidity risk, which is related to the ability to very quickly and more or less at the market price, to buy or sell that bond. We can go on and on and on. But what is important that you keep in mind is that when you calculate the present value in any of the three expressions that we have here. Well, that interests at that discount rate has those two components, has the risk-free component, has the risk premium component. The risk premium component that is made up of default risk and interest rate risk and liquidity risk. We'll mention a couple of other sources a little bit later on.
