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In prior presentations, we've been calculating the bond price, assuming a market rate, remembering that a bond can basically be thought of as us loaning money to the issuer of the bond, typically being a corporation or a government entity in return, receiving interest payments, typically semi-annually or annually, as well as a face amount lump sum at maturity, which could be equal to the amount we paid for the bond, which you can think of as, in essence, the return of the principal, but may differ in the event that the bond was issued at a discount or at a premium. Now, in practice, how would we get to or how would the market be determining the value of the bond? How would they know what and calculate what the market rate would be? Well, they would be comparing it most likely to bonds of a similar nature, bonds that have similar risk components to it. So when we purchase the bond, we have a risk component such as default risk, meaning what if we don't get paid the interest payments or the amount at the maturity of the bond due to the issuer of the bond going bankrupt or something like that and not having the funds to be paying us back. If we can choose between two bond issuers, one which is more secure than the other, the most secure typically being thought to be the US government bonds because it's not likely that the government will not be able to pay given the fact that they can tax and basically print money, then we're gonna go to the more secure bond. The issuers of the bonds that are less secure than you would expect that they would have to be paying out higher interest rates, paying bigger rent in essence on the money that they are going to be borrowing in order to get the funding there. So one of the major ways that we're going to be valuing that is by using the rating agencies which can give ratings on the bonds. So obviously from the issuer of the bonds perspective, they would like the bonds to be rated as strongly as possible because if the rating goes down, it would be perceived that there's gonna be more risk involved with investing in those bonds and therefore they would have to issue the bonds with a higher interest rate. It would cost them a lot more to finance things to get loan and to get funding. So, and obviously on the investing side of things, we're looking for the secure bonds. We would like to have a secure investment with low risk but obviously with the low risk also comes most likely a less of a return because it's more of a guaranteed return and that's how the market will react to it. So let's imagine a situation for example with a face amount of the bond is $1,000. It matures in 20 years, it's semi-annual interest payments. So we're gonna get the interest payments every six months, every half year instead of every year issued at the triple A rating. So when they issued the bond, it was at the triple A rating. We're gonna imagine that the rate or coupon rate on the bond is the same as the rate on the market because when they issued the bond, they issued it for the market rate. And then as time passes, which we're gonna imagine like right after for something happens suddenly, we're gonna say that the rating goes down to an AA3 rating. And there's three major rating agencies that help to kind of rate the bonds but we're gonna imagine it goes down to an AA3. And so you could see that that means that the market rate is going to be going up because in order for us to invest in a bond that's gonna be more risky, we would expect a higher return. So if the rating of a bond of a corporation's rating goes from a high rating of triple A to an AA3, that's gonna have an impact on the debt securities. So first, let's just prove this first calculation. We're gonna imagine that both the rate of the bond coupon rate and the market rate are 9%, which means when I present value, the first future cash flows, we should get to the issue price, the $1,000, the bond not being issued at a discount or premium at that point. So if we present value, for example, the stream of interest payments, we'd have the present value of the rate, which we're gonna say is the 9% market rate divided by the two because we're looking, we're gonna assume that's a yearly rate, we're gonna divide it by two to get to the semi-annual comma number of periods, we're gonna say is 20, we're gonna multiply it times two, and it get a little bit confusing when we go from semi-annual to annual, but we wanna practice these a little bit more complex calculations with the semi-annual calculations and assuming these are the annual rates. And then comma, we've got the payment, which is gonna be the $1,000 times the coupon rate, which we're assuming is also 9% because we kept that at the same rate as the point and they issued it divided by two. So how much interest payments are we gonna be receiving? We're gonna be receiving 1,000 times 0.09, that would be a year divided by two because it's semi-annual $45 every six months, not for 20 years or 40 time periods of six months. So same rate that we use for the coupon rate and the market rate present value of the 1,000, bringing it back, that would be the rate of the 9% comma, number of periods is gonna be 20, sorry, 9% divided by two, number of periods is 20 times two, comma, comma, future value $1,000, that's valued at the 171.93, adding them together, we should get to the 1,000 because we use the same rate for the market rate and the rate on the bond, which could be the case at the point of issuance. And then we're gonna assume the next day, right after that the rating agency just tanked them and they went down to an AA3. Well, now that bond looks much worse because now the market's gonna be demanding more interest for a similar type of bond given its current ranking system in terms of the risk involved with it. So now we've got the present value of the interest payments would be calculated as present value of the rate now at the 11%, which we're saying is the market rate divided by two to give us the semi-annual comma, number of periods we're gonna say is 20 times two, comma, and then the payments are still calculated the same, which is the 1,000 times this 9%, which we said was the coupon rate, that doesn't change, the market rate now is the one that changes. So now we've got a difference between the two rates that at the 9%, so 1,000 times 9% divided by two. So then we're gonna say the present value of the face amount, $1,000. We're gonna say the rate is now at the 11% divided by two, comma, the number of periods is now 20 times two. The future value is the $1,000. So did I get the rate right? The 11% divided by two should be the rate, comma, number of periods 20 times two, and the face amount 1,000 that is gonna be brought back. And so now we've got the discount. So clearly we would be purchasing it at a discount given the fact that now the market wants a return of 11% for similar bonds of a similar risk nature, but when it was issued, it was issued up here when it had a higher rating at the 9%. So it's paying out 9%, but now the market wants 11%. We can't change the 9% if it had already been issued. So we're gonna compensate for that by adjusting the price and we're gonna say we'll pay you 839.54 for that bond so that, and then you can pay me back basically the coupon rate based on the 9% and then we'll get the 1,000 at the maturity. So once again, bottom line, of course, being that part of the way the market is going to determine the risk level is gonna be by the bond rating agencies in comparing similar bonds that are grouped in basically a similar nature and as a bond goes from a very secure rating to a less secure rating, that's gonna be very bad for the bond, you can imagine if US government bonds, for example, if the rating goes down our debt would be very bad for the debt, right? Because then in order for us to finance it, it's gonna cost a lot more. So it's very advantageous for trust to be there with regards to the lending process. If the trust is there, the lending is more likely to be there as trust dissipates then the cash flow dissipates and it costs a lot more to get the lending. On the investment side, of course, we might be willing to invest in bonds that are much more secure, even though they have a lesser rate of return if we're investing in people that are less secure then we're gonna want a higher rate of return to compensate. That's the general idea.