So hopefully you've had the time to kind of stare at what that bond is trying to say, and so on and so forth. Let's, we did the timeline and formula. Just remember, match the interest rate, with the periodicity. Always make your interval of thinking the compounding into it. And it'll be pretty obvious when you're looking at the bond or whatever the idea and so on what it is. Match the compounding interval with the interest rate. Let's do some calculations. And here I'm going to go over to my friend Excel. And there are some numbers from the past which we have known for the time so I'm going to stick in cell C. If you can see me, hopefully you are fine. What I am going to do is I'm going to do PV. Why? Because I am trying to do a PV of a bond. And what was the interest rate on similar bond? Remember it was 6%, but we are doing everything semi-annual. 0.03. How many number of periods? 20. What is the pmt? 30. And what is the future value? You can do everything. What do you notice? I purposefully picked this example first construction. What do you notice? The price of the bond is equal to the face value. Yes? Do you notice that? So let's go here and I'll show you the intuition for it. The price of the bond is the face value. That means today, the price exactly go to the face value, even though that face value is coming 20 periods from now. And reason for it is, what do you see the relationship between coupon, which is like a percentage, and the interest rate. They are both what? The same. 30 over 1000 is 0.03 and what is my interest rate? 0.03. So what is happening? Very intuitively, the coupon is the new numerator, it's coming to you. But time is hurting you at the same rate. So they cancel each other. And what are you left with? $1,000. So this is a neat thing that they'll say in the real world, that the bond is trading at face value. Right? At par. Par, P-A-R, is face value. Let's assume now that the interest rate in the real world is actually 4% per year, which is what per month? 2%. What does happen to the price? It's gone up. It's greater than face value. It's called trading at a premium. Premium doesn't mean you're paying a higher price than you should. Premium simply is relative to thousand, right? Discount is relative to the thousand too. Okay, 1163, quick question. Why did this happen? Forget about the exact price, and this is what I want you to have in your gut, a feeling for finance, not just numbers. You know the answer has to be greater than thousand, why is that? Notice the coupon is still 30 and it cannot change once you've issued the bond because what’s the coupon, who determines the coupon, the person issuing it. And we are assuming the government is not going to default on the 30 right? But what can change is the market rate that we are using. So the market rate is now 2% and the coupon is 3%. So what is it going to do? It's going to make the value of the bond go over 1000, simply because the value you're getting it at a higher rate coupon than the discount rate. Now suppose the price is such that the rate of return that you're getting in a similar instrument out in the market is actually 8%. And half of eight is what? 4%. What will happen to the price? It will go below a thousand. And this is called selling at a discount. Zero coupons always sell at a discount. Zero coupon bonds always sell at a discount because there's no coupon compensating for it. Whereas coupon being bonds can and do sell at a discount, but what has to be true? Let's look at the parameters. The face value is $1,000, I'm not changing that. The coupon is 30, I'm not changing that. The n is 20, I'm not changing that, I'm standing today, what have I changed? The interest rate, now I'm hurting the bond's price at a higher rate than the coupon flowing in. So what happens? You get less than face value. So this tells you something about the pricing of bonds, which is this. Interest rates go up, price goes? Down, but for zero coupon bonds there's a very neat, I mean, for coupon paying bonds, government bonds, there's this neat relationship where the interest rate and the coupon rate are the same. The price of the bond has to be the face value. And then if the interest rate is higher, it's lower. And interest is lower than the coupon rate, price is higher. So let's try to take this learning and graph it. So you've done the calculations and I would really encourage you to go back and do those calculations again. Right? But I'll write out what you should find. So, if coupon rate is greater than r, price will be greater than face value. If coupon rate Is less than r at the specific time, the price will be less than fair face value, and if coupon rate is equal to r, price will be equal to face value. So this is what you should find, and just mess around with this, because it will help you. So what I would like to show you now is a graph, and this graph is important. Price, r, 0. It looks like this. So the price of a bond falls when interest rates goes up, all right? That's what it's showing. And that makes sense. So, if the interest rate is 6% or 3% per what? Six months. And the coupon rate of this bond was what? 3%. What would the price be? 1000. We just did this. Okay, one thing I really want to emphasize about this. Coupon rate is not a market thing. It's fixed by the government. Don't ask me why, right because that's like getting into detail. It's something determined by the ability to pay periodically versus face value, right. So, this curve is telling you the relationship between bond prices and interest rates. And let me just give you one little bottomline thing. Price goes down if r goes up. Second short term versus long term. Which bonds are more price sensitive? In other words, if interest rates changes, which bonds will be more sensitive? Bonds that are Which part? Long term. Finally, whose price will jump around most? Zero coupon or Fifth coupon bond? And let me for simplicity keep their maturities the same. Whose price for bonds around more? And it's kind of related to point number two. If you have a zero coupon bond, where is all your money coming from? And supposing it's ten years maturity. All your money is coming ten years from now. And you have a ten year same face value coupon paying bond. What has happened with this bond? Some of its moneys coming earlier and not all is coming at the end. So the zero coupon bond will be more sensitive to changes in interest rate compared to an otherwise identical. Coupon paying bond. It's not perfectly identical, but the only difference is the coupons. Okay, so let's take this break because this is an interesting point to think about and I want you to know this stuff inside out, because this is the simplest kinds of bonds and this is what the world talks about all the time. Every government issues these and so on. So we'll come back to issues related to it but in the next chunk, I will go dig a little deeper as we go further.
