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Coupon Paying Bonds

Coupon Paying Bonds
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We'll talk about the more commonly issued bonds across governments and companies. And I'm focused on the government because it borrows the most, it has the most interesting types of bonds, and also because the difference between a government bond and a corporate bond is complex, but not dramatic. In other words the structure of coupon paying bonds is the same with corporate bonds. Okay, so what is a coupon paying bond? Very simple, you should know that by now. It not only pays face value, but it also pays coupon. And so the nature of the bond is again explicit IOU between this time government and you. So let's just be a little bit crisp here and draw the timeline.
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I'm going to draw the timeline and what I'm going to do is I'm going to make sure you understand what's going on. You get face value here, but I'm going to make it real world now. Because coupons are paid every six months, you will do face plus C over 2. And every six months, so this is six months long.
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Every six months you paid a coupon and I'm writing it as C over 2. And you'll see in a second, when we do example why.
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Fundamental reason, and we'll see it, is that coupons are stated annually. Interest rates are stated annually. Interest rates are determined by whom? The market. Coupon is determined by whom? The issue of the bond. So the coupon is stated annually, and as a percentage of face value. So let's get to an example and then we'll do some number crunching. So the example is the following, pay attention, write it down. Suppose a government bond has a 3% coupon and a face value of $100,000. Immediately, what should you think? What is the payment being made? What is the coupon, 3% of 100 thousand. You do that calculation and it's $3000, right?
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Then you keep going and you realize that the maturity is six years, right? So you know now that six will be multiplied by two because actual life of the bond. In terms of compounding intervals, the actual life, the real life is six years but in terms of number of periods it's 12. What is the price of this bond, given that similar bonds yield a annual return of 4%. So as soon as you see 4% remember all interest rates are coded stated. So you'll take the 4% and you'll divide it by 2 to apply to a two-year bond. That's what we are focused on and we'll write out the formula. The formula will be like this.
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The formula will be C over 2. How many times c over 2. 12 times.
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How did I get 12? 6 times 2. One and then face value is 100 thousand.
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Now the formula is pretty straightforward but it's pretty cool. The price will be equal to the PV
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and in the function I'll just talk through it, and then when we use numbers we'll do it with Excel So if you look at this, the price will be present value, but they're three components to that present value right now. So the first component you will figure out is rate, yeah?
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The rate has to be what? We know that comparable bonds are paying 4%. But you'll think 2%. Okay so what do you do? You take rate and divide it by two. You can do it while doing Excel right, so you don't have to do it outside. Then you press comma. What else do you want to put in next? You want to put an n, but you know the stated n is 6, so you take n and multiply it by 2. So where n is the stated number of years, right? So you make the number of periods a function of twice as much. If the compounding was every three months, what would n be? N multiplied by four.
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If every 12 months, remember the loan example I did in module two. Is I made compounding every month because that's how you pay it back loan. So this is this. And then what is the third thing you enter in the formula? You enter payment, but the payment is happening as a function of, so this is what you'll do. You'll take 3,000, but divide it by 2, why? Because you're paying coupon every six months, which is half a year. You have to match with the timeline and the formula, otherwise, you're not gonna get much out of it, right? So if now I'm left with one last thing to enter, 800 thousand.
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Please remember, if you put a positive number here, you'll get a negative answer here. So you may want to enter a negative number because prices are never [LAUGH] never negative, right? So anyway, so that's something that we know how to do and so on. So let's do it in Excel and calculate it. So let's write out the formula.
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It's PV. So you do it with me. I'm going to do 0.04 divided by 2. Then I'm going to take n as 6 multiplied by 2, then I'll do what? 3,000 divided by 2. You can actually say 0.03 multipled by 100,000 right here in Excel, divided by 2. And then, I will enter a -100,000. So I've covered everything. Look that's the whole thing. In one form of PV I can enter the PMT and the face value. This challenge is, if the face value was in the middle of the period, which it doesn't happen for a bond. So suppose the bond was paying 100,000 suddenly in the middle.
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Then you can't use this formula because when you enter 100,000, it assumes that the future values at the end of your lifecycle of the bond. Okay and this, I believe, will work out to be $94,712.33. Okay, please do this because it's slightly different than what we did earlier. But now once you have this setup in your Excel, I'm going to ask you to try to do something fun with it.
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