welcome to course one unit two lesson three how do you value a bond and yield maturity this lesson has four lesson objectives the first is understanding simple interest the second is understanding compound interest on bonds the third is understanding the current yield and the fourth is understanding yield to maturity so let's get started okay as you can remember from the second lesson we have our bond investor Jesse and Jesse has his bond from real estate empires and what he's going to do is we're going to look at different ways in which Jesse can value this bond so really there's there's two different ways you can look at the simple interest or you can look at the compound interest and under each one of these you can see I have the coupon yield and the current yield under the simple interest and then the yield to maturity under the compound interest and that yield to maturity is really the thing that we've got to understand at the end of this lesson so I'm going to show you why all three of these are different and why the young to maturity is the one that you really need to understand so let's go ahead and get started with the simple interest so in order to understand simple interest all you're going to do is you're going to add up all the value of the coupons and you're not going to assume that you're reinvesting any of the coupons you're just simply collecting those $25 payments throughout the entire term of the bond and you're just adding those up and that's your simple interest the chart might look busy but as you as you zoom in here and you look at the first coupon you can see the first coupons for $25 the second coupon is for another $25 so the total that's a running total you see on the chart so after two coupons Jesse would have $50 in his hand after the third coupon he had $75 and after the fourth he'd have a hundred and as you continue to scroll down through the chart you can see as we arrive a coupon sixty that Jesse has $1,500 from all the coupons and the way that that was figured out was pretty simple and I guess that's probably why they call it simple interest is you just take the number of coupons which for this 30-year bond he would receive 60 coupons and you multiply that by the coupon payment which is $25 and you can see it adds up to $1,500 so the way to understand the simple interest on this is if Jessie with just simply by the bond at the very first day and he hold the bond through maturity and he wouldn't be reinvesting those the proceeds from his coupons and just simply holding on to them and you know holding on to the cash itself the value of the investment would be fifteen hundred dollars and we we're not going to count the thousand dollars he used to buy initially in the thousand dollars he gets back at the end we're just going to value all those coupon payments because because that's the money that he made on the investment so when we talk about the coupon yield okay and this is under simple interest the coupon yield is nothing more than taking one year's worth of those coupon payments which is $50 and dividing that by the par value you're always going to divide all the coupons for one year divided by the par value and that's going to give you your coupon yield which is five percent and that's all there is to keep on yield it's that simple so when you talk about the current yield on a bond you're typically talking about a bond that's been on the market for a few years you're not buying it on the very first day and so what you have to look at is the price that you're buying that bond for compared to the coupon payments so in order to calculate the current yield we're just going to take the the coupon payment that you would receive for one year and divide it by the price at which you bought it for that the bond itself and you just divide those two numbers and you come up with the current yield so you can see here if Jessie was going to buy this bond regardless of how much time it was after the initial issue date there could only be one year left on the bond or there could be 25 years left on the bond the current yield is taking that coupon which in the first scenario here is gonna be $50 and we're going to divide it by the price and we're just going to say that the price that he's going to pay for it is $1200 so when you do that you get a current yota of 4.2% just 50 divided by 1200 so as we move over to the the actual face value matches the actual price of a thousand and a thousand you take that coupon of $50 divided by a thousand because that's the price you're buying it at and you can see that the current yield would be the same as the coupon yield now if we talk about a bond that he's purchasing at a discount let's say $800 you can see that the current yield goes up to six point three percent so we're in this example we're talking about the same exact bond no difference in the bond just the price at which he's buying that bond at and how that price is affecting the yield because he's getting it at a more expensive price now the problem with the current yield in which you're going to find out later the problem with this is that it doesn't account for the amount of money that you lose or gain whenever the bond matures okay so as you can see let's look at this first one that we have where the let's just say Jesse bought this for $1,200 okay the current yield on that is four point two percent but what about the $200 that he's going to lose when this bond matures because we know whenever the bond matures he's only going to get $1,000 back because that's the par value so this does not account for that loss that $200 loss that he would have whenever he would go to sell the bond and so likewise when you look over at if he could buy the bond at $800 and regardless of how long he holds it when the bond matures the bond is going to be worth $1,000 so that's a $200 profit that isn't calculated into that current yield percent that you see there so when we talk about yield to maturity that's where that's going to really come into play so just just so you know when somebody quotes you a current yield it's not accounting for that difference between the price you're going to pay and the par value whenever the bond matures so let's talk about the compound interest on a bond so as we look at our chart let's go to the first coupon so after six months Jesse would receive and this is we're going to assume that Jesse bought the bond as soon as it was issued just like the very first scenario we looked at and so you can see Jesse would receive as $25.00 after the first six months and then the second coupon which would be six months later he's going to receive another $25 check but here's what's different that first coupon of $25.00 we're going to assume that jesse has invested that $25 into another investment nothing to do with this bond but he's invest that into another investment which is going to provide the same interest rate as what he's receiving on this bond which is 5% so that's the big assumption because in six months let's assume Jesse bought this bought the bond right now and then six months later he gets his first coupon then when he receives that first coupon there's no guarantee that he's able to reinvest that first $25 payment into another 5% yielding security so that's where when you get into the compound interest and figuring out what this bond is worth if there's a little bit of guesswork and I'm gonna give you some tools in in the second course to help you estimate what you think you could get on you know on an average throughout the duration of a bond but for right now let's just make this really simple and let's assume that whatever coupon yield he has on this bond is what he can reinvest his coupons back into at that same rate so if that was the scenario after he receives that first $25 payment let's assume that he reinvested that into a completely different investment that he invested it into something that's going to make 5% so as we look at the second coupon that initial $25 has matured into 26 dollars and then he received the $25 second coupon for a total of 51 dollars so as we look at the third coupon we know that jesse has 51 dollars that's maturing at a 5% interest rate as he's waiting for that third coupon which is going to be another $25 payment so each one of these coupons were assuming that the previous amount that previous total is compounding at 5% so as you can see when we when we go through these coupons when you get up to the 60th coupon Jesse would actually have three thousand four hundred dollars at the end whatever he receives his his last coupon payment okay so let's compare the simple interest versus the compound interest you can see in the simple interest this would be for the total duration as if the first day that Jesse bought it clear up to thirty years later on the simple interest calculation you're only valuing the bond that it's going to make $1,500 for you during that duration but when you look at the compound interest you can see that it's $3,400 if it's reinvested at 5% for each coupon so that's a pretty big difference I mean we're talking more than double the money on a bond so let's under the compound interest let's look at the yield to maturity now as we talked to earlier we said that we weren't going to when we were talking about the current yield we weren't accounting for the difference that somebody would pay for a bond versus what the bond would be redeemed for whenever it is whenever it reaches its term and that the face value is paid back to the investor so that's what the yield to maturity accounts for not only does it do the compound interest but it also accounts for that difference between the price that you pay and the face value so that's why this number is really important because it really wraps all the variables together and it gives you a real estimate of of what you're going to get if you would buy any bond and hold it clear to maturity and that's how you have to look at the value of the bond so let's take the very first scenario here and what we're going to assume is Jesse's going to be buying a 30-year bond but he's going to buy it 15 years after the bond has been on the market so there's 15 years remaining until the bonds mature and each one of these scenarios are exactly the same the only thing that we change between each of the three is that the price that Jesse's paying for each one of these bonds okay so the first one he's going to be paying a premium for the bond meaning he's paying more than the face or par value so the first one he's going to pay $1200 for okay so as we look down the coupon payments that he's going to receive over the next 15 years amounts to 1098 dollars now we're assuming that he's reinvesting each coupon at 5% okay so that's why you have kind of an odd number there so the coupons 1098 dollars the par gained and lost he's going to lose $200 on the fact that he he paid a premium for the bond and whenever it matures he's only going to get a thousand so he's going to lose $200 there so that $200 comes right off the top of his coupon payments for a difference of $898 so if he buy this bond at that price he at he held it clear to the maturity he's going to make $898 so as we look to the yield to maturity so that yield would actually be 3.3 percent for that for that purchase price okay which is significantly lower than the 5% coupon that you might think when you look at it from a simple interest in in coupon yield perspective so let's go to the second one let's assume that he bought the $1,000 par bond he bought it for $1000 he's got 15 years remaining on it and so the coupon that he agrees the coupon payments the compound interest on those coupon payments would be the same thing 1098 dollars but he has no gain or loss from from his purchase price to the face value so the difference is just going to be the 1098 dollars and the yield to maturity is 5% okay so when you're buying it for the same price as what the face or par value is you're going to actually get and you're going to see that coupon you'll be exactly what it says on the bond so here's where it's really interesting is when we look at buying a bond that's selling at a discount okay so we go down the coupon payments are exactly the same the par value you're actually gaining because you bought it for 800 but you're going to get a thousand back when the bond matures so you're going to get a $200 plus so your difference is 1290 dollars so your yield to maturity on that bond is 7.2 percent a year even though it's a 5% coupon bond so you can see how much of a difference here occurs based off the price that you're buying these bonds for anytime you're paying a premium for a bond your yield to maturity is going to be much different than what your coupon yield is and that's the thing you really got to understand and that's why understanding yield to maturity is the most important thing you can do when you're understanding how to value a bond okay so you might be thinking to yourself okay how did he figure that out how did he figure out the yield to maturity well here's the equation and it's I got this from Zen well calm it's kind of a complex equation but we've made it easy for you here buffets books we have the calculator on this page and you can go there we have some practical exercises a video for the practical exercise to kind of show you how to use the calculator and you can try this out for yourself and you'll see that using the calculator solves this really hard math problem for you you don't even have to worry about it so hopefully we've made it easy for you okay so just a quick overview I want to show you the difference as we looked at those different purchase prices and the terminology that we learned all in one so let's we're going to zoom in here and look at the very first one so this would be assuming that we're that the bond has been on the market for 15 years and that there's 15 years remaining until the bond becomes mature so let's look at if we would buy that bond for $800 and look at the terminology so the coupon yield is still 5% because in order to figure out the coupon yield all you're doing is taking the the coupon payment for the year divided by the par value so it's going to say 5% as you look across the board the thousand-dollar bond price would be 5% and the $1,200 bond price would be 5% so you can see that's really misleading when somebody gives you a quote based off the coupon yield that really doesn't mean anything because the price that you pay is going to drastically affect what you actually see on your on your yield so let's look at the current yield to figure out the current yield we're taking the coupon payments for one year and we're dividing it by the price that you're paying and as you can see the first one for $800 was 6.3% for the thousand it was 5% and for $1200 it was 4.2 percent okay but those aren't the real numbers we know that so when we go down to the yield to maturity this is actually counting for the difference between the price we're paying and accounting for what we're going to receive back on the face value of the bond as you can see the numbers get even more different than what you saw before with the current yield where the $800 bond is actually going to give you a 7.2 percent return which is great the thousand dollar bond price is going to give you a 5% return and the 1200 dollar bond is going to give you a 3.3 percent which is significantly I mean that's one point seven percent lower than what you would be expecting if you were just looking at the coupon itself so this stuff is really important I would recommend that you go back and re-watch this video if it really didn't sink in the first time maybe even go back to lesson 1 under this unit 2 and start from the beginning and watch all three of these videos again and it would really start to maybe click for you if you didn't get it the first time so make sure you understand yield to maturity that's the one you really want to understand and have fun working with our bond calculator below this video so in this lesson we had four lesson objectives the first was understanding simple interest understanding compounding for bonds the current yield and yield to maturity and thanks for joining us in unit 2 and we look forward to seeing you in unit 3