 Hello, and welcome to the session. This is Professor Farhad in which you would look at bond yields and yields to call. This topic is covered on the CPA exam as well as the CFA and an essential board principles of investment course. As always, I would like to remind you to connect with me on LinkedIn if you haven't done so and subscribe to my YouTube where I have over 1800 plus accounting, auditing, tax as well, finance and Excel tutorials. If you like my lectures, please like them and share them. If they benefit you, it means they might benefit other people. Connect with me on Instagram and Facebook. On my website, farhadlectures.com, you will find additional resources, a complement and supplement discourse as well, your other accounting and finance courses. Let's do a quick review about basics of bonds. How do bonds work? Now, if you don't have a good understanding, sorry, about bonds, please view the prior recording and display list because you need to know a little bit about bonds. Well, bonds have a fixed interest payment. And if you know about this, it's called the coupon payment. It means when you buy a bond, you are promised a fixed amount of money based on this coupon payment or based on this coupon. They give you a coupon rate, a coupon percentage. For example, if you have a bond with a face value of a thousand, they might say the coupon rate is 8%. That's $80 per year. They pay to you twice a year, $40 every six months. Now, although the payment is fixed, although this payment is fixed, the $40 is fixed, the yield on the bond will vary. Now, why will the yield vary? Why? Because the bond value varies with market interest rate because the bond might go up or might go down as time goes by. Now, why would that happen? Because of changes in interest rate, mainly changes in interest rate. So, when the interest rate goes down, and this is what we learned in the prior session, when interest rate goes down, when interest rate goes down, declines, bond prices go up. Why? Because if you hold the bond and the overall interest rate went down, your bond is more valuable because relative to the current interest rate, the rate went down. If your bond went up in value, your yield, your return will fall. In case you want to buy this bond, your return, your yield will fall. The opposite of the interest rate rises, your bond will fall because you have a bond that's relatively lower than the market. Well, let's use some numbers to kind of this make sense. So, let's assume you have a bond with a coupon. I mean, it's better to do it again. Coupon, and this is the market. We have the coupon and the market. Let's assume the coupon rate is paying 8%. Suddenly, interest rate declined to 6%. If you have a bond that's paying 8% and the market rate now is paying 6%, interest rate declined. Your bond value goes up. Then your yield on your bond will fall and we'll see why in a moment because you're paying more for that bond. When the interest rate rises, so if you have a bond of 8% and interest rate now is 10%, the market rate is 10%, your bond goes down in value. When your bond goes down, your return on that bond, somebody buys it, will rise. So, the best way to illustrate this is to just to take a look at an example real quick. Suppose an 8% coupon bond is selling right now for $1,276. What is the average rate of return would be earned by an investor purchasing this bond? So, if you purchase this bond, how much will you earn? Now, you might say 8%. I would say no. Your coupon rate is 8%. That's true. That's true. But here's what's going to happen. You're going to get $80 every year broken down into $240. So, what's going to happen is every six months, your return, because you paid this much, your return is $40 divided by $1,276.76. So, this is going to give you the approximate return, the approximate return. Now, let's take a look at how you actually compute the approximate return. But notice what happened here is, first of all, why would your bond sell at $1,246? Maybe because interest rate went down. Not maybe because overall interest rate went down. As a result, your bond went up in value. As a result, your yield went down. Okay. So, let's see how it works. So, to compute this, again, I told you it's around, it's $40 divided by $1,276. It's approximately 3%. Let's look at the computation. You could do this using your financial calculator. You input n equal to 60. We have 60 payments because it's a 30-year bond. The payment is $40, which is $1,000 face value times 8% times 1 half, which equal to $40. The payment, you're going to pay negative $1,276.76, and the future value you're going to get back $1,000 when the bond mature. So, when you do this, you click on compute, and you will find out that the interest rate is, as I said, approximately 3%. If you do this computation, it may be a little bit different. If you use Excel, it could be a little bit different, but it's around 3%. Simply put, what does it mean? It's around 3%. Well, you bought a bond that's paying 8% coupon, but you're not really earning 8%. You're earning 3 now annually times 2. You're earning 8 annually. You know, earning 8 annually because 3% every six months. So, it's very important to understand this. Let's take a look at this exercise to see how it works. And I'm going to go through a financial calculator online just to show you how this works. But before we go through the financial calculator, I want to make sure you understand the big picture here. A 20-year maturity bond with a par value of $1,000 makes a semi-annual coupon payment at 8%. So, here we have n equal to 40. We have 40 periods, i equal to 4%, because everything is semi-annual. Find the equivalent and effective annual. So, we have to find the equivalent and effective annual yield to maturity of the bond. If the bond price is $1,950 and $1,050. Now, let me tell you this. If we assume it's $1,000, the rate will be per year 8%. If we buy it for $950, the rate will be greater than 8%. If we happen to buy it at $1,050, the rate will be less than, our effective rate will be less than 8%. Why? Because think about it, you are constantly getting $40 every, sorry, yes, you are constantly getting $40 every six months, which is $80 per year. Well, if you're getting per year $80, $80 divided by $1,000 is 8%, because you paid $1,000. If you have to pay $950, $80 divided by $950, it's going to be an approximate, but it's going to be more than 8%. And if you pay $1,050 and you're getting $80, your return is less than 8%. Now, the best way to show you exactly, I'm going to show you, show it to you on a financial calculator I found on the web, but because I could not find an actual financial calculator, but it's good enough that it will illustrate the point let's take a look at. I'm going to be using this as a financial calculator. And basically here, let's start with $1,000. So what I did is I paid $1,000, so I paid $1,000, so negative $1,000. I paid $1,000. My future value is $1,000. The number of payments for this bond happens to be 40, happens to be 40. And the payment amount is $40, compute the interest rate. Notice the interest rate is 4%. 4% times 2 is 8%. Remember, if I paid $1,000, it will get me 4%. So the rate is 4%. Now, if I change this, if I paid $950, notice the rate will be higher than 4%. Whoops, negative $950. Calculate this, the rate is 4.2625, which is more than 8%, which is 4.26 times 2 is greater than 8%. If I paid $1,050, my interest rate is less. It's 3.75 times 3.756. Rounding is 3.76 times 2, I will be less. I will be less. So let's go back here and kind of just tell you what the rates were, and we can go back and answer the second question. So the rate were for the 9th, let's start with $1,000. With $1,000, we said it's 4%, or annually 8%. For the 950, we said that the rate is 4.26 times 2, which is 8.52. For the 1050, the rate was 3.76, which is 3.76 times 2, around 7.66. Those were the rate, okay? Find the bond equivalent and effective annual rate. Now, the effective annual rate, if you want to find the effective annual rate, what you do, because this is the 4.26 is semi-annually, what you do is you take 1 plus 0.0426 and what you do, you raise it to the second power because it's 2 period minus 1, so the effective rate is 8.7%, because this rate is compounded semi-annually and we'll do the same thing here, 1 plus 0.0376, raise to the second power minus 1. We did this in a prior session, we learned how to compute the effective annual rate, and that's going to give us, sorry, this is going to be 7.66. I apologize, this is 3.76 or 7.52, sorry, apologies about that, so 7.52. Now, what happened? Now, assume that the bond makes its coupon payment annually. What are the yields? Why are the yields you compute lower in this case? Why are the yields lower? Yes, they're going to be lower. Why? Because they don't compound. So the yield, if it's annually, it's 8.52. It's not 8.57. For this one, it's approximately 8%, and for this one, it's going to be the 7.51, not 7.66. Why? Because it's not, you're not getting the payment six months earlier, you're waiting till the end of the year. Therefore, the rate is the rate that you computed initially times 2. This is the annual because it's not compounded. Once you compound it, it's going to go up. It's going to go up. So the effective annual rate for a semi-annual rate is greater. Now, the other topic we need to discuss is yield to call, and what is the yield to call? When the bond has a callable provision. Callable provision means the company can buy it from you at any time, and you have to give it up. You don't have an option. Usually when they buy it, they pay you a premium, but what happened is they can buy it before it matures. So when you compute the yield, you have to call it yield to call. So this is how we do this. Suppose an 8% coupon bond 30-year maturity sells for 1,150 in a callable and 10-year at a price of 1,110. So let's compare this to another regular bond. So let's look at this. This is the bond that we're discussing. So it pays $40, the coupon rate, which is $1,000 times 4% semi-annually because the coupon is 8. Number of periods is 20. Why number of periods is 20? Because it's a 10-year. In 10 years, they can call it. So we have to know how much do we earn? What's the yield if we buy it? Because we have to assume it might be called. The final payment is $1,100. The price you pay today, $1,050. And we have another bond, the same bond, and if we let it go until it matures, this is the data. If it matures, they pass only $8,000. We paid $1,150. And we have to pay, we have to wait for another 10 years, I'm sorry, another 20 years, which is additional 40 periods in total 60 periods. So let's take a look. So yield to call is 6.64. All what you have to do, just input the same information in the calculator and equal to 20, the present value, what you're paying today, negative $1,150, the future value. You have to be careful. This is basically the key is to remember when you input the future value, you are getting the $1,110 payment equal to 40. So the yield to call is 3.32 or equivalent bond yield 6.64 multiplied by 2. The yield to maturity, again, here you put the what you are paying and the future payment is a tap that the future value is 1,000, not 1,100. The yield is semi-annually 3.41 or 6.82. So just in case you need to find the yield to call, remember, the future value is how much you are going to be getting paid. Here they're saying they're going to pay you 1,100, which is 110%. They're paying you 10% premium above the power value of the bond. Here they're at maturity, they'll pay you exactly 1,000. And in the next session, we'll talk about what happened to the bonds as they mature, which is bond prices over time. When they mature, I'm going to tell you right now, they would always go back to power value, whether the bond sold at a discount or a premium or trading at a discount or a premium. If you wait until the bond mature, it goes back to its maturity value, power value or face value. As always, I'm going to ask you to like this recording. Please share it if you find beneficial and don't forget to visit my website farhatlectures.com for additional resources for this course, as well as other finance and accounting and CPA preparation. Good luck, study hard and stay safe.