 Hello and welcome to this session in which we would learn how to find the price of a bond. This topic is important whether you are taking financial accounting, intermediate accounting, studying for the CPA exam, or studying for the CMA exam. Finding the price of a bond is important because it also covers the concept of time value of money and the concept of discounting. Whether you are an accounting student or a CPA candidate, I strongly suggest you take a look at my website farhatlectures.com. I don't replace your CPA review course, you keep it. I am a useful addition to your CPA review course. I can add 10 to 15 points to your score by providing you with alternative resources, lectures, multiple choice, true, false, exercises. Your risk is one month of subscription. Your potential gain is passing the exam. If not for anything, take a look at my website to find out how well or not well your university doing on the CPA exam. My course catalog include practically all of your accounting courses and my CPA review courses are designed to align with your CPA review course, whether you're taken Roger, Becker, Gleam or Wiley. I do have those courses aligned. I also have all previously AI CPA released questions for the past 10 years. You can find them on my website with detailed explanation. If you haven't connected with me on LinkedIn, please do so. Take a look at my LinkedIn recommendation, like this recording, share it with other, connect with me on Instagram, Facebook, Twitter and Reddit. So how to find the price of a bond? It's very important to understand what is a bond. What does a bond look like? What is a bond? A bond is a form of borrowing. When a company wants to borrow money, they can go to the bank and ask the bank for a loan or they can go to the market and ask anyone who's willing to give them money, lend them money. That's what a bond is, a form of borrowing by the company. Usually, bonds comes in $1,000 denomination. They have $5,000, but usually we're going to be dealing with $1,000 denomination and specifically we're going to be dealing with corporate bonds. The bond will always have a face value. What is a face value? The face value is how much this bond is worth once it mature. Sometime it's called the face value, sometime it's called the maturity value. Now I'm going to explain what the face value is. Think if you are looking at a $100 bill or a $50 bill. You would literally see the number 100. You would literally see the number 50 and this is how you know it's $100 or a $50. So the face value is something that's printed on the bond. That's the face value. What's on the face value of the bond itself? There's always an issue date. So when we issue a bond, there's a date. For example, for the bond that we're going to be issuing, it's going to be December 31st, 2022. And the face value for our bond, it's going to be $100,000 face value or maturity value. So basically, whoever have this bond at maturity will get back $100,000. Coupon rate, stated rate or contract rate. The bond will have to pay a certain rate. So when you want to borrow money from people, you have to promise them, you have to tell them, look, give me the money, I'm going to give you your money back, plus interest payment throughout the life of the bond. So you have to tell them, what is the coupon rate? What's the stated rate? And what's the contract rate? How much are you offering? And sometimes it's called the offering rate. So many terms are used for the same thing. For our purposes, we're going to assume this is 8%. 8% means the bond will pay 8%, 8% of $100,000. Well, because you want it, you want to be compensated. Also, you're going to have to have interest payment dates. Okay. The first thing I need to tell you, this 8%, that coupon rate, stated rate, contract rate, this is a fixed amount. Fixed means once that rate is offered, it no longer changes, because this is how much this bond is paying. It's a printed on the bond itself. Notice here, it's on the bond. So imagine this is the bond, it's printed on the bond itself. Also, bonds, usually corporate bonds, they pay interest semi-annually. For example, for the purpose of this bond, we're going to assume it's going to pay interest on June 30th and December 31st. So it pays interest twice a year, rather than once a year. And that will make a difference as well in computing the price of the bond. So that's also a part of the bond. And the bond will have a maturity date. The maturity date is when can the bond holder, the person that holds this bond, can go back to the company and say, I would like my $100,000 back. This is the maturity date. I want my face value. In the maturity date, for our purpose, it's going to be December 31st of 2024. So simply put, this is a two-year bond. So it's a simple bond. But the concept will be the same, whether it's a two-year bond, 20-year bond, 30-year bond. The concept is the same. So those are the basically the main component of a bond. Now also for a bond, there's another thing that we have to worry about. And I kept it separately for a purpose. I gave you some space here to talk about the market rate, the market rate or the discount rate. And I talked about this in the prior session when I discussed how a bond is, when is a bond sold at a premium, discount or par. And what is the market rate? This company here, let's assume this is Adam Company. Adam Company is offering 8%. So Adam Company says, I want to borrow $100,000. I'm willing to pay 8% if you are willing to lend me your money. Well, here's what's going to happen. All the lenders, they're going to look at the market. They're going to look at the market of similar interest rate, similar companies to yours. And you pay the market, they're going to have a market rate. And we're going to have your coupon rate. And remember, I can go with the coupon rate. I can go with stated rate, whatever. So if you are paying 8% and the market is paying 8% and this should be a review for us. If you are paying 8, the market is paying 8, the bond will sell at a par. It means you will get your 100,000 when you try, when the company tried to sell the bond. If the coupon rate, if you're paying 8% and the market is paying 10%, no one will give you the full 100,000 because they can give it to someone else and earn 10%, which is $10,000 a year, you're paying them $8,000 a year. Therefore, your bond will sell at a discount. If your coupon rate is 8% and the market is, and let's assume, let's assume, yeah, let's assume you are, what are we going to change? Let's assume you are paying now, you are paying 12% and the market is only paying 10. Well, in this situation, your bond will sell at a premium. Why? Because you are paying more than what the market is paying them and you have to understand those relationships. Once again, we discussed them in the prior session. Now, what we're going to be learning, adding to this session, the addition is how to actually find the discount price, how to find the premium price. Simply put, how to find the price of the bond. If it's at par, if it's at par, it's you're going to get 100,000. So I'm going to illustrate when the bond sells at a discount, when a bond sells at a premium and how to find exactly that exact price. So we're going to find the price of a bond. So to illustrate this concept, I'm going to be working with the add-on bond. Par value 100,000, they want to borrow 100,000. The stated rate, they are saying we can afford to pay 8%. The market is paying 8, the market is paying 10. And this is the interest dates, June 30, December 31, the bond issued on December 31, 2022, mature on December 21, 2024. Now, you have to understand, I'm going to try to draw a line here to illustrate what a bond would look like. So this is what this bond would look like. It's very important to see it on a graph. This bond is a two-year bond, which is that you're making four payments. We're going to have one, two, three, four. We're going to have four payments of interest. And in addition to the four payments of interest, we're going to get our money back, which is 100,000. The first thing you want to compute is how much is that interest payment? And this is an important formula. You will take the face value times the stated rate, which is 8%, times one-half. Now, why did I compute this by one-half? Because the interest on this bond, as I told you, most corporate bonds pay interest semi-annually. Simply put, the holder of this bond would receive $4,000, $4,000, $4,000. And another $4,000, the last payment. In addition to the last payment, they would receive also 100,000. Now, to value this bond, what is a bond looks like? Hopefully, this is, we're starting to complete the picture and things are starting to hopefully click. The bond, from the buyer's perspective, is a future payments. You're looking at future payments, and you want to find out how much you will pay for those future payments today. So this is the price of the bond. How much will you pay for one, two, three, four payments of $4,000? And how much will you pay for the 100,000 two years from now? Well, guess what? We have to use the present value. We have to discount those payments. Now, how do we use the discount? Well, if you're not familiar with the time value of money, please go to my website and I have a whole lesson about the time value of money. So I'm not going to explain the time value of money in details here. I'm going to show you the application of the time value of money. Okay. The first thing you need to understand is this. Once you go and you want to compute the price of the bond, simply put, once you go to use the tables, you would always use the market rate. Why the market rate? Because whoever buying the bond, they want to earn the ongoing market rate. The ongoing market rate is 10%, not 8%. 8% is what the company is paying. The buyer of the bond, they want to say, I will pay for the bond a rate that's going to consummate the market risk, which is 10%. Now, this rate is the interest rate will be always quoted annually. You have to adjust the interest rate. So if it's 10% annually, I have to divide by two. In other words, when I go to the table, I will use five. Why? Because this is the interest rate is compounded semi-annually. So 5% every six months. It's not the same thing as 10% annually. Again, you can go to the time value of money lessons and I explain this in the tail. I just want to let you know here that you will have to use 5% rather than 10. And although it's a two-year bond, you have four periods because it pays interest semi-annually. Twice a year, that's going to be four. So when you go to the table, I will be equal to five and will be equal to four, period four and I5. Now, what we're going to do, we're going to discount those two components. First, I'm going to start with the 100,000. The 100,000, I'm going to be getting this money only once. It means this is, I'm going to have to find the present value of a single payment. What do I do? I'll go to the present value table and this is the present value table. This is make sure you are using present value of $1, present value table. My interest rate is 5%, 5% is right here and my period is four, four period. I'm going to go across and I'm going to find out the rate is 0.82270. Okay, this is the rate, 0.82270. What does that mean? Simply put, my 100,000, this 100,000 right here, this 100,000, I'm going to take this 100,000 and I'm going to multiply it by 0.8227, which means the 100,000 alone, I'll pay for it 82,270. So 82,270 is the present value of the 100,000. So this is how much I'll pay for this, for this 100,000. If I buy it today, this 100,000 for 82,270 and I wait two years, it's going to earn me 10% if I get 100,000. Now I'm not only getting the 100,000, I'm also remember I'm getting four, $4,000. Well, I'm getting the same amount repeatedly. I need to discount the same amount repeatedly. This is called an annuity. Well, guess what? The $4,000 is my annuity. Annuity is a series of payment. I'm going to be getting those series of payments. Again, how much will I pay for those series of payments? Well, depending on my market rate, my market rate is 10 annually. It means 5% semi-annually. Well, I have to go to the present value of the annuity table. So I'm going to go to this table here. Present value, remember, making sure you are working with the right table, present value of an ordinary annuity. Again, 5%, four period and the factor will be 3.54595. I'm just going to round it to 3.5460. And that's going to give me 14,184. Now I'm going to compute, add up my the present value of the face value, which is 82,270. The present value of the payment, it's going to give me 96,459. And this is my price for the bond. And this is a discounted price. And hopefully you knew it was a discounted price from the beginning. And the reason you know it's, you should know it's a discounted price because what the company is offering 8% is not compensating the market. The market is paying 10. So no one in the right mind will pay you 100,000. Therefore, the bond sells at 96,459. And this is how we found the price of the bond. And if you get something more than 100,000, you should know your answer is incorrect because the bond should be discounted because I'm not paying enough of interest. Let's change the scenario. And let's assume we are offering 12%. The market is offering 10. Immediately before you do the computation, if you're trying to borrow 100,000, you know immediately you're going to be getting more than 100,000, the bond will sell at a premium. In this example, it looks something like this. We're going to have 1, 2, 3, 1, 2, 3, 4. And since you're paying 12%, it means the buyer of this bond will get 6,000, 6,000, 6,000 and 6,000. So we're going to discount this annuity. And we're going to have to discount also the 100,000. Remember we have to adjust the market rate. The market rate is 10% annually. Since we are paying interest semi-annually, we have to divide the rate by 2. Again, if you're not sure why do we do this, go to my time value lessons and I will explain this in detail. So simply put, I'm going to do the same thing. The first thing I'm going to take my 100,000, go to my table, to my present value table and 5% for period. And obviously it's the same amount, 0.82270, same amount as the prior time, 0.82270, because we did not change the market rate. So I'm going to get 82,270 for the face value of the bond. That year 4, I'm going to be getting this 100,000. Today, this amount alone is worth 82,270. Okay. And if you want to do the math, you can take 82,270 and make it earn 5%. Keep that money, make it earn 5%, 5%, 5%, 5%, you will see you will get 100,000. Now the second thing I'm going to do, I'm going to take my 6,000, it's an annuity multiplied by the present value annuity factor. I'm going to go to my present value and I'm going to go to my present value annuity factor, 5% for period, and that's equal to 3.54595. Again, I'm going to round to 3.5460 and I'm going to get 21,276. Now this is the present value of the face value, the present value of the payment in total, my bond is worth 103,546. My bond, as I predicted from the beginning, it's sell at a premium, indeed it's sell at a premium. The premium is the 3,546 and this is how to find the price of the bond. And in this recording, that's all what I wanted to show you, not how to read the bond, not what does the price mean, whether it's a premium discount par. I just wanted to show you mechanically how to find the price of a bond. If you find this recording helpful, please take a look at my other resources. Again, I don't replace your CPA review material. I am supplemental. I compliment your material. Add me and you'll add 10 to 15 points on your exam. Your risk is one month of subscription. Once again, I do have resources for other CPA review courses, Wiley, Gleam, Roger, everything is organized to match your course. And I do have access to your AI CPA previously released questions. Good luck, study hard. And of course, stay safe.