 Hello and welcome to the session. This is Professor Farhad in which we would look at bond prices over time. So what happened to bond from the time it's issued until the time it matures? What happened to the yield to maturity? What happened to the holding period if you hold this bond? This topic is covered on the CPA, BEC exam as well as the CFA exam. As always I'm going to remind you that farhadlectures.com is a supplemental tool. If you are studying for your CPA exam or CFA exam it covers topics such as this one as as well as other similar topics. I don't replace your CPA course. I supplement. So if you're looking for additional resources please check out my website. Also link with me on LinkedIn. Subscribe to my YouTube. I have 1800 plus accounting, auditing, tax, finance as well as Excel tutorials. If you like my lectures please like them and share them. If they benefit you it means they might benefit other people and this is my website where I have various accounting and finance courses. Let's start by looking at a bond. Well what happened to bonds? Let me tell you real quick you want to know this relationship very well when we are dealing with bonds. When we are dealing with bonds the company will offer a coupon rate. What is a coupon rate? It's how much the company is willing to pay the investors, the people that's going to borrow money, lend money to the company. Okay then we have the market rate. The market rate is the ongoing market rate for similar companies. So for example your company might be offering 8%. It means they want to borrow money, $100,000. They're willing to pay 8% to lenders. Now lenders they're going to look at your offer and they're going to look at the market because they want to see what other companies are offering that are similar to yours. If other companies are offering 8% which is we consider others is the market, what does that mean? What means is you're going to sell your bond at par. At par means you're going to get exactly for the sake of illustration you are borrowing $100,000. You will get exactly $100,000. Let me put the $100,000 here. Now if you are offering 8%, the market is offering 6%. Well guess what? You're offering better than the market. Everyone's going to jump to your bond and try to buy your bond. What's going to happen as a result? What do you think happened when we have when we have more demand for something? The price will go up. It means we say that the price sells at a premium. This is basically an accounting term but simply put the bond would sell at $104,000. I just made up this number but there's an exact formula how to find the price the price of the bond. What does it mean? $104,000. You wanted to borrow $100,000. They paid you $104,000. Now bear in mind although they paid you more they didn't pay you more because they like your company. Well they do like it but what they like is this extra 2% that you will be paying them over other options. So your bond will sell we say at a premium but simply put the person that bought the bond the person that bought the bond when they commute will see shortly then when they compute when they compute the return they're really they're really earning 6%. It's what they because when they discount the payment they use the 6%. Same example the company is offering 8% competitors are offering 10% which is greater than you are offering less than the market. Well guess what? No one in the right mind will pay you the full $100,000 if others are paying 10%. Therefore your bond will sell at a discount and I'm going to make up the number. You can't sell your bond for 96%. What does it mean 96%? It means whoever buys the bond because they want to earn 10% because when they do the discount they discount everything based on the market rate. So here you earn 8%, here you earn 6% and here you earn 10%. You always earn the market because as an investor you are looking to earn the market. So having said so this is the this is the big idea that you have to understand that bond what effects bond prices interest rate the market interest rate. When interest rate is more than the coupon rate your bond will sell at a discount when it's less it will sell at a at a premium so on and so forth. So let's take a look at what happened the bond over time. So when the bond will the bond will sell at par when the coupon rate equal to the market rate coupon eight market eight we sell at a par. In these circumstances the investor receives fair compensation. How do we know it's fair compensation? You're paying me 8% which is equal to the market which is I'm good okay so I don't need any anymore because I can't get any more. No further capital gain is necessary to provide fair compensation. Now when the coupon rate is lower so when the coupon rate is lower than the market rate so you're offering less than the market. Guess what no one's going to give you the par no one's going to give you the exact 100 000. The coupon payment alone will not provide bond investors as a high return as they would earn somewhere else. So what's going to happen to receive the compensate the competitive return they also need some price appreciation. Price appreciation means lower lower your price because I want you to lower your price so when you lower your price later on when the bond mature I'll get more money I will make up the difference. So you will sell your bond at a discount okay therefore will bond will sell below the par value which we call a discount to provide a built-in gain built in gains because you you paid less than a thousand for it later on you will get the thousand the difference is a built-in gain. Conversely also if the bond rate exceeds the market the interest income by itself is greater than the available elsewhere in the market here your coupon rate you are more generous because you have somehow you have extra cash you are willing to pay to attract lenders so you pay more in interest so the coupon rate is greater than the market rate okay so investors will bid up the price of the bond above the par value the bond will sell at a premium as the bond approaches maturity its prices will fall because fewer of these above market payment remain so as the bond mature and we have to understand this whether we have so this is a bond sells at par so the bond is sells at par here so it's 100 100 percent so if the bond sells at a premium and what's going to happen to that premium the price of the bond will go down in value as it approaches maturity which is 30 years here's the maturity why because as as as as you get closer to maturity date you have less and less of those coupon payment so the bond value will go down same thing if you sell a bond at a discount same thing in a sense that it will go back to par value as well so the bond when it matures you always get the par value which is also the face value whether it's a whether it's paying 12 percent it will go down whether it's paying four percent it will go up the bond value would will go back to its par value okay so the prices will fall because fewer of these above coupon payment remain the resulting capital loss offset the large coupon payment so the bond holder again receive a competitive return so what happened when you have a bond like this one which is which is a premium bond you are getting more money you are getting more money you are getting more money in coupon payment but you already pay too much for the bond so as you get closer to maturity you're going to have less of those payments therefore the bond will go down and basically in accounting we work this you amortize the premium and you amortize the discount so when you amortize the premium it brings the bond down because the bond is above face value it brings it down when you amortize the discount the bond will go up to the par value tolu straight the built in gain or loss suppose a bond was issued several years ago when the interest rate was seven percent the bond annual coupon rate set at seven percent and for simplicity for this example we're going to assume the coupon payment are made annually to make this simple now with three years left we have a five yeah within with with three years left we don't know what the bond is with three years left in the bonds life the market rate interest rate is eight so let me let me ask you this what happened to this bond when the market rate is eight well this bond loses value why because because if you hold this bond and if you want to sell it let's assume you hold it you want to sell it if you want to sell it to someone they're gonna look at your bond and sprinted on it seven percent and you would say well that's good but i can go to the market and buy the bond at eight percent why would i buy your bond maybe i like your company i want to hold your bond i will do it but i'm gonna pay you less than a thousand dollar okay so the bond fair value is the present value of the remaining annual payment plus the coupon payment hopefully we know how to compute the price of the bond we did this in a prior session so you will take seventy dollars times the annuity factor of eight percent um at three periods or for this because this is simple you'll take seventy thousand and basically multiplied by n equal to basically divided by one plus oh eight raised to the third power which is the sum of dose and you factor the same thing you this is the sum of those which is three payment and you do the same thing with a thousand dollar you discounted eight percent one thousand dollar divided by one plus oh eight raised to the third power when you add those two figures together the bond is nine seventy four point two four as i told you the bond will go down in value so your bond value is worth less why because when you discounted everything when you want to sell it you're going to discount based on the market on the current prices so the bond went down in value so here's what's going to happen it's less than the par value which is at selling at a discount in another year after tax coupon is paid and the remaining maturity fall to two years now let's let's assume now we're going to go from year two to year one now they make the payment let's see what's going to happen the bond will sell at 982 we're going to do the same thing discount the seventy dollars eight percent two years remaining because one year went by one thousand dollar discounted at eight percent two years remaining again the bond is 982 notice the bond went up in value from 974 23 to 982 why because the bond keeps on moving until it reaches maturity right until it reaches and until it reaches maturity but let's see what happened here what happened is this it provided a capital gain notice it went from 974 23 to 982 it provided a capital gain of seven dollars and 94 cents this is capital gain so if the investor purchased the bond at 974 the total return will be the coupon payment plus the seven dollars and 94 cent which is a total return of 77 dollars and 94 cent if we compute the return 77 97 divided by what you paid you'll get eight percent and this is exactly what we wanted to earn so if somebody wanted to buy this bond they will pay you exactly seven i'm sorry you'll pay exactly 974 which will give them eight percent return now let's assume a year later what's going to happen a year later a year later the same thing you're going to take 70 dollars it's going to have one year left in the in the life of the bond and you're going to discount this one plus oh eight one plus oh eight plus one thousand dollars you have one payment left plus one plus oh eight i don't have to put race to the first power it's always race to the first power and what's going to happen now is the bond it's going to be valued at 990 dollars and 74 cent same thing if you compute if you compute the increase in value which is it went the difference between 982 12 and 990.74 which is approximately 12 dollars approximately 12 dollars plus the 70 dollars coupon payment and you divide this by 982 if somebody bought it at 982.17 you will get exactly eight percent so the point is you are earning eight percent on this bond because you are discounting everything at eight percent so you discount everything at eight percent and you would earn exactly eight percent so you might be thinking hold on a second it's paying seven percent why am i earning eight because you did not pay a thousand dollars if you pay the full thousand dollar for it you will earn seven percent well what happened is depending on what you paid that's your basically you're holding period return so this is your holding period return so let's take a look at few let's look at few bonds and just let's kind of take a look at them maturity date 2018 2020 22 26 20 6 20 30 20 43 and 20 47 so notice as time is increasing this is for us treasury bonds so the first thing i want you to know as time you know as time goes into the future the yield to maturity is higher and hopefully this makes sense because if somebody wants to buy a bond that's gonna pay that's gonna pay the maturity value in 20 47 they want to be compensated compensated for what compensated for the risk that they are taking so the lot generally speaking generally speaking if two bonds are equal and everything except the time value the bond that it has more time to mature should pay more to compensate for the holder let's take a look at these two bonds that they have the same basically the same maturity one bond pays six percent the other bond pays 1.65 this is the coupon hold on a second this does not make any sense well it does make sense because if we look at the real to maturity it's almost the same they should be very similar but they're not now why why is that the case why is this bond earning 2.58 because if you're gonna buy this bond you're gonna pay 92.91 if you're gonna pay the six percent bond it's you're gonna have to pay 128 percent so notice for the six percent bond okay you're getting more money but you are paying a premium you are paying a huge premium 28 premium over the bond the bond with the lower coupon you are not paying that much premium actually you're buying it at a discount of the face value because the face value is 100 but you're not getting anything this bond is paying 1.6 not not getting anything means a low rate it means the yield to maturity is 2.2.05 and hopefully you know how to compute the yield to maturity because we did it in a prior session so of course the yields across bonds are not all precisely equal so they don't have to be precisely equal however we can say that the longer term bond okay promise a higher yield why because you want to be compensated for the time value because you're holding this bond for a longer period of time so let's take a look at a 30 year bond paying an annual coupon of $80 and selling at 8 per at a thousand well the bond is initial yield is to maturity ytm is eight percent that's how much it's paying it's selling for a thousand if the yield remain at eight percent the bond will price would remain at par so the holding period would also be eight percent so suppose the bond price increased to 1050 what will the holding period now will be greater than eight percent so how do we compute the holding period now if it went up to 1050 you're going to have a $50 appreciation plus $80 in coupon so you're looking at the return of $130 between appreciation and the coupon divided by a price of a thousand your holding period is 13 percent well suppose let's just switch this example a little by the end of the first year the bond yield to maturity is 8.5 find the one-year holding period and compare it to the initial eight percent yield to maturity so the same bond except that now the yield to maturity is 8.5 well let's go ahead and find the price of the bond well we have n equal to 29 because by the end of the first year year one went by we're going to assume i equal to 8.5 the interest rate is 8.5 the payment of the bond is equal to $80 that's going to stay fixed and the future value of this bond is a thousand dollars so first what we have to do is find the price of the bond the price of the bond so let's go ahead let me show you on a financial calculator basically you input everything and click on compute the price a compute pv but let's let me show to you on the on the website so i don't have a financial calculator at least but it's the same thing so n the number of periods here is for our example is 29 years left we said the payment is $80 the future value you're going to get back a thousand dollar and the the the present value we're looking we're looking for that the interest rate is 8.5 and let's compute the present value so you'll pay for this bond the price of this bond is $946.70 let's go back to the power point and figure out exactly what's the holding period now well of the price we said 9 46.70 so the price went down 9 46 so we have a thousand minus 9 46.7 so we have a reduction of approximately what 53 dollars and 30 cent yes yes i think my math is right yes uh 53 dollars and 30 cent this is how much the price went down in value so we have $80 in coupon payment so the coupon payment is $80 but we lost in value 53 dollars and 30 cent it's a capital depreciate capital depreciation and remember we paid a thousand dollar now the bond is returning 2.66 or 2.67 percent so notice here what happened is the our holding our holding period or the rate of return went went down why because because the the yield to maturity is 8.5 if we discount everything based on that rate we're only paying eight we're only paying eight percent this bond paying eight percent well guess what it's 2.69 so simply put remember that the holding period and yield to maturity they don't have to be the same the same thing in the next session we would look at zero coupon bonds and treasury strips again if you like this recording please like it and share it connect with me and don't forget to visit my website farhatlectures.com study hard and stay safe