 Hello and welcome to this session. This is Professor Farhad in which we would look at zero coupon bonds, which is a form of original issue discount bonds and treasury strips. These topics are covered on the CPA as well as the CFA exam. Farhadlectures.com can help you prepare for your CPA exam, as well help you with your accounting and finance courses. I strongly suggest you check out my website. As always I would like to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1,800 plus accounting, auditing, tax, as well as finance and Excel tutorials. If you like my lectures, please like them and share them. Put them in playlists. If they benefit you, it means they might benefit other people as well. And this is my website where you will find the additional resources. So let's talk about the original issue discount bond. And basically they're less common than the coupon bond. And these bonds are issued intentionally, on purpose, with low coupon rates. Or often it's, there's no coupon, there's no coupon stated, but low coupon rate that caused the bond to sell at a discount from the par value. The most common type of these bonds is something called the zero coupon bond, which what I just told you carries no coupon. No coupon. It means you don't receive any payments. So hold on a second. Why would I buy a zero coupon bond if I'm not going to receive any payment? Here's what happened. It provides all the return in form of a price appreciation. So let's assume you purchased a $1,000 zero coupon bond. What happened is you buy the bond for, just for the sake of simplicity, $300. But the face value of the bond is $1,000. So as time goes by, let's assume it's a 10 year or 15 year bond, you keep accumulating interest until you get the $1,000 face value. So you would wait 15 years. You don't get anything, but you will get the $1,000 all at once. So zero provides only one cash flow to their owners. And that's at maturity. At maturity, you'll get your $1,000. So this is, so zero coupon bond is a form of OID, original issue discount bonds. And we'll talk about this for tax purposes. Actually, we're going to discuss tax purposes in this session as well. But in my tax course, you know, I go a little bit in details over this. Strips, what are strips? Basically a brokerage house that purchases treasury coupon bond, which is they have coupon, ask the treasury to separate the cash flow into a series of independent securities. Remember, when you buy a treasury, treasury bond, what happened is this with the bond comes the coupons. Let me put them in different colors. So remember, the coupons are the payments on the bond. So each piece is a coupon. Each x is a coupon. So fill out all these x's, then you have the face value of the bond, the face value. So what you do is you ask the treasury to separate those, separate the face value into one investments, separate each coupon payment into a separate investment. So with each security claim to one of the payment of the original issue discount bond. So it's easier to sell. So if you want to, you could just buy two payments of this bond. That's all what you do. So this is what strips are. So for example, a 10 year coupon bond will be stripped into 20 semiannual payment because you pay, it pays every six months and each coupon payment would be treated as a standalone zero coupon bond. So each, what you do is you pay for that, for that payment. Let's assume the payment is $50. Maybe you'll pay $27 for it. Well, it's going to be higher because it's only for six months. Let's assume you paid $47 and you'll get $50. The maturity of these bonds will thus range from six months to 10 years, depending if you're going to buy each one of them or all of them, but they could range if you only buy one coupon, it's only a six month coupon. So the final payment too of the face value will be treated as another standalone zero coupon security. The face value also will be discounted obviously more than the coupons because you're going to get it last. Each of these payment will be treated as an independent security and assign its own QCIP number, which is the security identifier that allows electronic trading over the Fedwire system. Each security has a QCIP. That's what it is. So the payments are still considered obligation of the US Treasury. It's still the same Treasury bond except it's separated into separate component. The Treasury program under which the coupon stripping is performed is called STRIPS. This is what we're talking about. Separate trading of registered interest and principle of securities. So you are separating the interest payment and the principle. We have many interest payments and the principle, which is one payment into separate securities and you are trading them as zero coupon securities that are called Treasury STRIPS. So what happened to zero coupon bond as time goes by? Well, let's take a look at a 30-year until maturity and suppose the market rate is 10% per year. Here's what's going to happen. The price of the bond will be today. We're going to discount $1,000 at 10% for 30 years. So the value of the bond today is $57.31. And year after year, what's going to happen next year? We're going to discount the $1,000 divided by 1.10, which is the interest rate, 1 plus i, 1 plus the interest rate raised to the 29 because we still have 29 years. Therefore, what happened? The bond went up in value from $57.31 to $63.04, which is a 10% increase over the previous value. This is what happened. And guess what's going to happen in year 3? In year 2? In year 3, or in year 2, you're going to take the $1,000 divided by 1 plus 10 raised to the 28 power and you'll find the price. So what happened over time? The price goes up. The price of the bond, the price of the bond goes up because you are close because you are getting closer to maturity. And notice it goes a little bit steeper because the value is, you have more. You are adding the 10% to a larger number. Therefore, it goes up steeper toward the end. It goes up basically to maturity. It goes back up to maturity. So after 30 years, this bond will start at $57.31. And if you keep it for 30 years, you will get your $1,000. So here's what happened. What happened to those OID's original issue discount bond? And my tax students hate this topic because it's always a tricky question. So here we go. The tax authorities that the built-in price appreciation of those OID coupon bond represent an implicit interest payment to the holder of the security. And guess what? That implicit interest payment is taxable. So the IRS calculate a price appreciation schedule to impute taxable interest income for the built-in appreciation during the tax year, even if the asset is not sold or does not mature. So you're not getting any money. You're not selling it, regardless. You still have to pay taxes. Any additional gains on losses that arise from the changes in the market interest rate are treated as capital gain or losses if the OID is sold. Only if it's sold during the year, then you'll have capital loss or capital gain. If it's not, you don't have to worry about that. But you would still compute an implicit interest and pay taxes on that implicit interest. So the interest rate originally is 10%. You remember the 30-year-zero coupon bond, we said it starts at $57.31. The following year, the IRS would calculate what the bond price would be if it's yielding 10%. And this will be computed at $63.04. Therefore, you have a taxable interest income of $5.73. Yes, this amount is subject tax. And this is the hardest thing for students to understand. And partially, it's my fault because at the beginning of the course, I keep emphasizing the point that the IRS only tax you when you have the ability to pay. In other words, you have access to the cash and you can use that cash. Here, you don't have access to the cash. You can't use that cash. Well, guess what? There's always an exception in tax law. And this is one of them. There's many, but this is one of them. So notice the imputed interest income is based on a constant yield method that ignore any changes in the market rate. Maybe your bond is worth more than $63.04. Maybe it's worth $70. We don't care about what the market value is. It's based on that interest rate, imputed interest that you pay the taxes. So if the interest rate actually, let's say it fell to 9.9, then you do your discount based on 1.009. And it's now it's worth $64.72. Well, that's the market. That's how much it's worth today. It doesn't matter. If the bond is sold, then the $64.72 and the $63.01 will be treated as capital gain in tax based on the capital gain tax rate. That could be 0.15 or 20 depending on your capital gain tax rate. If the bond is not sold, then the difference is unrealized capital gain. And we don't pay any taxes on that unrealized capital gain. But we do pay taxes on, quote, unrealized interest income on the imputed interest income. In either case, the investor will have to pay $5.70 taxes on $5.73 of imputed interest at whatever tax rate applies to interest income. Interest income is just FYI. It's ordinary income. Let's take a look at another example. Let's assume a 30 year maturity bond that's issued with a coupon rate of 4%. Actually, it's the same example. No, it's a different example. Coupon rate of 4% and yield to maturity of 8. So the coupon is 4, but it's yielding 8%. It means the market rate is 8%. So for simplicity, we're going to assume the yearly coupon payment. So now, because of the low coupon rate, the bond will be issued at a price way below. Think about it. It's offering the coupon is 4 and the market is 8. So it's going to be really, really deep discounted. So the bond, when it's issued, it's issued at $549.69 and you could confirm this yourself. If you're interested, we learn about this. Well, in the prior session, if the bond yields to maturity, it's still 8%, then its one year price a year later will be $553.66, which is we reduced one year, which went from 30 to 29. So the pre-tax holding is exactly 8%. And let's compute that, which is you're going to get $40 in coupon payment in cash. Then the difference between the old price and the new price, add the $40 to the difference, which is capital appreciation divided by original price, original cost, and you will earn, you are earning a holding, you're holding a period return is 8%, is 8%. Now, the increase in the bond price based on the constant yield is treated as interest income. So the investor is required to pay taxes on the difference in this, on the difference in this. So the difference in this, the capital, well, implicit interest is $3.97 and you have to pay obviously, of course, interest on the $40 in cash that you received as well. So you'll pay taxes on both. So if the bond yield actually changes during the year, the difference between the bond price and the constant yield value of $553.66 will be treated as capital gain and it's taxable only if the bond were actually sold. So any difference in capital gain, if it's not sold, well, that's good, you have capital gain, it's unrealized, you don't have to worry about it, but the implicit interest is taxable. So suppose the yield to maturity of the 4% coupon bond falls to 7%. Okay, at the end of the first year and the investor sells the bond after the first year. So let's assume the coupon went down to 7% and we actually sold the bond. If the investor federal plus state taxes are 38 and the combined tax rate on the capital gain is 20%, what's the investor after tax return? So now we need to compute what's the price of the bond. So we're going to have to compute this and then compute what are we going to get an interest every year in order to find out what is our tax bill, basically simply put what is our tax bill. So first let's find the price of the bond. So simply put what we're going to do, we're going to go to the financial calculator and this is at the end of the first year. So n equal to 29, we're going to put n equal to 29, the interest rate i equal to 7, we're discounting everything at 7, the future value of this bond is $1,000 and the payment is $40 which is because it's paying a 4% interest, 4% rate. So let's go to the calculator, first get the price of the bond, then the price of the bond, then we will compute what needs to be done because the originally, it was originally $553.66, notice $553.66 and not originally, the price of the bond was $553.66 after a year and at the beginning of the year it was $549.69. So let's just come, let's get those numbers down. So originally, just so we know it's $549.69, this is when kind of at .0, at the end of the year it was $553.66. Okay, now we're going to say well, now it's 7% and we sold it. So first let's find how much it's going to sold for because now we're going to have to find the market price of this bond that's important at 7%. So let's go to the financial calculator. So what's going to happen for this bond is the future value, it's going to be $1,000, that's right, the coupon payment is $40. The number of periods here is 29, that's correct and what else do we have? We have I, 7% and now we need to compute the present value which is how much it's worth. So this is worth based on the, based on discounting the bond at 7%, based on discounting the payment of $40, 29 period, future value of $1,000, $631.71. So I'm going to copy this number down, $631.71. Let's go back to the PowerPoint slides, price based on 7%, is $631.67. Now, so what is the, okay, so what taxes do we have to pay? Well, first we have to pay taxes on the $40. Remember we received $40, but that taxes is subject to federal and state taxes. So what's going to happen? We're going to take $70 multiplied by one minus 0.38, which is the combined taxes. Simply put, you have to pay 38%. What's left is really 62% of the $40. So of the $40, your net after taxes is $28, $24.80. Now also you have to compute the difference in, remember, because that the imputed interest, the difference between those two, and I believe it was, how much was it? $3.97. So you're going to have to go back there. The difference is $3.97. Again, this is the imputed, this is also taxable, and you're going to multiply it again, you're only keeping 62% of that, you're going to keep $2.46. And now you actually sold the bond, you actually sold the bond. Well, the bond has a value of $553.66, like kind of a book value, and now you sold it for $6.31. So you have to take $6.31, this is what you sold it for, the proceeds minus $553.66, which is the basis. Now I'm using tax terminology, maybe some of you don't like this, but I am an accounting professor after all. So $6.31.67 minus $553.66, you have a capital gain of $78.01. Now of this amount, you're only going to keep, oh, of this amount, this is capital gain. It means you're going to be taxed at 20%. If you're going to be taxed on 20%, it means you're keeping 80% of this, we multiply it by 0.8, so you're keeping $62 and rounding $0.41. So simply put, for the capital gain, your capital gain is, we said, let me go back to the calculator, I did not copy the numbers down, $6.31.67 minus $553.66, it's $78, that's what I thought. So you're going to have capital gains of $78.01 to be more specific and you're going to multiply this by 1 minus 0.2, so you're keeping 80% because you're going to have to pay 20% in taxes. Again, the capital gain tax is different than your income, therefore you will keep $62.42. So what is your overall after tax return? You add all this up and it's $89.67 to find out what's your rate of return on this investment. Well, you earned $89 overall in 67 cents and you invested $549.69, so you're looking at a rate of return of 16.3%, not bad at all, not bad at all. In the next session, we would look at the default risk of a bond. Once again, if you like this recording, please like it and share it and don't forget to visit my website, farhatlectures.com, for additional resources for this course as well as your other accounting and finance courses. Good luck, study hard and stay safe.