 Personal finance practice problem using OneNote. Bond purchase on margin leverage investment. Prepare to get financially fit by practicing personal finance. You're not required to, but if you have access to OneNote, would like to follow along. We're in the icon left-hand side practice problems tab and the one, one, two, nine, five bond purchase on margin leverage investment tab. Also take a look at the immersive reader tool practice problems typically in the text area too, with the same name, same number, but with transcripts. Transcripts that can be translated into multiple languages and either listened to or read in them. We're imagining a situation where we're investing in bonds, but this time we're paying for some of those bonds by taking out a loan in essence, purchasing the investment on margin, leveraging the investment to some degree. Now remember when we're investing in bonds, we can basically think of that as though we are loaning money to the issuer of the bond, typically being a government entity or a corporation in return for interest payments, usually semi-annual or annual interest payments, as well as the face amount that we receive at maturity in a lump sum, which could be thought of as the principal, return of principal, but it might be different than what we bought the bond for if we bought the bond at a premium or at a discount. So keeping that in mind, we've got the information on the left. We're gonna imagine the par value, the face amount of the bond is gonna be $1,000. The coupon rate is 10%, the years to maturity are 20. Therefore, we're gonna be receiving, this bond will be paying out interest payments of 1,000 times the coupon rate, $100 a year. So the bond was purchased. We're imagining we purchased this bond at $1,135.55. Therefore, we purchased it at a premium. We purchased it at a price higher than the par value of the bond. So the amount we paid, however, in cash was only 20% because we borrowed the rest of the money in order to purchase the bond. Now this is where it gets a little bit confusing. It gets a little bit risky when we're thinking about leverage situation because we're investing money in the bond. So now we're borrowing money that we're gonna have to pay interest on ourselves in order to invest money that we're trying to get interest on. So when we have a leveraged type of situation, it could be a little bit more risky, but it can amplify, for example, if things turn out well, if we have a gain on the bond, it can amplify the problem or the loss if we end up with a loss. And most people are familiar with this from an individual standpoint with a similar example with like a home. Typically when we purchase a home, we're going to be financing part of the home. Usually we purchase the home not just as an investment, but because we wanna live in the home, but it's still an investment as well. We're gonna finance a large portion of the home. And if you have a situation where you only have basically 20,000 to put down on the home, but you purchased a home worth 100,000 because you financed the rest of it, if that home goes up in value, if it increases, well, now that whole investment, most of which you financed is going up in value and that leverage, that loan you took out to invest in the home, looks really good at that point in time. However, of course, if the home did go down in value, then that could amplify the loss on the negative side. So similar kind of concept here, we're gonna say that when we purchased this bond, we got the 1135.55 times the .2. We actually only paid like $227 for it in terms of a cash flow, and then we borrowed 80% of it. So the rest of it, 1135.55 times .8, we borrowed 908.44 in order to pay the rest of that bond purchase price. So next we're gonna say, well, now we've got a loan that we're gonna have to pay back and we're gonna have to pay interest on the loan. Now note, usually when we think about interest on us borrowing money, we usually think of it kind of like a mortgage structure, meaning we pay back equal installments, each installment having an interest and principal portion when we pay back the loan. But that's not the only structure we could use as long as the lender and the borrower agree on it. We could structure it and say, hey, look, I will pay back the principal, the 908.44 and possibly just be paying you then the interest on the loan, for example, if we structure it in that way, we can do so possibly in such a way that's to say, hey, I'm gonna get interest on the bond equivalent to 1,000 times .10% every six months, I'm gonna use that interest to pay off the amount that I loaned or borrowed in order to purchase the bond. My hope then being that the bond goes up in price and if it goes up in price, then I can have a gain on the sale of the bond, for example, and having that only investing a small amount of money compared to the price of the bond would be the idea. So we're gonna say the market rate is the 7%. The loan rate is 11.01%. The loan that we took out is gonna have to, we're gonna have to pay back at the 11.01. We're gonna say, okay, so the current price of the bond, if we're gonna value the bond, then we're gonna say that the present value of the interest payments, if we do that calculation, present value, the rate is gonna be the 7%. We're gonna say it's yearly, so no dividing by two or anything. And then comma, number of periods is gonna be 20, comma, the payment that we're gonna have is gonna be the 1,000 times the 10% or the $100. So the $100 annuities that we discount back at 7% gives us the 1,059.40. And then we're taking the present value of the face amount at $1,000, discounting it back rate, then 7%, market rate, comma, number of periods, 20, comma, because it's not a payment, not an annuity. We're taking the future value, that 1,000 lump sum that we will be receiving at the end. We get 258.42, and that would total up to the sales price of 1,382. Now we bought it for 1,135.55. So if we sell it at this point in time, we can sell it for more than what we bought it for. We could have a gain at that point. So let's say we did that, let's say we sell it, the sales price is this price that we calculated up top and then the purchase price was 1,135.55. The gain that we have is the difference between the two, 182.27 gain that we have. Notice that the interest component kind of cancels out. We got interest income related to it, but we use that interest income in order to finance the loan. We have to pay off the loan on it. So we had a profit here between the difference between the sales price and the purchase price, 182.27. If we compare that to the purchase price, we would then have 16.05 of kind of a profit percent. We've got the 182.27 divided by what we, was the cost of this 1,135.55. We had moving the decimal over 16.05. However, we didn't really pay this amount when we purchased it because we paid that amount but we financed 80% of it. So in terms of cash flow, that's not really what we put down for it. So if we think about it in terms of cash flow, we're gonna say the amount paid in cash at the price of 1,135.55. We only paid 20% in cash because we financed the rest of it. So then we said that 20% of that is really, we only paid 2,711 in actual cash. And if we compare that to the profit, so now I'm gonna say, okay, we had a profit of 182.27. If I compare that to the cash flow that we actually put down, which is 2,27.11, now we've got an 80.26 return on the cash flow. And the interest kind of nets out given the fact that we took out a loan and we paying the interest on the bond to the loan. So we can imagine the loan, what does the loan look like? We took out a loan, remember for the 908 in order to purchase the 1,135.55. So for example, we took 1,135.55 times 0.8, that's the 908.44 loan. We've got to pay 11.01% we're gonna say in order to pay back the loan. So we're gonna pay back 11.01%. So that times each year times 0.1101. And I tried to work that out. So it comes out to about $100, which is the amount of the bond interest. So what we're gonna say is that until we sell the bond, we're just gonna take the bond interest that we're receiving from the investment and pay off the loan with it of the $100. And then we're gonna hope that the bond goes up in value and the gain and then have the gain on the bond that we basically leveraged with the loan. So let's look at it from a cash flow basis then. If we got a cash flow basis, we can say, okay, if we sell the bond it went up to 1,000, what do we say? 1,382 and then we pay down the loan. So we're gonna sell it. We're gonna get the 1,382. We're gonna have to pay off the loan, 908.44. I'm not gonna take into consideration the cash flow from the bond interest payments and the payment of the interest on the loan because those are canceling each other out until we sell the bond. So now we're gonna have to pay off the principle of the loan and then we're also gonna have the cash that was paid for the bond upfront, the amount that we paid, not the amount that we financed, which was the 1,135.55, 1,135.55 times .227.11 that we paid. So the cash flow that we have here, once again, we can see that 182.27 in a kind of different format from a cash flow format. We're gonna sell it for 1,317.82 minus the 908.44 to pay off the loan that we used to purchase the bond in the first place minus the 227.11, the amount that we paid in cash for the bond in the first place. We got the net cash flow, 182.27. If we compare that to the cash we paid for the bond on a cash flow basis, once again, 182.27 divided by 227.11. We've got an 80.26 about percent return, which again, is better on a cash flow basis than if we purchased the bond straight out and paid full cash for it because then we would have had the 16.08. So the leverage that we had because things happened to turn out good, meaning the bond went up in value, means that we've amplified our profits due to the leverage. That kind of concept of leverage is critical, but it also is something that you've got to be quite careful of because if things do not turn out correct, good, right? If the bond price goes down, then it also can amplify basically the losses. So there's, we might dive into kind of leverage as a general concept, how much leverage is healthy and so on in more depth in other areas, but, and it can be one of those areas that people can kind of go overboard because if you increase the leverage, you have potential for further gains, but you're also putting yourself out there for more risk that's gonna be involved and we always have this trade off between the risk and the potential gains in the future. So I highly recommend doing this in Excel and then you can adjust these rates. If you do it in Excel, which we do do, then you can adjust these rates in your data input and say, well, what would happen if we had a loss, for example, and you can kind of get a feel for this concept in general.