 In this presentation, we will present value bond cash flows using formulas. Support accounting instruction by clicking the link below, giving you a free month membership to all of the content on our website, broken out by category, further broken out by course. Each course then organized in a logical, reasonable fashion, making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files, and more like QuickBooks backup files when applicable. So once again, click the link below for a free month membership to our website and all the content on it. There's a few different ways we could do the present value of bond cash flows. One is that we could use tables over here. This is often done for test questions so that we can use tables and have a limited functionality calculators possibly. We also could do it with Excel formulas or have calculators to do it in terms of financial calculators. All of them will be derived, however, from basically the formulas. So the formulas give us the idea. Once we have that concept, we want to know how to do it in the other ways to make it more efficient and just to know what other people are doing when they're doing basically the same thing with a different format. So here we're going to use the formulas. Bonds are typically what is used to introduce these present values because bonds by their nature have the two kinds of present value equations that we need, the present value of 1 and the present value of an annuity. So what this means is that this bond has a face amount of 100,000. It has a stated rate on the bond, 8%, the market rate, which isn't on the bond. That's just what we think the market rate is, is 10%. Semi-annual payments, we pay every two times a year, or every six months. And there's going to be two years here. So that means that what that means then is that at the end of two years, we're going to get the face amount back, so we'll pay back the 100,000. So we're going to have the present value 100,002 years from now. And then we're going to make interest payments. The payment being for the stated rate, 10% of the 100,000 divided by 2, or 4% of the 100,000 every six months, because it's a six month rate. And we'll take that and get those payments every six months, so there's going to be four of them in other words. So that's like an annuity that we'll have the present value. So whenever we think of bonds and present valuing it, you want to think about it in those two kind of separate components. We've got the one lump sum, we're going to have the present value, and then we've got the interest payments, which are like an annuity. So the lump sum is going to be this formula, the annuity, this formula. We won't get into how to derive the formula. What I just want to note now is that what these formulas are doing is taking that future value and put it into today's dollars. And therefore, how much is this cash flow worth today? We know how much it's worth in terms of just dollars, because we're going to have 4,000 that we're going to get. That's going to be the 100,000 times .08 divided by 2. That's the amount of interest we're going to pay every six months, four times, two years, twice a year. So if we took that times four, we'd get 16,000 plus the 100,000 that we're going to pay at the end, 100,000. This is going to be the cash flow in terms of dollars that are actually going to go out with relation to this bond. However, the present value is going to be something less than that, of course, because it's sometime in the future. And so today in today's dollars, it's going to be something less. So we're going to do that with our two components. The first one is going to be present valuing 1, present valuing the 100,000. And we're just going to plug that into our formula here. The formula is future value over 1 plus i or interest to the n power. So let's plug that in or now we're just going to put our numbers in there. We're going to say 100,000 is the future value. What is future value? It just means that at the end of four years, this is what we're going to get in terms of this 100,000, 100,000 in the future. But that's future value because it's 100,000 in the two-year time period. Its present value will be something less. So future value just means the actual dollar amount in the future in this case. And then we're going to say that the formula here is going to be 1 plus the rate. Now the rate is going to be the market rate because this is the rate we need to use the present value. This is what the current market rate is, not the stated rate on the bond, but the current market rate is this and that's what we have to use in order for present value. Now the confusing thing is that the market rate is 10% but it's every six months. Therefore the rate for the time period that we're going to be dealing with, which is going to be four time periods of six months, is half of that or 5%. That's often the most confusing component for many people. Note that when we see 10%, it just means a year. That's what percentage means. So even if we're talking about a mortgage percentage, if I say the mortgage for the home loan, the 5% loan, that means 5% a year. So in order for us to get it to six months, we're just going to divide it by two and we're going to say it's going to be 0.05, so 10% 0.1 divided by 2.05. And then I'm going to say that we're going to take it to the power up, which is shift six, and that's going to be four time periods. Again, two years, semi-annual, so four time periods. So then we can just do the math. And this is one that you don't want. If you want to do it longhand like this, which is probably easier than to try to write this as one big formula and have Excel do it for you because you'll have to use a lot of brackets, it's easier to write in this format than just try to put it into Excel in a linear format. And then you want to write this down in a piece of paper. So I'm trying to do this how you would see it on a piece of paper. We'll do one calculation at a time. Just do the algebra, it's going to be the 100,000 over. And then we'll say 1.05, I just did the operation here, shift six to the fourth. So I did one operation at a time. Now we'll do this operation here. So 100,000 is the same, equals 1.05, shift six, four to the fourth power. That gives us this. And then we can do the division problem, which is going to equal this 100,000 divided by this. OK, so again, once you have this, you probably want to write it down in a piece of paper and do the steps of the math, of course. And you get 82. What that means is that this two years later, four time periods, that six months periods later, is only worth in today's dollars present value, present value of 82, 270. So now we've present valued the one lump sum. We've got to do the same thing for the annuity now. Also note, if you wanted to just do this in Excel with one calculation, it would look something like this. So you couldn't put over, that's the problem, to put in the same formula. So you have to use a bunch of brackets. So it would be 100,000 divided by brackets, and then brackets again, 1 plus 0.05 brackets to the fourth power, and then brackets close it all up. And that'll give us our 82, 270. Again, if you're practicing doing it by hand, you want to do one calculation at a time, might be easier to do it if you're using the formulas. If we're going to do it this way, we may as well use the Excel functions, which we'll learn in a later presentation. So now we've done that piece. Now we've got those 4,000 annuity portion. Remember, what that means is we're also going to pay interest of 100,000 times 0.08. That would be 8,000 a year. We're paying, this is what we're actually paying, so we're using the stated rate. But we're paying it every six months, so we're going to divide that by 2, and that would be 4,000. The other way we can calculate it is 0.08. The yearly rate divided by 2 would be the semi-yearly rate times 100,000. That'll give us the 4,000. So that means we're going to do that every six months. So that means it's going to be obviously 4,000 times 4, is the cash flow we're going to have. But we're not going to have a present value of 16,000, because as of today's dollars, the question is, how much is that worth in today's dollars? So this is an annuity because it's happening at a constant rate, a constant amount in a periodic payment. So instead of us going in present value in each one of those, one year out, two years out, using this formula for year 1, then year 2, or period 1, 6 months, period 2, period 3, period 4, that would be tedious. We're going to use this formula, which is a little uglier, but it will do the whole calculation in one time. Rather than us breaking it out. So to do that, I'm going to try to do that by just plugging the stuff in there again. We're going to say 4,000. That represents, of course, the annuity payment that we're making each time. We're going to say times. And then try to put this information in. It's going to be 1 minus, we'll put brackets, 1 plus R, which is the 0.05, the market rate. And then we're going to say shift 6 to the, and they say negative 4. Now we'll just do the math in a similar way we would do in an on paper. It's just going to be 4,000. I'm just going to do one operation at a time, as I would recommend to do it on paper. So we're going to say 1 minus, and then I'm going to add these two here. So it's just going to be 1.05. Brackets, shift 6 to the negative 4 over 0.05. Again, I'm just doing one operation at a time, as I recommend doing the algebra paper in pencil if you're doing it in an algebraic way here. And then we're going to take the 4,000, doing one operation at a time. And I'm just going to do the math up top, all of it here. So it's going to be equals 1 minus the, I'm going to say 1.05, shift 6 to the fourth. And we'll do that operation. And I double clicked on it, it should be to the negative 4. So negative 4 and enter. And there we have that. And then we're going to divide that by the 0.05. And then we'll do the next operation 4,000 times. And we're going to take the, I'm just going to do this with an equals, this number divided by this number. And then finally we can do our last calculation. If we did this right, we're going to say 4,000 times the 3.55. Okay, so again, that's just an attempt to do this as you would see it on a paper in pencil, one operation at a time, if you have to do this in a test type format with formulas. So what that means, of course, is the 4,000 that we're getting paid, the cash flow is 4,000 times 4, 16. Present value, of course, will be something less than that because these are happening in the future. As of today's value, there's something less than that. So then the total then of the bond cash flows, we would have got 116,000 cash flow, but present value, it's only the 82 for the 100 plus the 14184 for the annuity. So therefore, if we were to issue this bond, we would think that on a market basis, we would get 96454 for it. And that would be the present value of it. So if we had to sell this bond on the market, we probably couldn't sell it for 100,000 because we are given an interest rate at 8%, which is lower than the market rate, lower than someone could get if they took their 100,000 and put it somewhere else. And therefore, we have to issue it for something less if we present value the cash flows, you would think that we could issue it for 96454 according to our rates that we have stated here. Now, if you wanted to do this whole thing in just a linear format, it would look something like this. So if you plugged into a scientific calculator or into Excel, we could do this again. If you're gonna do it this way, you may as well be using the function, which we'll show later, but it would look something like this because we can't put it over something here. So everything has to be linear. So it would be the 400,000 times brackets, the one minus brackets, one plus 0.05 to the negative four and then bracket the whole thing divided by 0.05. And that'll give us our same 14184 that we have here. What does all this mean in terms of the journal entry? Well, if we were gonna issue this bond, what this means then is that we're gonna get cash, cash is gonna go up, that's why we're issuing the bond. And even though we're gonna get 100,000 later, we're only gonna get cash equivalent to the present value. If we sell this for what we believe is the difference between the present value, market value of these rates, if we present value, we would think that we could sell it on the market here. So if we did so, cash would go up by the 96. The bond payable, what we have to pay at the end of the time period would be the liability of the 100,000. 100,000, and of course we're left with, I'm gonna do the negative sum, a difference, 100 minus the 96,454, a debit's what we need in order for the debits to equal the credits. And that then is gonna be a discount because we're selling it for less than kind of a sticker price, we're selling it at a discount. So we're gonna copy the discount and we'll put that here. Okay, so and again, I put the debits on the bottom here just because I'm doing it in a way that is easiest for me to think through how to record this. So then if we post this, then the cash is going up, the bonds are going up to 100, but then there's also this discount. And so there we have it, if we subtract those two out, the carrying value is the 96,454. Now note, when we do the recording of the bonds, there's often a disconnect because when we record the bonds, they don't wanna have us go through the whole present value, that's usually taught at a separate time, meaning they usually give us these two numbers when we learn how to record it. And then when we calculate present value, we usually don't see the journal entry. So it's hard for us to link the two as to how do they fit together? This is how the whole thing would kind of fit together, but when you see them, a question is usually gonna ask in terms of a book problem, what's the journal entry, in which case they give you these two numbers, or how do you present value something, in which case they typically do not ask for the journal entry.