 In this presentation, we will calculate the bond price using present value tables. 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. Remember that the bonds is going to be a great tool for understanding the time value of money because of those two cash flow streams we have with relation to bonds, meaning we're going to pay the bond back, the face amount of the bond, and we're going to have the income stream. And those are going to be perfect for us to think about time value of money, how to calculate time value of money, our goal being to get a present value of those two streams. So we're going to think of those two streams separately, generally, and present value each of them to find out what the present value of the bond will be. We can do that at least three or four different ways. We can do that with a formula, actually doing the math on it. We can do it now, which is probably more popular, now do it with a calculator or with tables in Excel, I would prefer Excel, or we can use just tables, pre-formatted tables. The goal here, the real point is to really understand what we're doing in terms of what is happening, what can it tell us, and then understand that these different methods are all doing the same thing so that whatever you're being taught or whatever you have to work with, whether it's just the paper and pencil on a test or in practice where you have a calculator, it's all the same type of calculation that's coming from the same place, it's coming from the math of course, but us here are how can we apply that. Now accounting textbooks often use tables, so we're often going to use a table, look something like this, and the confusing thing about tables is one, there's just a lot of numbers, so that's confusing, but once we understand them that's not that bad. The other thing that's a little confusing is just to know which table we need to work with. Remember there's two different types of streams that we have here, and one's going to be doing with the present value of one, typically called the present value of one or equivalent to this formula, so the table's going to have the time periods, it's going to have the rates. That's going to look the same on any of these kind of present value or future value tables. What's going to different, we got to make sure that we look at the name of the table and are picking up the correct one for what we're doing. So if anything says future value, that's not the one we want right now, we're not trying to calculate what the future value is. What we're trying to do is calculate what the present value is, so you can eliminate those two tables and you're left with a present value of one or present value of an annuity. When you're considering the present value of just one payment, such as the bond payment that we're going to pay back the hundred thousand at the end of four time periods or two years, we know that the present value is going to be less than the face amount of the bond. If we're going to pay a hundred thousand two years from now, in other words, the current value today is going to be less than the hundred thousand. So if you just look at this table you could say well this makes sense because I'd have to multiply that time something less than one in order for the payment to be something less than the amount that we're paying out because time value of money would state that the amount today is worth less than the amount we actually pay out two years for now or four time periods from now. So this then is the table we'll use when we do the face amount of the bond calculation. The other component of the bonds that we'll have to deal with in terms of present valuing is the interest component. We're going to pay interest and we're going to pay interest every six months, in this case four thousand. So we're going to pay four thousand each six months for four times and that's going to be an even. We call that an annuity. So we're going to have the present value of an annuity type table. It looks really the same because we're going to have the same periods. We're going to have the same interest amounts that we'll be using to figure out what the rate what this amount will be. We'll be using for a calculation. However, if you look at the table, of course, you've got all these numbers that are greater than one now. And if you think about it, that of course makes sense because if we're talking about an annuity, we're trying to present value an annuity that what we're doing is we're saying, well there's four thousand that's going to be paid four times in this case every six months for four time periods. So if we multiply that times four in dollars, we're actually going to pay sixteen thousand. So it's going to be something less than sixteen thousand, but it's going to be something greater than four thousand. So what we're going to do here is we're going to take the four thousand, have to multiply it times something and we would expect the result to be something less than sixteen thousand, more than four thousand, less than sixteen thousand. And so that would make sense that these numbers, of course, are greater than one in order to get a calculation that would make sense. So if we do this, then we're going to say, OK, well, how can we figure this out? First, we're going to take a look at the face amount calculation. It's the same calculation we did with the formulas. We have to think about the face amount calculation. We're going to pay at the end of the time period and then the interest. So if we take a look at the face amount calculation, we're going to pick up the amount from the table for the present value of one, the amounts that are less than one. And we're picking up five percent and four periods. Why? It's two year bond and we're going to pay it semi-annual. So just remember, make sure that you don't pick up once a year. We're paying every six months. So if it's two years and we pay twice a year, then we'd have four time periods. Where does the five percent come from? Well, the market rate and we will be using the market rate here to present value things because we're present valuing using the market rate is 10%. And that would be for per year, but we're paying every six months. So we're going to say there's four time periods and the six month rate then would be the market rate divided by two. This is often one of the most confusing components, by the way. So just make sure to think through that. Every time we see an interest rate, it means per year divided by two. So then we're going to take the bond face amounts, 100,000. We're going to just multiply times that rate. So they've done the math for us here and broke it down into just this percentage. And so all we have to do is take that times the percentage. We get the 82, 270. That would match the math if we did the math to do the same thing. So all that means is, of course, that we've got 100,000 that we expect to pay for two years from now or four time periods for six month time periods. Then if that was the only thing happening, and we weren't paying any interest today, we would expect to get 82,270. In other words, if I was just going to pay 100,000 at the end for money today, then you would think the market would say I would get 82,270 from somebody today willing to give me 82,270 for me to pay back 100,000 at the end of four time periods or two years. Then we have the other component, which is going to be having to do with the interest, which we're paying 4,000, which is 1000 times the 8%. So we're going to pay interest of 100,000 times 0.08. That would be the yearly rate stated on the bond divided by 24,000. That's what we're actually going to pay every six months for four periods, two years. So we're going to use our table again, but this time for an annuity, and you can tell it's an annuity table because they're greater than one, the amounts are greater than one. And we're going to pick the same area, the 5%, four periods, four periods, two years times two for a semi-annual 5% because we're taking the market rate now. And we're dividing it by two so that it's not a yearly rate, but a per six month rate. And then we'll just take our interest per period, 4,000, and just multiply that times the 3.5460. They did the math for us. That's the point of the table. And if we get multiply that out, we get 14184. In other words, if we wanted to get money today, and we're said we're going to pay back 4,000 each time period for money today, we're going to pay back 4,000 times 416. We would expect to get 14184 today, in order to pay back 4,000 every six months based on the current market rate. So the bond has both of those components. It has the face amount we're going to pay back worth 82, 270 in today's dollars present value, and the 4,000 we're going to pay back in an annuity every four every six months, 16,000 dollars. And that's worth 14184. Of course, if we add those two up, the 82, 270, the 14184, we get the 96454. So then the journal entry would just be if we issued this bond, we're going to get 96454 for it. And we're going to put the bond on the books 100,000. That's what we owe at the end of two years. The difference then is that discount 3,546. So of course, the cash is going up. We're saying the bonds going on the books for the 100,000. And then we discounted it by that 3,546. So the actual value of the bond is 100,000 minus the or the carrying value the book value minus the 3,546.