 In this presentation, we will calculate the present value of cash flows for bonds using tables. Support accounting instruction by clicking the link below giving you a free 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 can do this and it's important just to know what the different ways are so we know how we can do it in different settings and know what other people are doing when we're in essence getting to the same point with different methods. Tables are very useful if we are in a situation where we are having test situations because often tests will allow us to have a calculator but a very simplified calculator that doesn't allow us to use present value functions and the table will allow us some kind of in between zone so we don't have to do the actual math of the formula but we don't get to use the calculator as well and so we do the table. So just note that it's the same thing in practice of course you would probably use a calculator or Excel so we'll show how to do that. You want to know that we're doing the same thing with these different methods and use the tools that are available to us whenever we're doing these different methods. So here we're just going to use the tables to do the same type of calculation that we saw in terms of math calculation and that is here's our information we've got the bond and it's a face amount 100,000 stated rate the rate on the bond 8% the market rate the rate that's not on the bond that we think is just the market rate is 10% semi-annual payments and there's two years so that means there's going to be four payments because we pay every six months or twice a year and there's two years so the cash flows we know that the cash flows are going to be 100,000 at the end and we know that there's going to be interest payments of 100,000 times 0.08 that would be for a year divided by 2,000 4,000 so we're going to make four to two two years two times a year four four thousand dollar payments or times for sixteen thousand dollars worth plus the 100,000 that we're going to pay back at the end so the total cash flow we know is 116,000 but that's not present value cash flows because all those happen in the future there's two components to the cash flows remember one and this is why we love bonds so much when we talk about cash flows because there's one cash flow that's just a lump sum at the end and one cash flow which is that annuity which gives us a good way to use our two types of tables and formulas for cash flow so we always want to think of that separately if I want to present value this first I'm going to present value the 100 that we're going to get at the end and then present value the annuity so let's do that first we're going to say first we're going to take the present value PV of one that's kind of like the table name we can call it and we're going to take the face amount of a bond so we take the bond face amount and that's going to be the 100,000 and all we have to do then is find the correct you know number from the table to plug into here to figure out what what we should be multiplying by and that's it so the difficult thing is one finding the correct table and two just making sure we're using the right percentages to look at it the tables look intimidating but if we know how to do that we're okay there's going to be at like four tables that they may give you here when dealing with bonds we want to use present value tables so anything that says future value we can eliminate those we're not looking for future value that typically brings us to two tables that have a present value and we call it present value of one or present value of an annuity typically and if you look at the tables you can kind of tell you can say well hmm if I'm talking about present value of one for example I need to multiply this hundred thousand times something less than one because I know the answer is going to be something less than a hundred thousand so if you look at a table here you can say well all these are less than one that looks like the right table whereas if I look at the table for an annuity they all are over one so that doesn't look right that's that's going to work for an annuity so that means that this looks like the right table it's going to be present value of one here's kind of the formula if we were to do it with the formula but the whole point of the table is not to have to do that this table is derived from the formula and now we just need to pick out you know our our correct spot and we know that we're going to use the market rate here because we're present valuing at the market rate not the stated rate on the bond but we think what's actually happening what's the real rate in the market which is something that we have to kind of guess at we don't know that for sure it's not on the bond but it's going to be given in a problem and we know that there's going to be two years but that means it's it's semi-annual so there's really four time periods and this is going to be the other kind of confusing thing we're not going to go two two years out we can't because there's going to be payments within that and so we have to use four time periods so the periods will be four but they're not yearly periods and that means we can't use the interest rate of 10 percent because that's 10 percent a year so what we do then is take that 10 percent divided by two and five percent so we're going to have four time periods two times two at five percent and so if we know that then we can just go okay four time periods at five percent it's going to be this amount so point eight two two seven so remember that point eight two two seven that's what we're going to use and then we can just go back up here and just type that in here point eight two two seven now that may not be exact because of rounding but it's four decimals out so it's pretty it's pretty good and i'll just put here that it's four periods at point oh five or five percent on the table that's where we're getting that number from and so then we're just going to present value of the bond face amount the amount that we're going to pay at the end is just going to be equal to the 100 000 times this number we'll just multiply them out there it is so the math of course here is very easy the only difficult part is finding the table finding the right number on the correct table okay so in order to do that we need to know the correct rate and the correct number of periods which is different to the number of years and different than the yearly rate you have to break it down to whatever period rate we have okay so then we need the present value of the other piece present value of annuity now the annuity we could do this remember remember that there's four four thousand dollar payments four four thousand dollar payments so we could present value each one of them using this same method not this number that would be the number used for the last one but we could go to this table and say okay well it's going to be five percent for one year out times four thousand five percent two years out times four thousand five years three years out this number times four thousand and five years four years out and then add them up that would work possibly with four time periods but if we had more than four time periods it would be very tedious to do that way luckily there's another table for us it's the annuity table so that's going to be down here and again you know which table it is because it's got to be something over one in other words what we're going to do is take this four thousand that we know how many payments there are there's four of them that would be sixteen thousand so what we need to do is multiply that four thousand times something greater than one but get to a result that's going to be something less than sixteen thousand in other words we're going to multiply something that's going to be greater than four thousand obviously and less than sixteen thousand that would be that's it has to be in there somewhere to be present value and that's going to be multiplying by something greater than one so once we get the right table we just do the same thing we're going to go five percent for a semi-annual rate the yearly rate divided by two and then we're going to take it out for how many time periods did we have two years four time periods so it's going to be this three point five four six zero so remember that number so it's going to be that number i'll say then we're just going to go back over here and we're going to take the i'm going to write that down before i forget it okay so we'll we'll put that number here actually i'll put it underneath here and we're going to say this is going to be the interest per period which is going to be four thousand we're going to pay four thousand four times for every six months four periods two years and then the table once again is going to be i'm going to give the same indicator but just note that it's a different table it's the annuity table that we're pulling this number from but it's going to be the same four periods at five percent if we multiply that out then we're going to say the four thousand times the three point five four six zero and whatnot and that's going to give us the present value of the interest payments say and then if we add those two up then we're just going to say that we have the present value of the one hundred thousand plus the present value of the interest payments so it's issued then add of course a discount and again you can think about this it should make we're going to say well there's going to be four thousand cash flow times four four periods plus one hundred thousand at the end one hundred sixteen that's how much cash flow that that we're going to have but we're actually going to to present value that at only ninety six four fifty four because the eight percent rate that we're paying in interest is less than people could get elsewhere which is the ten percent so what does this mean in terms of recording it well if we were to record this then uh we're going to say that is cash affected if we were to issue a bond yeah it's going to go up so I'm going to say cash is going to go up and it's only going to go up however for the ninety six four fifty four even though we're issuing a bond the payable the loan amount kind of the liability that we're going to pay at the end of four time periods two years is one hundred thousand and the difference then of course is going to be the discount which i'll do with our plug formula negative sum and that's going to be the three thousand five forty six and that's going to be the discount so here's our journal if we post that out then cash of course is going up bonds are going up and then we have this discount so we got cash here we got the bonds going up and the bonds minus the discount is the carrying amount of the bonds so again note that when you when you see this in book problems they're probably going to ask you to either calculate this or to do the journal entry and when doing the journal entry they're probably going to give you these two numbers just so they don't have a really long problem so and then when they do this they probably don't ask you for the journal entry because it'd be a really long problem or to post it so just note that you often these two things are kind of in limbo and separated in book problems and you got to kind of know if you know what they're doing and how to put them together it makes more sense