Effective Interest Amortization of Bond Premium or Discount

11. Long Term Liabilities

Effective Interest Amortization of Bond Premium or Discount

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IMPORTANT:Before you watch the videos on the Effective Interest Method, make sure with your professor that you will need to learn this concept. This concept is one of the most difficult for the course and you do not want to waste your time learning it now if you don't need to!!!!

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Calculating Bond Price with Time Value of Money

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Alright, so this is about as tough as this course can get. It's the effective interest method of amortization for the bond premium or discount. Okay, that's a lot of words. The effective interest method for the amortization of bond premium or discount. Let's Check it out. So first thing I want to review with you is the the relationship between the stated rate of the bond and the market rate on other similar bonds. Okay. So if the stated rate of a bond is says 10% and the market rate is 10%, well, the price of the bond today when we sell it, it's going to be equal to the face value. Okay. Just like we've been discussing The stated rate and the market rate with the stated rate let's say is 8% and the market rate is 10%. The price of the bond is going to be less than the face value. Right? And if the stated rate is greater than market rate, so 12% stated rate, 10% market rate. Well now the price of the bond will be greater than face value. Now if you're still struggling with that, I suggest going back to the previous videos and studying again the discounts and the premiums and those journal entries because it's about to get a little more complicated with the effective interest method. Okay. Because now what we're gonna use is we're gonna use those time value of money concepts that we learned previously, we're going to start applying those to the value of these bonds. So let's check out this example here on january 1st 2018 abc company issues $100,000 of 9% bonds, maturing in five years. Interest is payable semiannually on january 1st and july 1st, the market interest rate was equal to 10%. So notice they tell us 9% is the stated rate of these bonds And 10% is the market rate. So what does that tell us? Do you think we're gonna have a discount or a premium? We're gonna have a discount right? The stated rate, we're saying, hey look, we've got 9% bonds over here, but everyone else is offering 10% investors would rather earn 10% interest. So they would pay more for the 10% interest bonds than they would for ours, ours are going to sell at a discount, right? Because we're offering less interest. But notice in this example they didn't give us a percentage, they didn't sell, they didn't say these bonds sold at 90 for these bonds sold at 96. They didn't tell us what the price was. What they want us to do is use our our use our present value tables. We want to use our present value tables for the present value of a dollar and In the present value of the annuity of $1 to find out what the price of the bond is today. Okay, so remember the price of a bond, the real way that we know what the price of the bond is is by finding out what is the value today of all of those interest payments we're gonna receive in the future. And what is the value of that final principal payment that we're going to receive at the end? How much is that worth to me today? Well that's the price of the bond. Okay, so let's go ahead and let's draw a timeline here like we did when we learned time value of money and if this starts to look a little hairy to you, I suggest going and reviewing time value of money as well because like I said, this is about as complicated as this class is gonna get. Alright, so what we wanna do, remember there's gonna be a five year bond, but this is going to be a five year bond and paying semiannual interest, so there's going to be instead of five periods, there's gonna be 10 interest payments, right? We're gonna pay interest 10 times not five times. So we're gonna have 10 periods on our timeline here. So let's go ahead and break this up into 10 periods and I'll extend it here, Nine and then 10 out there. Okay, so we've got our 10 periods on our timeline and that's the 10 interest payment period. Right? Remember zero is right now and then we're gonna have interest payments at each period in the future. So you can imagine this is going to be right here. This first one, this is july 1st 2018, this is uh january 1st 2019, 1, 2019 and so on. Right all the way up till the interest until the final payment on January 1, 2023, which is five years from now. Okay. So what we need to do is we need to find out how much all the cash flows are gonna be, where are the cash flows that happen? And how much are they going to be? So the first thing we want to know is the cash interest. So the cash interest is going to equal the $100,000 value of the bonds times the 9% stated rate, right? That's going to be the yearly interest, but we're paying interest semi annually. So instead of 9%, let me put .09. So since its semiannual, well, we need to divide by two, just like we've been discussing, so 100,000 times point oh nine is 9000 divided by two is 4500 semiannually right? Per semiannual period, That's the amount of cash interest that we're gonna pay. So We're going to have on our timeline, we're gonna have cash flows of 4500 every semiannual period For the next 10 semiannual periods, right? We're gonna be paying out 4500 in cash, That's a lot of 4500 payments. But we got them all in there. Okay, but is that all the cash flows? No, there's also the principal payment. Right? There's going to be a principal payment of $100,000. Put that in a different color. $100,000 in the final year. Right as we make our final interest payment. Well, we're also gonna pay back all that principle. Okay, So now what we need to do to find the price of this bond today? Well we need to find the present value of all of these payments so let me do it in a different color. So all of these. Excuse me. Okay. All of these. Right here notice what they are when we think about our time value of money? When we did time value of money, what did we call a stream of payments that happened in equal intervals equal amounts of payments and equal intervals was called an annuity. Right? So this right here is the present value of an annuity. Okay. And we can use our annuity table to find the present value of those interest payments. And how about this? Right here it's a one time payment. Well this is a lump sum. Right? We talked about a lump sum. So we need to find the present value of the lump sum and that's the present value of the principal payment at the end. And if we add these together, so the present value. So the price today is gonna equal present value of interest plus the present value of principle. Okay, So what we need to do is we need to use our tables twice. We need to do one for the annuity of the interest and one for the lump sum of principal at the end. Okay. So let's go ahead and find out what each of those are. And we're gonna use our tables. I've reprinted the tables. If you look a couple of pages ahead we should have the printed tables there that were to use to solve this equation. Ok so remember when we use those tables we need to have a value for N and a value for our so our value for N is going to be equal to the number of periods which is five years times two periods per year since its semiannual R N is going to be 10. Now, what about our our, Remember whenever we use our our time value of money tables we use the market interest rate, we don't use the stated rate. We use the market rate and the market rate in this case was 10%. But we divide it by two because we're talking about semiannual periods so we're gonna look up 5%. This is the numbers that we need for our table and equals 10 and r equals 5%. Okay, so if you remember our formulas for present value of an annuity and present value of a lump sum, well the present value of the annuity. Well that's just gonna equal the 4500. Right? The amount of the annuity payment. 40 500. Mhm times the present value factor. Okay so let's go find what the present value factor is for an annuity of 10 periods. 5%. Okay so let's go ahead and go to our present value table two pages down. And which table are we gonna use? Are we gonna use the top table? Present value of $1 or present value? Ordinary annuity of $1. We're gonna use this bottom table. Right? Ordinary annuity of $1. And what were things? We had 5% for 10 periods. So this is our number 7.722. Okay that is our present value factor. Let's bring that up here. So our present value factor is 7.7 to 2. 4500 times 7.722. What is that equal? Right here. Let me scroll up. So you see the timeline. Let me get out of the way. Just make sure you see everything there. Okay so 4500 Times 7.722. Well that comes out to 34,000 7:49. Okay that is the present value of our annuity. That is the present value of the interest payments. We're not done yet. We need the present value. We need the present value of the lump sum. Right, this is the principal payment. That's happening in the final year. Well we need to take that 100,000 times the present value factor. Okay? So in this case it's gonna be the 100,000 times now. We've done the hard work of finding R. N. And R. Are already. So let's go back to the table. And which table are we going to use this time? The top one or the bottom one? We're gonna use the top one. Right Because now we're doing a lump sum, the present value of $1. That's the lump sum table. So we're gonna have 10 periods 5%. And let's find what that is there? 0.614. So that's what we need to bring to our table or to our our formula here. 0.614. And that's gonna come out to 61,400. Okay so all the hard work is behind us now all that's left to do is find the present value. The price of the bond. The price is going to equal the sum of these two 7 34,049 plus 61 400. That comes out to $96,149. That is the present value of the bond. That was a lot too right. But in the end I showed you a lot of steps here but in the end what did we do we took the interest payment 4500 per period times the present value factor. So we needed to find this end in the R. And then we do the 4500 times the factor from the annuity table and then we find the lump sum, we know that the principal value is 100,000 and then we find the present value factor using those same N in our in our in our present value table for lump sums. Okay take those two numbers and add them together. And that is the price today. And just like we expected we got a price 1 96,049. That was less than the face value right? The stated rate of the bond was 9% and the market rate was 10%. So it sold at a discount and this is the exact amount that it would sell for 96,149. So now we can make our journal entry where we debit cash, we know how much we're gonna receive, 96,149. We're gonna credit bonds payable. And how much do we credit bonds payable for the full 100,000? Right, just like we have done every other time the entire amount. And guess what the difference is going to be. Our discount discount on bonds payable is going to be this difference. So let's find out what that is. 100,000 minus 96 149. Well that comes out to $3,851. Okay so our discount on bonds payable is $3,851. Cool. Let's pause here, and you might want to even rewatch that to get a real good grasp of how we came up with that discount on bonds payable, and then let's move on to how we're going to actually advertise this discount using the effective interest method. Alright, let's do that in the next video.

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Important Equations for the Effective Interest Method of Bond Amortization

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Alright, so here I have listed some really important formulas that you're gonna use when you do the effective interest method. Okay, If you if you got these down then you're gonna have no problem with this method. Alright, so the first thing you want to know is the bonds carrying value, the carrying value is the book value of the bond. Okay. So if we are going to release our our balance sheet at any point in time, this is the amount that would show on the balance sheet, it would show the bonds payable account which is the principal amount, right? There's gonna be the principal in the bonds payable account minus whatever discount or plus whatever premium just like we saw when we were when we were studying discounts and premiums. Okay, So we need to know that bond carrying value and we're going to use the table to keep track of it. But that's a very important part of the effective interest method is the bonds carrying value. Okay, so then each of our journal entries is gonna have three parts, We're gonna have the interest expense, has a debit, we're going to have the cash payment as a credit and then we're gonna have the amortization of the discount or the premium and that's going to depend on whether it's a discount or premium, whether it's a debit or credit, but you should start to be familiar with that from our previous previous videos about that. So let's look at each of these these formulas, let's start with the interest expense. So we're taking the bond caring value, right, what it's currently sitting at on our book times the market interest rate and that is going to be our interest expense. That it will always be the debit to interest expense in this method. We're taking the caring value times the market interest rate, the cash interest payment. Well that's gonna be the principal amount of the bonds. So notice we're using both were first using the bond caring value, what it's worth on the books, but then we're for the cash payment. Well, that's always gonna be the principal amount just like we studied before times the stated interest rate. And I want to know if we're doing semiannual payments. Well we're gonna have to divide these by to write the stated interest rate would be half the market interest rate, would be half the amount as well if those were semiannual periods. Okay. And then finally the amortization of the discount or the premium, that's gonna be the plug in the in this method. Okay. Before the plug was the interest expense. When we did the straight line method, Well, the amortization is the plug in this method. Okay, So we calculate our interest expense, we calculate our cash interest payment and then we subtract the two to see what's gonna fill in this entry. So every time we do a journal entry for interest expense. We're always gonna debit interest expense. And we're gonna use that formula above and we're always going to credit cash, right? And this cash could also be interest payable if we're gonna pay it later. But 99% of the time we're gonna see it as cash. You're gonna pay it out as cash. Or it could be interest payable if we're gonna pay the interest at a later date. Okay. And that's gonna be in both journal entries. We're always gonna have a debit to interest expense whether it's a premium or a discount and a credit to cash. Okay. The difference is going to be in the discount or the premium right? The amortization. So when it's a discounted bond, remember that discount? Had a debit balance. So we're gonna use a credit to get rid of that debit balance. So the discount would be credited. Yeah. And it's always gonna be like this when we deal with these journal entries. So we would have some amount for interest expense. Some credit to discount on bonds payable and some credit to cash. The opposite for premiums, right? The premium has a credit balance. So to get rid of it we need debits. So we would have a premium on bonds payable as an additional debit in these transactions and we would have the credit to cash. Okay So now we're gonna take this onto a table and we're gonna see how the interest expense um changes every year. And the the amortization of the discount changes every year. But what's gonna stay constant is the cash payment right? We said we have the principal amount and the stated rate. That's not changing the carrying value that we use in the interest expense formula. That is changing as we go through, Right? So that's gonna affect our interest expense and then it's going to affect our amortization of the discount or premium. Okay? So let's go ahead and apply these formulas to our example that we just calculated the price for. All right, let's do that on the neck.

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Effective Interest Method:Amortization Table

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14m

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Alright so on the previous page we calculated the beginning value of this bond, we've calculated the price and the amount of cash that we collected. So what we're gonna do is use this table to calculate our interest expense. Each period are cash amount that goes to the credit in the interest expense entry and the amortization of that discount. Okay so let's go ahead and use that information to do this table here. Okay So remember on January 1, 2018 well that's when we sold the bond right, it had a beginning value as we saw was 96,149. That's what we calculated right, 96,149. Well on that date we don't pay any interest nothing. The discount balance is going to be that full balance that we started with 3851. And we're gonna have our ending caring value is the same as the beginning at that point. Right? There's no interest been paid yet. So we're gonna have the 96849 as the carrying value of the bond. Okay so remember the interest payment. So as time passes we're gonna start paying interest and this is going to be the cash interest payment here. So remember when we do this it's going to be our principal amount times our stated rate and then we'll divide by two if its semiannual in this case it was semiannual right? It was a semi annual bond as you can see right above. So we will divide by two. So our principal was 100,000 Times The 9% was our stated rate .09 times are excuse me divided by two. Right? Because it is semiannual so we will divide by two and this will give us our constant cash payment that we're gonna make every period. Right? Remember the cash payment does not change in this case because it's always gonna be the same stated rate and same principle amount 100,000 times point oh nine divided by two. It's always going to be 4500 will always be our our cash payment of interest every period. Okay so that's what we're gonna put remember now it's been half a year. So we're looking at july 1st 2018 so we would have started the year with the beginning value in the bond of 1 96,049 we're gonna pay cash interest of 4500. Right now what about our interest expense? How did we say? We're going to calculate that? That's going to be the carrying value of the bond times are market rate and we'll divide by two if the if its semiannual and in this case it is semiannual. So what are we gonna do? We're gonna take the carrying value times 0.10 right. It told us the interest rate on the market was 0.10 and then we're gonna divide it by two. Okay that is how we're gonna calculate it in this case notice I wrote carrying value because that's gonna be changing every period. So we're gonna have to do this calculation every period. So let's do it for this first period right here. What is going to be the interest expense? It's gonna be the 96,149 times 20.1 divided by two. And the interest expense comes out to be we're gonna be rounding here every now and then. We don't want to have a bunch of decimals. So we're just gonna keep the math simple. 4807. Right I remember the discount amortization that's gonna be the difference between the cash and the interest expense. Okay and that's gonna be changing from period to period as well. The cash minus the interest expense. And don't worry about signs if one's positive or one's negative. Remember when the journal entry? We never have signs, we just have the number. So we'll do 4807 -4500. And we're gonna get discount amortization of 307. So right here these three numbers that we just calculated that is our interest expense. Journal entry, we would debit interest expense for 4807. Credit cash for 4500 credit discount on bonds payable for 307. Okay we'll see that down below, we'll get more into the journal entries but let's go ahead and finish filling out this table using uh the this method. Okay so how do we calculate the discount account balance? Well it's going to be the previous balance minus amortization during the amortization during the current period. So previous balance minus amortization will give us the new account balance. So 3851 minus the 307 right, 8 3051 while we advertise 307 of that. So that's no longer part of the balance and we're gonna be left with 3544. Okay so how do we get to the ending carrying value? Well that's gonna be the face value of the bond face value minus the discount balance. Right? Just like we saw when we did the straight line method, the face value minus the discount uh amount it kept getting us to the to the carrying value. And just like we have in our formula above. So our our our our face value is always going to be 100,000 in this example. Right? And then we're gonna subtract whatever the discount balance is. Okay so we have 100,000 in in face value minus in this case 3544. So 100,000 minus 3544 gives us 96,456. So now the bond if we're gonna release our financial statements for july 1st we would show a balance of 96 96,456 for these bonds. Okay, so let's go ahead and fill in the rest of this table using the same logic. So we start at 96,456 for the next period. Right? And we're gonna have the same amount of cash interest. This will never change, right? Because we had um the same principle balance times the same stated rate divided by two. That gives us 4500 again. But now what about our interest expense? Now we're going to multiply 4 96,056. Our new carrying value. Let me leave the formula on the screen. There are carrying value of 4 96,056 times the 10% divided by two. And that's gonna give us our interest expense for this period of 4000 823. Okay, so interest expenses now. 4823. So the difference between the 2, 4008 23 and 4500, that comes out to 323 and there we go. This is our interest expense. Journal entry for the next period. Right? So notice the interest expense. Journal entry changes every period. That's why this method is much more difficult than the straight line method. But this is the method that gap proposes and the reason for it is because it more closely relates what you would have paid an interest had you used the market rate to start with. Okay, we don't need to go too much into the details other than how to calculate it here. Okay, so this is the gap method. Let's go ahead and finish filling out this table. So the discount account balance. Well that's our previous balance of 5 3044 minus 3 23. And that gets us to a balance of 3221. Okay, so our face value of 100,000 minus the discount balance, notice that this keeps getting bigger as we get closer to our maturity date and you can expect by maturity that it's going to be the full $100,000 balance. So our ending balance in that period is gonna be the beginning balance in the next period, 96,007 79. Our cash interest stays the same. 4500. Okay. Our interest expense. Well now it's gonna be our new carrying value 96 779 times 10% divided by two. And we're going to get 4839 as our interest expense in that period. The difference between the 2, 339 and there is our interest expense journal entry for that period, those three numbers. Cool. Alright let's keep it going. You can see that this is kind of just a flow now. Right? 2882 is gonna be the balance here and 97,000 118 right, we got that new discount balance by taking the previous 3000 to 21 minus the 3 39. Got us to the new balance and then 100,000 minus that discount balance is our new carrying value. What I want you guys to do is pause right here and I want you guys to finish filling out the table and then come back and let's see if you did it correctly. So I'm gonna wait five seconds while I wait for you to pause it and get guilty and if you don't you'll just see me finish the table up and you'll get no extra practice. Alright, so I'm gonna wait here. Alright I'm guessing you guys paused it and now you're back and you're ready to finish up the problem. Let's go ahead and see how you did. Okay, so our new carrying value is gonna be the 97118 to start this period. And what do we got? 4500, we're gonna do 8 4056 356 for our discount amortization. And our discount account balance is going to be 2526 right? If we subtract 100,000 minus 5 2026 we're gonna get 97,474. Now, I want to make a note to you guys. If you guys were to see this on a test, I would not expect you to have to do this whole effective interest table for for 10 payments. Right? This would take forever. They would usually just ask you for the first few payments to make sure that you understand how this works. Right? So let's keep going here and let's see how this finally uh finishes out. So 4 97,074 was our ending balance there and then we're gonna have the same 4500. So what's going to be this one is 4,874. And notice how our interest expense keeps climbing throughout the period because our caring value is higher each period. Okay, so 3 74 there's our interest expense journal entry. We're left with 2152 which gives us an ending balance of 97,848. Okay, let's go ahead and finish these up. So 8 97,048 guess what? Our cash interest is gonna be the same every period. Now our interest expense this period is 4,892,. In our amortization leaving us with a balance of 1760 which gives us an ending balance of 98,240, which is our beginning balance of the next period. And guess what cash interest is the same And what is our amortization or interest expense this period? 4912 so 412 is our discount amortization. The difference between the two. There's our journal entry for interest expense. 1348 is our discount balance after that amortization which gives us an ending balance of 6 98,052. So notice how our ending balance has been increasing this whole time. Right? Let me get out of the way here, notice how the ending balance has been increasing this whole time because we're getting rid of the discount right? We're advertising the discount And it's increasing the ending caring value of the bond as we reach maturity where it will equal 100,000. So 98,006 52 And our cash interest 4500 9 4033 in interest expense. 433 will be our discount amortization leaving us with 915 here in our discount account 99,085. All right, so we're almost done here 99,000 and 85. So we're still paying 4500 interest cash. Our interest expense is now 9 4054 which is 450 foreign discount amortization leaving us with 461 in our discount account balance leaving us a 99,539. And I want to note something about the last period in the last period. We need to get rid of the remaining discount balance right? We have this much in our discount balance. Well we're not gonna do the same formula anymore. We just know that our discount needs to disappear. So that is going to be the amount of our discount amortization in the final period 461 we know we're gonna pay cash the same amount 4500 And now we're going to plug in our interest expense. That's just the 4,961. The sum of this and this together. Right? So we didn't really do the same exact formula in the final year because it's a plug to make sure that all of our numbers work out, we no longer have a discount balance And we've got 100,000 as the carrying value of the bond. So now it's the final day, it's maturity day and the carrying value of the bond, 100,000 is equal to the face value of 100,000. The amount that we're going to pay back to the investors. That was a lot of work right. There were a lot of number crunching that went on and that's why they call us the number crunching accountants here. Okay, so we just learned pretty much the hardest thing that you learn in this course. Let's go ahead and see how this translates to the journal entries in the next vid.

So once we've created our amortization table Building the journal entries is the easy part. We've already done all the hard work. Now we just take those numbers that we we've got in our amortization table and bring them down into our journal entries. So the july 1st 2018 journal entry. Well those are going to be the numbers from july 1st 2018 in our amortization table. So july 1st 2018 Here is our journal entry. Right here we're gonna debit interest expense for 4807. Just like it says in our table 4807 We're going to credit the discount On bonds payable for 307 and we're gonna pay cash interest of 4500 right now. How about at the end of the year December 31, 2018. So notice we've got 112019 because that's the day we're actually gonna pay it. But on the last day of the year we are going to have to accrue for the interest that we have earned over the last six months. Right? So on December 31, 2018 6 months have passed. And we're making our journal entry. So we would debit interest expense. And that would be for the amount that we see there Which was, I forgot it. 4008 23. We would credit the discount on bonds payable for the 323 in the table. And we would finally, instead of cash in this case, remember we're accruing just like we did when we first learned our interest accruals, what we were not paying it till tomorrow till january 1st 2019. So we have an interest payable at this point. Okay? It could be cash if we're gonna pay it today or interest payable if we're paying it tomorrow. Right? 4500. That's exactly what's happening here. Okay. And now on january 1st 2019 when we finally pay off that interest payable, What we would do interest payable For the 4500 that we owe in cash and we're gonna pay that in cash for 4500. Right, so that was just an adjusting entry really to make sure that we accrued for that interest expense that happened during those six periods or during those six months. And then finally when we do pay it, we just get rid of that liability interest payable to pay for cash on the next day. Cool. Alright. So that was pretty tricky. I hope you guys understood that. And if not I know if you watch it one more time you're gonna get it. All right, Let's go ahead and move on to the next topic.