5. Amortization

In this video, we are gonna look at an amortization table. Now, these can get pretty gnarly, but I promise they're not that bad. Before we start, let's figure out what amortization actually means. Amortization is an accounting term that refers to the process of allocating the cost of an intangible asset over a period of time. It also refers to the repayment of loan principal over time. The two things that these guys have in common is it's over a period of time. Now, what we're gonna be amortizing is either the discount or the premium, depending on the bond. We talked about in the last videos that the cost of borrowing is always the market rate.

Now, how do you have a cost of borrowing at the market rate? So if the market rate is, let's say, 8% and your coupon rate, the bond's printed rate, is 10%, wouldn't you assume that your cost of borrowing would be 10%? Well, you would, except that if your coupon is higher than your market, you're going to get extra cash in the form of a premium. So this extra cash here actually reduces your effective cost to borrow the money down to this 8%. In the same way that if your coupon rate was 6 and the market rate was 8, you may think you're getting a good deal because you're only having to pay 6% interest when the market is paying 8.

But when the coupon is less than the market, you have what's called a discount, or you get less money. So if you issue a bond that's 6% rate in an 8% market, people aren't going to pay full price for that bond. The amount of money that you get short-changed brings you up to this market rate. No matter what happens, the market is going to be efficient, and you will always end up paying 8%. Now, the question is, if we've got... we'll say we've got a 100,000 semiannual, three-year, 10% bond. That's the coupon. And market, we'll say, is 8%.

In this case, we know that our cash payments are going to be $5,000 because it's 100,000 times 5% because it's half of 10. So our cash payments are going to be $5,000. But the journal entry can't be cash 5,000, interest expense 5,000.

This part is right. This part has to be right because we're paying 5,000 cash. That's not arguable. The interest expense, however, isn't $5,000 because this would be a 10% cost to borrow, right? 10% divided by 2 for semiannual is 5%. We said that the cost to borrow money has to be this market rate, and if we put 5,000 in there, we're putting it in at 10%, not the 8% we should. What we end up actually doing is saying cash is indeed 5,000, interest expense is some portion of that, and then we decrease our premium by some portion of that because this premium is going to lessen our interest expense.

Because our bond is better, people paid more money for it. So that extra amount that they gave us decreases the amount that we're recognizing as interest expense, and that is where amortization tables come in. Amortization tables come in when we're trying to figure out what's the premium and what's the interest expense here.

For a bond selling at a discount, we'll say it's a $100,000 bond. Coupon rate is 10%. It's semiannual. It's three years. And market is, we'll say, 12%. I'm not gonna go through the whole thing on this one because this is actually the exact same bond that we did the discount video for, but I do wanna look at this journal entry. In that video, we decided that the selling price of the bond was gonna be 95,083. We know we have to pay back face value, so the bond payable always sits at face value, which is 100. So that leaves the gap to be filled with a discount, and that discount is 4,917.

In the same way, we can't just say cash 5,000, interest expense 5,000 because in this case, we're putting it in at a 10% interest rate when really the market is 12%. And because we sold at a discount, that increases our effective interest rate all the way up to this 12%. So in the same way, we end up with something like this. Cash of 5,000, interest expense of some amount, and then our discount is going to be decreased by some amount. And to figure out what these amounts are, we're gonna do an amortization table. Now, I've set up a spreadsheet here because this is gonna make everything so much easier for both of us.

All right, let's first go over these columns and talk about what each of them are. This interest expense column, this is going to be how much you actually record as your interest expense in your journal entry, and it's gonna be different than your cash payment, remember. 'Cause if we issue a bond at a discount or if we issue a bond at a premium, our interest expense still has to come out to be the market rate, not the coupon rate. The cash payment is what we promised to pay. So we promised to pay 10%, and so our cash payment is going to always be the same.

This column is for the discount amortization. That's how much of the discount are we eating up each period. How much are we amortizing? How much are we allocating? The carrying value is simply the bond payable minus any discounts plus any premiums. How much are we carrying the bond at on our books? Let's take a look back and see what we actually recorded. So we recorded the bond payable at 100,000 and the discount at 4,917. So let's work this problem. So here you're gonna have 100,000 minus the 4,917. That's the face value of the bond minus the discount. That's what you're carrying it on your books at.

Okay. Another thing we can fill in is our cash payment. We know that our cash payments are going to be $5,000 each time. Let's go ahead and do 1, 2, 3, 4, 5, 6. We're gonna make six payments of $5,000. The cash payment never changes. Remember, that's what we promised to pay. So you can go ahead and fill those in. Cash payment's always gonna be the same. Okay, now it gets exciting. For interest expense, you are always, always, always, always and forever going to take the carrying value and multiply that by the market rate. And in this case, that's gonna be 0.06 because it's a 12% market rate divided by 2 for semiannual.

So our interest expense for our first journal entry is 5,704. And the reason we use the market rate here is because you always end up paying the market rate. You only ever use the coupon rate for the cash payment. Everything else is gonna be market rate because that's what investors outside of your company are looking for and are willing to pay. So if we say that this is 5,705, our cash payment is 5,000, then the difference between those two is how much of the discount we just ate up or we just amortized or reallocated or we got rid of.

So we took our discount down by $705 now. Okay, I rounded those to whole dollars to make it easier. Our interest expense is the carrying value times the 6%. Then we have our cash payment that's always going to be 5,000, and the amount of the discount that we amortized is $705.

So I'm gonna put another column out here, remaining discount. You won't really need to do this on the test or anywhere else, but I wanna show you what happens over time. So our discount was 4,917. Now that we've gotten rid of 705 of it, let's say it is 4,917 less 705.

So our remaining discount is $4,212. And I'm just gonna keep that column out there to kinda track the discount. Now, our carrying value has gone either up or down. In our case for this problem, it's gone up because we got rid of some of the discount. So we're no longer taking away 4,917. We're actually now taking away this 4,212. What we're gonna do is we're gonna say the carrying value was the old carrying value plus any discount that we got rid of because if the discount goes away, the carrying value of that bond goes up. So you can see that we're now at 95,788.

Now, I wanna do the journal entry for this first payment. So let's remember 5,705. So what we have now is basically gonna fill this in. Our cash payment was 5,000. Should have that drilled into your head by now. Our interest expense was the 5,705, and the gap that we filled in was the 705 of the discount. So our discount account originally looked like this. We had, I think, 4,917 in there. Now we've just taken out 705, and we're down to, I forget, whatever it was, but we are decreasing the amount of the discount, and that effect is increasing the carrying value of the bond payable.

The bond payable on your balance sheet is gonna be presented as bond payable, some amount, plus any premium, some amount, minus any discount, some amount. And that gives you your carrying value of bonds payable. So if our discount is going down, then our carrying value is going up. And as it approaches maturity, if the face value is 100,000 and maturity is somewhere out here, the carrying value is going to approach 100,000. Whether it's a discount, this would be the discount. This would be remaining discount. Or if it's a premium, it's going to approach the face value. So as we're doing the amortization table, this is what we're doing.

We are getting rid of discounts and increasing the carrying value such that at maturity, the carrying value and the face value are the same. Let's go back to the amortization table. We have these formulas set up now. We said that interest expense is the carrying value times the 6%.

Cash payment is always the same. Discount is the interest expense minus our cash payment. Discount amortization is basically the filling in the gap, the plugging the hole, the finding the difference. And the carrying value is the previous carrying value plus any discount that was amortized.

So if I've done this right, you'll see that at the end, after the last payment, the carrying value is the face value. Let's go ahead and drag this out too. You'll see that at the end, the remaining discount is 0.

So we've effectively amortized the entire discount. Our interest expense kept going up. Our cash payment obviously stayed the same, and our discount amortization kept going up also. Now, a question for thought is, why did our interest expense continue to increase? Why did that happen? Well, it happened because our carrying value continued to increase, and our interest expense is the carrying value times the market interest rate. As our carrying value increases and begins to approach face value, then our interest expense increases also because if you look, we're multiplying by bigger and bigger numbers, right? So we've multiplied to start by 95, then 95.7, 96, 97, 98, 99.

So our carrying value keeps increasing, which makes our interest expense keep increasing also. And this over here is just a little proof to show you that as it goes on, the carrying value and the remaining discount begin to swap places. So if you look, we'll do another formula. You add the discount plus the carrying value.

It's always gonna be 100. Over time, it just begins to recharacterize. It goes from discount into carrying value, from discount into carrying value. So the remaining discount decreases while our carrying value increases. Let's do another one, except instead of doing a discount, let's do the one that we worked through in the premium video. I'm gonna clear all this stuff out so that we can work through it again together. And now this is instead of discount amortization, it's gonna be premium amortization. And instead of remaining discount, we're gonna have remaining premium. Now, in our premium video, we came out with a bond that was at 105,242.

So we will say that the remaining premium is 5,242. Our cash payments were 5,000. And then this is the exact same bond, but we're saying that instead of a market rate of 12%, it's a market rate of 8%. So what we're gonna do here is we're gonna have the carrying value times 0.04.

And you can tell that we're doing it right. Well, you can tell that we're close at least to doing it right because the interest expense is less than the cash payment. Remember, when you sell a bond at a premium, your interest expense should be lower than your cash payment because your bond is better. You're paying more than the market is paying, which is why you got that extra cash up front. So your interest expense should be less than your cash payment because your interest expense is calculated at an 8% rate, whereas your cash payment is calculated at a 10% rate. Now, in this case, we'll take the cash payment minus the interest expense, and so we get $790 of premium that was amortized.

Now, as you're doing these amortization tables, I want you to be thinking. I want you to be thinking, what am I actually doing? Which way should this carrying value go? This carrying value, we know should end up at 100,000 because it's a $100,000 face value. And if you look, we said that as it approaches maturity, it's going to go down in the case of a premium and approach this face value.

So you know that it should go to 100,000. So that makes your decision easy. You should say, "Okay. Well, I need to take away that 790," 'cause 105 down to 104 is great because it approaches 100,000. If you were to, instead of take it away, you were to accidentally add it, you should look at this and go, "Well, that's not approaching face value. I can tell that that's getting bigger and bigger and bigger, so I must have done something wrong. I'm just gonna go ahead and switch the sign." 'Cause if I do it that way, it at least is approaching 100,000.

And then this just-for-fun column out here will say, I mean, this one is easy 'cause you'll notice 4,452, 104,452. This is obvious and very easy to see what the remaining premium is.

Now again, if I've done this right, we should be able to drag these all the way down and get to 100,000 over here and 0 in the remaining premium column. Did it right. I don't know about you, but I find this to be actually very cool that as it finally gets to maturity, it just automatically works out to be 100,000. The math just works such that it comes out to be $100,000. I think that the one column that you really need to remember is this column here. The other column, let's go through all the other columns.

Cash payment is always the same. It's printed on the bond. Here's my face value. Here's my interest rate. Cash payment never changes. This third column, premium or discount amortization, is based on these first two columns. This fourth column, carrying value, is based on the column next to it and the row above it. So I kinda think that the only hard column, the only column that you really need to remember, is this column, and this column is simply the carrying value from the period before times the market interest rate. If you can remember that, then you can kinda guess here. You can take the difference, and like I showed you, you don't even really need to remember if it's plus or minus over here.

You just need to know which way are you going. If it's above face value, well, then subtract it so you're getting closer to face value. If the carrying value is below face value, well, then add it so you're getting closer to face value. I would recommend that you work through a couple of these because as you can see, it's not super complicated, but you need to be familiar and you need to be in the habit of doing these so that on the test it doesn't take you a ton of time. Now on the test, your teacher's probably gonna ask either do the first journal entry, which is gonna be these three numbers here, or do the first two journal entries.

I doubt that she's gonna make you do all six periods. My guess would be that she makes you do probably the first two. And even the journal entry is easy. You should by now know which side cash goes on to decrease it. And then the only other thing that you have to do is figure out where to put these two numbers such that they either add up to 5,000 or their difference is 5,000. Here you can tell, well, we're gonna put these two numbers on the same side. If this number here was 5,790, well, then you'd put those two numbers on the same side to match up with this 5,790.

Like I've said many times before, accounting is a puzzle, and if you know where to put some of the big pieces like your cash payment, then you can figure out where everything else goes.