Straight Line Amortization of Bond Premium or Discount

Alright. So we use the straight line method of amortization. When we first discuss discount on bonds and premiums on bonds. Let's go ahead and compare the two right now and let's do a focused video on the straight line amortization. So the first thing we want to remember is our summary here of why we have discounts and premiums and it's all related to our interest rate. So remember when the stated rate equals the market rate. So a situation where they both equal 10%. Well the price of the bond today, it's going to be equal to the face value of the bond. Right? So that's when we have a face value bond sometimes called a par value bond. Well, what about this next situation where we have a stated rate less than the market rate. So now the bond is offering 8% when similar bonds on the market are offering 10%, people would rather buy the other bonds, the bonds on the market than our bond. Right? So in that case our bond will be selling at a price less than the face value, this will be at a discount. And finally, the final situation was where the stated rate was greater than the market rate and this is where the price of the bond will be greater than the face value, right? Greater than the face value. And this was the premium situation, right? Because if this bond is offering 12% interest when other similar bonds are offering 10% interest, well, investors would rather buy our bond because they're paying more interest. So they would sell at a premium. Okay. So let's start with the premium bonds and let's discuss this straight line amortization all in detail a little more. Okay, So like are similar example before on January 1, 2018, ACC Company issues $50,000 of 9% bonds, maturing in five years. Interest is payable semiannually on January one and July one, the market interest rate was equal to 8%. The bonds were issued at 108. So we know this is a premium first because the stated rate on the bonds is greater than the market rate, Right? So since these bonds are paying more than the market, well they're gonna sell for more than their face value. And then we also know it's a premium for sure because they were issued at a price above 100%. They were issued at a price 108% of their face value. So how much cash came in? Well, like we learned before, right, we would do the 50,000 times 108%, which is 1.08. And that comes out to 54,000 in cash. Right? So since the cash is 54,000. But later on when we pay off these bonds, we're only going to pay off 50,000, we have this premium of 4000. Right? So our journal entry, as we learned, We had a debit to cash for the 54,000. We just calculated we had a credit to bonds payable. Right? We are gonna have this liability in the future. And as we discussed, this is always gonna be the principal amount of the bonds. This 50,000 up here. That is always what goes into the bonds payable. And then we have to balance this out with the 4000 going to the premium on bonds payable. Okay, so that 4000 is the premium on bonds payable. And that's it for our issuance entry for a premium bond. Right? Where we had our cash come in in this case 54,000. This is very similar to an example. We've done previous bonds payable Is a liability that increased by 50,000. But then we also had plus the premium Of 4000 gave us a net increase of 54,000 to the bonds payable uh, to the liabilities there for this bond payable. Right, so let's go ahead and pause here and then we'll discuss the amortization of this discount, this $4,000. Excuse me not discount the $4,000 premium. Let's discuss uh the amortization over the life of the

So the amount of amortization that goes into our interest expense entry is always going to follow this formula we have here notice in the top it's gonna be the total bond premium or discount. And this was the amount at issuance, right? So from our issuance entry, how much was that total bond premium? And then we're gonna dis uh disperse it over the life of the bond. So we want to be careful that it's the total number of interest periods, right? It might not be years because if we have semiannual periods, well we're gonna have to multiply it by two, the number of years by two. Right? So let's go ahead and see it in this example. So we've got that same information And now it's the July one entry. Right now it's been six months we are paying semiannual interest. So it's time to pay the first six months of interest. So how much is that interest gonna be? The cash interest that we pay is always gonna be the principal amount, the 50,000 times the bonds uh stated rate 9%. And in this case we divide by two. Right, we divide it by two because it's for six months not the full year. And we're gonna get cash interest of 2250. Now what about that amortization of the premium. Well we're gonna use this formula that we have above and that tells us the total bond premium goes in our numerator divided by the total interest periods. And this will tell us per period and that's why it's straight line because it's the same amount every period. So we have 4000 in the total premium and we're gonna divide it by 10 interest periods right? Because it's five year bond to interest periods per year 10 total interest period. So it comes out to 400 per period will be advertised. Okay So each period is a six month period and we'll advertise 400 into the interest expense. So every time we do an interest expense journal entry we're gonna have interest expense as a debit right? Because it's an expense. So we know it's gonna be the debit in the entry and when we pay cash what we are going to have a credit to cash right? This could also be interest payable if we didn't pay the cash immediately say we were just accruing for the six months interest. Well we could either credit cash if we paid it or will credit interest payable if we're gonna pay it soon may be the following day or something like that. Like we've seen in previous examples. Okay So we know our cash is 20-50 so that's gonna be a credit to cash. 2250. Now what about this premium? Amortization. How do we remember if it's going to be a debit or a credit in the interest expense. Century. Well it has to be the opposite of what our original entry was. Remember when we have a premium it's increasing the liability right? Because we we received more money than the face value of the bonds. So as we saw above we had the 4000 that was an additional credit entry. So to start advertising it and getting rid of that credit we need debits. So we're gonna have a debit here to the premium on the bonds payable and it's gonna be lowering its value Right? So it started at 4000. Well we're taking 400 out of that 4000 now. And the interesting events is what's gonna be left over. So whenever we do the straight line method we calculate calculate this amount using um the formula principle times stated rate and then you possibly divided by two if its semiannual if not you do the full uh you do the full years interest if it's for the if its annual interest payments. So you divide by two if it's for the half year. Like in this example and the premium. Well that's gonna use our formula that we have at top, the formula at the top Inbox right in that green box at the top. That's how we calculate that. 400. Okay. And then what's left over? Well we plug this in this is the plug in the situation that makes it balance. Okay so this is how we're always going to do it when we're doing the straight line method. Now if you guys have to learn the effective interest method, you're gonna see it's a little bit different in the calculation. Don't don't get too caught up in it at this point. Just focus on the straight line method. So this is how we do it. We calculate our cash interest, use the formula for our amortization and then the interest expense will be the plug. Okay, so just like we've seen before, let's go ahead and fill this in. We had cash come out For 20 to 50 and that was a decrease to our assets for the cash. We actually paid the premium. What is that doing to our liabilities? Were advertising the premium right? It had a 4000 credit balance and we're getting rid of it, right? It's lowering our liabilities. We had a $54,000 balance for the carrying value of the bonds. Well, we took 400 out of that, right? As we advertised the premium. So that's lowering our liabilities by 400 as we advertise it. And the interest expense over here. Well expenses, they lower our equity, right, 1850. You can see that 18 50 that's a decrease to our equity right there. Cool. Alright, so let's go ahead. And now let's move on to discounts, let's see the same thing using straight line method for discounts on bonds payable

So when we issue the bonds were always gonna have our issuance entry where we receive cash and we make our bonds payable and we're either gonna have a discount or premium depending on the stated rate and the market rate. Okay, so let's go ahead and check it out in this case. On january 1st 2018. Abc company issued 50,000 of 9% bonds maturing in five years. So this 9% that's our stated rate on these bonds. Interest is payable semiannually january 1st and july 1st, the market rate is equal to 10%. This is the market rate on these bonds. Right? And notice the stated rate is less than the market rate. So our bonds are only paying 9% when the market is paying 10, they're going to sell at a discount and we can tell it's a discount because they're issued at 90 for right, 94% Of their $50,000 value. So the cash we receive is going to be equal to the 50,000 Times 94%, which is .94. So let's see what that comes out to 50,000 times .94. That equals 47,000. Okay, so that's the amount of cash we're gonna receive. But that's not what the amount we pay back when these mature. Right? We're gonna have to pay back the full 50,000. So we're gonna debit cash here because we received cash of 47,000. We're gonna credit bonds payable Now, how much is the bonds payable amount? You guys should have this down by now. Right, we're gonna put the entire 50,000 into bonds payable here. Cool. So we credit bonds payable. This liability for 50,000. Well, we need 3000 more in debits. And guess what? That's our discount on bonds payable notice in this case. Since we have a discount, we have a debit here and it's lowering the value of our liability. Where with the premium it was increasing the value of our liability. So let's see how that works here. The cash went up by 47,000. But notice what happens with our liabilities? We had bonds payable for 50,000. Right? But then we have less the discount because this is a debit, right? We have a credit in bonds payable and a debit in the discount. Well, the discount is gonna lower this value by that 3000 Leaving us with 47,000 in our liabilities there. That's the increase. Cool. Let's pause here. And then we'll deal with the interest expense

Alright now let's do the same thing with the interest expense. But now for the discount example notice we've got the same formula, the amortization is always gonna be that total amount of the premium or the discount divided by the total interest periods. Cool. So let's do that here, notice we have semiannual interest again. Right so that means twice per year. So our cash amount of interest that we're gonna pay, well that's gonna be the 50,000 times .09. And we're gonna divide that by two, right? Because it's for half a year and we'll get the 2250 in interest. Now how about the amortization in this case we had 3000 of total discount divided by the 10 periods, right? We've got five years to interest periods per year. That's 10 total periods. So that's 300 per interest period that we're gonna advertise of our discount. Okay 300 getting advertised per period. So let's go ahead and go straight to our journal entry. We know we're paying cash, right we're going to credit cash for 2250. And we're gonna in this case remember our our discount had a debit balance right? It was lowering the value of our liability with a debit balance. Well to get rid of that debit balance we need credits. So now we need to credit the discount on bonds payable to start getting rid of that debit balance. So this will be a 300 credit to discount on bonds payable and then our debit, we always have interest expense as a debit. And notice this is again our plug. So we need to add the other two numbers right? We found our cash, we found our discount. Well the interest expense is just the sum of the two of them. 2550. So just like we had before cash, we use our formula principle time stated rate. And then we're going to divide by two if its semiannual, right, if its semiannual then we divide by two and the 300. Well that comes from the formula in the box. Right. This number is a plug that balances our equation. So let's go ahead and fill these out. Our cash went down by 2250. Now, what about with the discount we have this credit to the discount? Well this is increasing our liability right before we had the 50,000 and bonds payable and 3000 in the discount. Well we've credited 300 out of the discount. So there's less discount our liabilities are increasing by that 300. Right, So that's less of a discount. So our liability is getting closer to that 50,000 value that originally had and our interest expense. Well that's equity, right, interest expense. And that's for the 2550. And that's a decrease to equity right there. So right behind me, 2550 decreased to equity, right from the interest expense. So we stay balanced here. The left side went down by 2250. The right side went down by 2250. Everything balances here. Alright, so let's go ahead and do a practice problem now related to the straight line method.