Let�s go through, and what we’re going to
do, is we’re going to go through and do our example that we did earlier, which is five
year term bond, a million dollars, and we’ll go through doing both of these discounted
premiums. So the way percent stated, issued at 10. Eight percent stated, issued at six.
And then we’ll go through, and do the effective interest table.
Now, my numbers aren’t going to be exact, because I kind of want to make it a little
bit easier for me to get through the calculations. But you’ll see how it works. So we’re going
to set up our amortization table, which has the face, plus or minus, and we’re going to
have plus or minus our premium, or discount, that equals your carrying value. Times, the
effective interest rate. Now, the effective interest rate that is the
rate that you effectively want to yield. That is the effective interest rate. That equals
your interest expense, or interest income, because one guy’s expense is another guy’s
income. So, we’re looking at one guy’s expense as another person’s income. That’s kind of
the difference between the two, to understand the difference between them. So we’re trying
to see interest expense, interest income, so that way, we can understand it for the
formula. So that’s interest expense, interest income, minus the cash payment, so, minus
cash payment. Now, with cash payment, this is an important
concept, because the cash payment is going to be, what. It is going to be– And how did
we calculate the cash? Remember the cash is which way, the effective or the stated? The
stated rate, exactly, very good. So it’s going to be your face, a million dollars, times
stated rate, times time. That is going to be the cash payment. The difference between
those, equals what? Amortization of your discounted premium.
Okay, so that’s how we’re going through. That is our basic formula. Okay, so let’s do this
again. We start out, face, so that would be the million dollars. Plus or minus your discounted
premium of a hundred, equals 980– I’m sorry, minus a hundred, is 900, that’s our carrying
value. Times the effective rate. Now, I wanted to earn at a discount 10% equals
90. That’s your interest expense. My expense is your income, expense income. Minus cash
payment, now how much cash? A million times eight percent, times time is 12/12. That they’re
paying semiannually, times 6/12. So, a million and eight percent is 80,000, boom, equals
amortization, is 10. So, when we go through that discount, and
let’s kind of go through my steps again that I erased, but we want to learn them anyway,
so let’s try it. We have one, two, three, four, and five. So, credit bonds payable for
a million. Accrued interest payable, none. Cash, 900. BIC, zero, difference, discount
of hundred. All right? So notice in most questions, they
don’t have this, they don’t have this, credit bonds payable, debit cash, difference is discounted
premium. What’s the carrying value, 900, okay? So, we have face of a million, discount of
a hundred, carrying value 900. What is it? It is stated rate, eight percent, effective
at a discount, in this case 110. Now, setting that up, we come back here, we
go, a million dollars, plus or minus, in this case, minus the discount is 900, at 10% is
90 minus 80 is 10. Now, this face doesn’t change, right, it’s a million. But this has
to go a million minus– This has to go to zero, because this has to get bigger to a
million, so on a discount, notice it starts small and gets bigger, bigger, and bigger.
So, you take the 10 and you go, “Okay, that’s 90.” A million minus 90 equals 900, plus 10
is 910. 910 at 10% is 91, minus 80 is 11. This goes up, 921, at 10% is 92.1, minus 80
equals 12. What do you need to know? Very important for
theoretical type questions. In a discount, it starts small and gets bigger, bigger, and
bigger. If you’re multiplying it times an effective rate, as the carrying value gets
bigger, your interest expense gets bigger. 80 versus 90. 80 versus 91, 80 versus 95,
80 versus 99. What’s happening to the difference every year? It also gets bigger. So in a discount,
this goes up, interest expense and amortization. Okay, because it starts small at 900 and end
up at a million. So the concept here is every year– And this
is your journal entry, it comes right out of here. So, let me clean this up. First journal
entry is that you credit at bonds payable for a million, debited cash for 900, debited
discount for a hundred. So what do we do every year? Boom, journal entry comes right out
of here. What are we going to do? We are going to credit out your discount, and we’re amortizing
the discount right here of 10 bucks, and we’re going to have interest expense, and some cash.
Now, how much cash are we paying every year? Cash, cash, cash, and I’ll put that, should
be underneath it, 80. Notice the cash doesn’t change. They’re going to give you these tables
blank, you have to fill them out. So if they give you cash once, you got cash for the next
three questions. Okay, that was a good look, wasn’t it? So, how much is cash, 80 bucks.
What’s your plug? Interest expense, 90. So notice, your journal entry comes right
out of here. So now what happens, your discount was a hundred, went down by 10, so how much
is the carrying value or discount? Discount is down to 90. What is the carrying value
of the bonds, 910 and so on? The next year, what your journal entry, same 80, but this
goes to 11, 91. This is 80, 12, and 92 and so on.
So after five years, what happens? This goes to zero, then at the end, I’ve amortized out
the discount, which did what? The discount made my interest expense more than the cash.
This was eight percent, this is more like nine, nine and a quarter and so on. And that’s
why, when you do the real calculation, the real amount should have been 924, not 900,
that’s why the numbers don’t work exactly, but I want you to learn the concepts, because
in most questions, they’ll give you the numbers to use, you just have to understand the flow
of the formula. That’s what happening at discount. So remember, every year, this is getting bigger,
so interest expense goes up, boom, and this goes up.
Let’s do the same question in a premium. So let’s come back over here and start out. What
are we doing? Credit bonds payable for a million. None of that, we’re charging a million and
one, that gives us a premium for a hundred. What’s my carrying value, boom, a million
and one? What’s it have to go down to? A million. What do I have to do? Amortize out the premium.
So you can see, just based on this journal entry, instead of a discount, the word’s going
to be up here, premium, which then means this number’s got to be smaller than this. That’s
going to make my interest expense less, why, because I want you to earn less, than what
I’m paying you. Hm, okay. So let’s come over here and set this chart up again.
So here, we’ll do, that’s a discount, let’s do a premium, starting here at a million,
plus a hundred is a million and one. How does it have to go? It has to go down, down, down
to a million, get smaller, smaller, and smaller. Times, now remember this is six percent, because
we were issuing it at a premium, which means, I’m going to pay you still eight percent,
but I only want you to earn six percent. That equals, let’s just say, about 66 minus 80,
equals 14. Now, taking away 14, gives me 1086, at six percent equals, I don’t know, let’s
just make up 64 minus 80 equals 16, minus 16 equals 1070, at six percent and so on.
Notice every year on a premium, it starts big and gets smaller. So, as this goes down,
times the interest, this goes down, now watch, 80, 66, 80, 64, 80, 60, 80, 52. What happens
to the difference every year? It still gets, what, bigger. So in both cases, amortization
gets bigger each year. In a discount, it starts small and gets bigger, interest expense goes
up. In a premium, interest expense goes down. Hm, so, let’s look at this. What’s your journal
entry? Well, we’re going to credit cash of 80, that’s easy. We started over here with
this journal entry of premium, so we’ve got to debit it out, debit out the premium, and
in the first case, we’re going to debit it out for 14. What’s your plug? Interest expense,
which is 66. The next year, this is still 80, but instead
of 14 its 16, difference 64. Next year, next year, next– So, you know, like your home
mortgage, right. Your home mortgage starts high, and it goes down eventually to zero.
So you could go home and set this up for– If you have a 30 year loan, times 12, 360
months, you could do an amortization schedule for your home, by hand, that’s good practice.
Yeah, yeah about 360 different ones. There’s programs that do that for you, but
notice here we’ve got a five year bond, term bond, boom, boom, boom, boom, maybe a serial
bond, matures twice a year and so on. But, that’s what I, again, I want you to see the
difference between discount amortization. Look at the discount amortization. Underneath
the journal entries, “Note.” Didn’t mean to wake you. “Note, when amortizing a discount,
interest expense increases each year, and the amortization of the discount increases
each year.” So, interest expense increases, and your discount
amortization. Look over here, interest expense increases each year, and amortization increases
each year. Notice the premium. “Note, when amortizing a premium, interest expense decreases
each year, however,” right? This decreases amortization of the premium increases each
year. So, those are asked in theoretical type questions. It’s really important that you
understand that, okay? In a minute, we are going to talk about a few other issues that
go hand in hand, with bonds.