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.