Now, how do you figure out how much to charge? How much cash should I charge you? How much
cash should I charge you? How much cash should I charge you? Basically we're going to try
to figure out what the carrying value or the amortized cost should be. In this case it�s
a thousand net of a 100 is 900 which happens to be the cash. Here it happens to be a thousand
which is a thousand. Here it happens to be a million one which is this plus this.
Okay, there could be other factors that fall into that but we've got to figure out, okay,
how much should the present value of the bonds be? When you�re present valuing the bonds,
there are two things we need to present value. We need to present value the face and we need
to present value the interest. Now let's think about it. The million dollars
is what? Some amount you're going to be getting down the road. What we need to do is you know
a $1,000,000 today is worth more than a $1,000,000 in five years. What we're going to do is we're
going to have to figure out the $1,000,000 value, the present value in five years because
that's what I'm going to give you plus the present value of the 80, 80, 80, 80, 80 you're
getting for five years. That means we're present valuing two things.
We're present valuing the face as a lump sum. We're present valuing the 80, 80, 80, and
80 when you have an equal amount to be received or paid that's called an annuity. What we
have to do is present value the annuity to see what that value is. When you add those
two up, that's how much we should charge you. Let's think about it. When I'm looking at
the $1,000,000. Here's the face, the present value of the face or the par value and that
would be the $1,000,000 times what was the stated rate? The stated rate was 8% equals
80,000 and that is the interest. We have to present value two things, the face and the
interest. The face will be a lump sum, the interest will be what? The interest will be
an annuity, an equal amount to be received or paid. In this case 8% of a million.
We use the stated rate to figure out the cash. We're going to take the $1,000,000 times the
present value of a lump sum in five years at what percent? What percent do you want
to earn? Let's assume it's the discount example two. We want to earn 10%. Notice you use the
effective rate to present value the lump sum. In this case, let's say a million present
value five years 10% is this, plus what? $80,000 annuity times the present value of an ordinary
annuity and not in but for five years at whatever rate you want to earn, 10%.
Now notice the difference. It says present value even ordinary annuity. We're going to
learn about different types, you have an ordinary annuity. Your ordinary annuity is your arrears
at the end of the year. In other words if I buy the bond today, have I earned any interest
today? No, you haven't earned the interest until what? Until the end of the year.
That's called an ordinary annuity or annuity in where's your end? At the rear, your arrears
versus there's certain things where let's say your mortgage, do they say oh yeah or
your rent, you rent an apartment. Do they say, "Pay me at the end of the month"? No,
they want the money upfront. That would be, excuse me, that would be annuity due in advance
or an annuity due and they call annuity due or annuity due now.
Think of annuity due now or annuity in advance. That's when you receive or make the payment
at the beginning. For example a lease payment you make it at the beginning. A bond interest
you haven't earned until the end. In a bond, we're going to use 80,000 times a present
value of ordinary annuity for five years at 10%. That gives us this, this plus this equals
how much we should basically charge you for the bond. That's what we're looking for. That's
what the cash proceed should be. That is present valuing those two elements.
If you look in your notes, it says, the next consideration is how to handle to calculate
the proceeds from the issuance of the bond. It says here, to calculate the present value
to amounts present value of the face of the bonds, face times present value of a lump
sum plus present value of the interest which is annuity face time, state of time, times
time of an ordinary annuity. Now, a couple of things. The sum of these
two amounts represents the present value of the bonds. If it's semiannual, now what is
semiannual mean? It means you get interest not once a year but every six months or twice
a year, semiannually. In that case let's say it is a five year 8% or let's do present value,
let's do 10%, five year 10%. When you're doing a present value table, instead
of doing five periods at 10% and looking for the present value factor. You would do five
times two is 10 periods divided by two at 5%. Now the difference between five years
at 10% and 10 periods of 5% is what? The difference is a compounding interest difference.
In other words when you put money in the bank, how often does it earn interest? Every day,
compounds daily. That's why it says the interest rate is 3% but the APY, the annual is not
3% but 3.0146 because it earns interest on interest. If I put a $1,000,000 in the bank
today by the end of the day, I've earned a million and one dollar. I have one dollar
extra but tomorrow I'm going to start earning interest on a million and one dollars and
then a million and two plus interest, a million four, six, 10, 12. That's called compounding
interest of compounds daily. Here, the difference, is not a huge difference
but it's a compounding interest difference because here you're just earning interest
every year. Here you earn interest on interest on interest and that's going to be the difference
in that factor. You'll see in your notes semiannual. Take
the years times two, the interest divided by two. Sometimes they'll just say in the
exam that the bonds were issued at 101 or 98. What is 101 or 98 mean? 101 means 101%
of face or 98% of face. Generally not always but generally this would
be a what? Premium because you got more money. This would be a discount because you got less.
It's not always the case because sometimes there's other things included. Maybe it's
a bond with detachable stock purchase warrants which means that you have to give some value
to that stock purchase warrant which we'll cover later.
I don't want you to say always premium, always discount. Not necessarily the case, however,
it tells you how much you got. I got 101% of face or I got 98% of face. That's how much
cash I got. Those are important concepts in understanding the basics of how to calculate
these amounts.