8. Value a Bond and Calculate Yield to Maturity (YTM) Video Lecture | Become an Expert: Value Investing - Business Basics

welcome to course one unit two lesson
three how do you value a bond and yield
maturity this lesson has four lesson
objectives the first is understanding
simple interest
the second is understanding compound
interest on bonds the third is
understanding the current yield and the
fourth is understanding yield to
maturity so let's get started okay as
you can remember from the second lesson
we have our bond investor Jesse and
Jesse has his bond from real estate
empires and what he's going to do is
we're going to look at different ways in
which Jesse can value this bond so
really there's there's two different
ways you can look at the simple interest
or you can look at the compound interest
and under each one of these you can see
I have the coupon yield and the current
yield under the simple interest and then
the yield to maturity under the compound
interest and that yield to maturity is
really the thing that we've got to
understand at the end of this lesson so
I'm going to show you why all three of
these are different and why the young to
maturity is the one that you really need
to understand so let's go ahead and get
started with the simple interest so in
order to understand simple interest all
you're going to do is you're going to
add up all the value of the coupons and
you're not going to assume that you're
reinvesting any of the coupons you're
just simply collecting those $25
payments throughout the entire term of
the bond and you're just adding those up
and that's your simple interest
the chart might look busy but as you as
you zoom in here and you look at the
first coupon you can see the first
coupons for $25 the second coupon is for
another $25 so the total that's a
running total you see on the chart so
after two coupons Jesse would have $50
in his hand after the third coupon he
had $75 and after the fourth he'd have a
hundred and as you continue to scroll
down through the chart you can see as we
arrive a coupon sixty that Jesse has
$1,500 from all the coupons and the way
that that was figured out was pretty
simple and I guess that's probably why
they call it simple interest is you just
take the number of coupons which for
this 30-year bond he would receive 60
coupons and you multiply that by the
coupon payment which is $25 and you can
see it adds up to $1,500
so the way to understand the simple
interest on this is if Jessie with just
simply by the bond at the very first day
and he hold the bond through maturity
and he wouldn't be reinvesting those the
proceeds from his coupons and just
simply holding on to them and you know
holding on to the cash itself the value
of the investment would be fifteen
hundred dollars and we we're not going
to count the thousand dollars he used to
buy initially in the thousand dollars he
gets back at the end we're just going to
value all those coupon payments because
because that's the money that he made on
the investment so when we talk about the
coupon yield okay and this is under
simple interest the coupon yield is
nothing more than taking one year's
worth of those coupon payments which is
$50 and dividing that by the par value
you're always going to divide all the
coupons for one year divided by the par
value and that's going to give you your
coupon yield which is five percent and
that's all there is to keep on yield
it's that simple
so when you talk about the current yield
on a bond you're typically talking about
a bond that's been on the market for a
few years you're not buying it on the
very first day and so what you have to
look at is the price that you're buying
that bond for compared to the coupon
payments so in order to calculate the
current yield we're just going to take
the the coupon payment that you would
receive for one year and divide it by
the price at which you bought it for
that the bond itself and you just divide
those two numbers and you come up with
the current yield so you can see here if
Jessie was going to buy this bond
regardless of how much time it was after
the initial issue date there could only
be one year left on the bond or there
could be 25 years left on the bond the
current yield is taking that coupon
which in the first scenario here is
gonna be $50 and we're going to divide
it by the price and we're just going to
say that the price that he's going to
pay for it is $1200 so when you do that
you get a current yota of 4.2% just 50
divided by 1200 so as we move over to
the the actual face value matches the
actual price of a thousand and a
thousand you take that coupon of $50
divided by a thousand because that's the
price you're buying it at and you can
see that the current yield would be the
same as the coupon yield
now if we talk about a bond that he's
purchasing at a discount let's say $800
you can see that the current yield goes
up to six point three percent so we're
in this example we're talking about the
same exact bond
no difference in the bond just the price
at which he's buying that bond at and
how that price is affecting the yield
because he's getting it at a more
expensive price now the problem with the
current yield in which you're going to
find out later the problem with this is
that it doesn't account for the amount
of money that you lose or gain whenever
the bond matures okay so as you can see
let's look at this first one that we
have where the let's just say Jesse
bought this for $1,200 okay the current
yield on that is four point two percent
but what about the $200 that he's going
to lose when this bond matures because
we know whenever the bond matures he's
only going to get $1,000 back because
that's the par value so this does not
account for that loss that $200 loss
that he would have whenever he would go
to sell the bond and so likewise when
you look over at if he could buy the
bond at $800 and regardless of how long
he holds it when the bond matures the
bond is going to be worth $1,000 so
that's a $200 profit that isn't
calculated into that current yield
percent that you see there so when we
talk about yield to maturity that's
where that's going to really come into
play so just just so you know when
somebody quotes you a current yield it's
not accounting for that difference
between the price you're going to pay
and the par value whenever the bond
matures so let's talk about the compound
interest on a bond so as we look at our
chart let's go to the first coupon so
after six months Jesse would receive and
this is we're going to assume that Jesse
bought the bond as soon as it was issued
just like the very first scenario we
looked at and so you can see Jesse would
receive as $25.00 after the first six
months and then the second coupon which
would be six months later he's going to
receive another $25 check but here's
what's different
that first coupon of $25.00 we're going
to assume that jesse has invested that
$25 into another investment nothing to
do with this bond but he's invest
that into another investment which is
going to provide the same interest rate
as what he's receiving on this bond
which is 5% so that's the big assumption
because in six months let's assume Jesse
bought this bought the bond right now
and then six months later he gets his
first coupon then when he receives that
first coupon there's no guarantee that
he's able to reinvest that first $25
payment into another 5% yielding
security so that's where when you get
into the compound interest and figuring
out what this bond is worth if there's a
little bit of guesswork and I'm gonna
give you some tools in in the second
course to help you estimate what you
think you could get on you know on an
average throughout the duration of a
bond but for right now let's just make
this really simple and let's assume that
whatever coupon yield he has on this
bond is what he can reinvest his coupons
back into at that same rate so if that
was the scenario after he receives that
first $25 payment let's assume that he
reinvested that into a completely
different investment that he invested it
into something that's going to make 5%
so as we look at the second coupon that
initial $25 has matured into 26 dollars
and then he received the $25 second
coupon for a total of 51 dollars so as
we look at the third coupon we know that
jesse has 51 dollars that's maturing at
a 5% interest rate as he's waiting for
that third coupon which is going to be
another $25 payment so each one of these
coupons were assuming that the previous
amount that previous total is
compounding at 5% so as you can see when
we when we go through these coupons when
you get up to the 60th coupon Jesse
would actually have three thousand four
hundred dollars at the end whatever he
receives his his last coupon payment
okay so let's compare the simple
interest versus the compound interest
you can see in the simple interest this
would be for the total duration as if
the first day that Jesse bought it clear
up to thirty years later on the simple
interest calculation you're only valuing
the bond that it's going to make $1,500
for you during that duration
but when you look at the compound
interest you can see that it's $3,400 if
it's reinvested at 5% for each coupon so
that's a pretty big difference I mean
we're talking more than double the money
on a bond so let's under the compound
interest let's look at the yield to
maturity now as we talked to earlier we
said that we weren't going to when we
were talking about the current yield we
weren't accounting for the difference
that somebody would pay for a bond
versus what the bond would be redeemed
for whenever it is whenever it reaches
its term and that the face value is paid
back to the investor so that's what the
yield to maturity accounts for not only
does it do the compound interest but it
also accounts for that difference
between the price that you pay and the
face value so that's why this number is
really important because it really wraps
all the variables together and it gives
you a real estimate of of what you're
going to get if you would buy any bond
and hold it clear to maturity and that's
how you have to look at the value of the
bond so let's take the very first
scenario here and what we're going to
assume is Jesse's going to be buying a
30-year bond but he's going to buy it 15
years after the bond has been on the
market so there's 15 years remaining
until the bonds mature and each one of
these scenarios are exactly the same the
only thing that we change between each
of the three is that the price that
Jesse's paying for each one of these
bonds okay so the first one he's going
to be paying a premium for the bond
meaning he's paying more than the face
or par value so the first one he's going
to pay $1200 for okay so as we look down
the coupon payments that he's going to
receive over the next 15 years amounts
to 1098 dollars now we're assuming that
he's reinvesting each coupon at 5% okay
so that's why you have kind of an odd
number there so the coupons 1098 dollars
the par gained and lost he's going to
lose $200 on the fact that he he paid a
premium for the bond and whenever it
matures he's only going to get a
thousand so he's going to lose $200
there so that $200 comes right off the
top of his coupon payments for a
difference of $898 so if he buy this
bond at that price he at
he held it clear to the maturity he's
going to make $898 so as we look to the
yield to maturity so that yield would
actually be 3.3 percent for that for
that purchase price okay which is
significantly lower than the 5% coupon
that you might think when you look at it
from a simple interest in in coupon
yield perspective so let's go to the
second one let's assume that he bought
the $1,000 par bond he bought it for
$1000 he's got 15 years remaining on it
and so the coupon that he agrees the
coupon payments the compound interest on
those coupon payments would be the same
thing 1098 dollars but he has no gain or
loss from from his purchase price to the
face value so the difference is just
going to be the 1098 dollars and the
yield to maturity is 5% okay so when
you're buying it for the same price as
what the face or par value is you're
going to actually get and you're going
to see that coupon you'll be exactly
what it says on the bond so here's where
it's really interesting is when we look
at buying a bond that's selling at a
discount
okay so we go down the coupon payments
are exactly the same the par value
you're actually gaining because you
bought it for 800 but you're going to
get a thousand back when the bond
matures so you're going to get a $200
plus so your difference is 1290 dollars
so your yield to maturity on that bond
is 7.2 percent a year even though it's a
5% coupon bond so you can see how much
of a difference here occurs based off
the price that you're buying these bonds
for anytime you're paying a premium for
a bond your yield to maturity is going
to be much different than what your
coupon yield is and that's the thing you
really got to understand and that's why
understanding yield to maturity is the
most important thing you can do when
you're understanding how to value a bond
okay so you might be thinking to
yourself okay how did he figure that out
how did he figure out the yield to
maturity well here's the equation and
it's I got this from Zen well calm it's
kind of a complex equation but we've
made it easy for you here buffets books
we have the calculator on this page and
you can go
there we have some practical exercises a
video for the practical exercise to kind
of show you how to use the calculator
and you can try this out for yourself
and you'll see that using the calculator
solves this really hard math problem for
you you don't even have to worry about
it so hopefully we've made it easy for
you okay so just a quick overview I want
to show you the difference as we looked
at those different purchase prices and
the terminology that we learned all in
one so let's we're going to zoom in here
and look at the very first one so this
would be assuming that we're that the
bond has been on the market for 15 years
and that there's 15 years remaining
until the bond becomes mature so let's
look at if we would buy that bond for
$800 and look at the terminology so the
coupon yield is still 5% because in
order to figure out the coupon yield all
you're doing is taking the the coupon
payment for the year divided by the par
value so it's going to say 5% as you
look across the board the
thousand-dollar bond price would be 5%
and the $1,200 bond price would be 5% so
you can see that's really misleading
when somebody gives you a quote based
off the coupon yield that really doesn't
mean anything because the price that you
pay is going to drastically affect what
you actually see on your on your yield
so let's look at the current yield to
figure out the current yield we're
taking the coupon payments for one year
and we're dividing it by the price that
you're paying and as you can see the
first one for $800 was 6.3%
for the thousand it was 5% and for $1200
it was 4.2 percent okay but those aren't
the real numbers we know that so when we
go down to the yield to maturity this is
actually counting for the difference
between the price we're paying and
accounting for what we're going to
receive back on the face value of the
bond as you can see the numbers get even
more different than what you saw before
with the current yield where the $800
bond is actually going to give you a 7.2
percent return which is great the
thousand dollar bond price is going to
give you a 5% return and the 1200 dollar
bond is going to give you a 3.3 percent
which is significantly I mean that's one
point seven percent lower than what you
would be expecting if you were
just looking at the coupon itself so
this stuff is really important I would
recommend that you go back and re-watch
this video if it really didn't sink in
the first time maybe even go back to
lesson 1 under this unit 2 and start
from the beginning and watch all three
of these videos again and it would
really start to maybe click for you if
you didn't get it the first time so make
sure you understand yield to maturity
that's the one you really want to
understand and have fun working with our
bond calculator below this video so in
this lesson we had four lesson
objectives the first was understanding
simple interest understanding
compounding for bonds the current yield
and yield to maturity and thanks for
joining us in unit 2 and we look forward
to seeing you in unit 3