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Bonds | Pricing a Bond | At Par / Premium / Discount — Transcript

by Joefessor · 2,150 words · 357 segments · language en · Watch on YouTube

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0:00hello there in this video we are going
0:02to discuss the basics of bonds
0:05we're going to start with understanding
0:07some of the basic terminology behind
0:09bonds
0:10and we're going to learn the differences
0:12between bonds and stocks or shares and
0:16later we look at how to price a bond
0:19and also understand what yield to
0:21maturity is in detail so that we can
0:23clearly understand what it means
0:26when they say that a bond trades at
0:28power or at premium or at discount okay
0:31so to begin with bonds are instruments
0:34of fixed income okay
0:36a bond can be issued by a company or the
0:39government or different sections of the
0:41government such as municipalities for
0:42example
0:43okay the structure of a bond is very
0:46similar to that of a loan
0:48so instead of borrowing money from the
0:49bank if a firm needs a huge amount of
0:52money
0:53they could ideally issue bonds to
0:55potential investors okay who who pay the
0:59price of the bond to buy today
1:01and in return they collect these
1:03interest payments in the which in the
1:05case of bonds are known as coupon
1:07payments
1:08and they keep collecting these coupon
1:10payments until the bond matures after a
1:12certain period of time let's say five
1:14years or ten years right okay
1:17so what's the difference between a bond
1:19issued by a firm or stock or shares
1:22issued by a firm okay a bond
1:25offers periodic coupon payments okay
1:27this is fixed it doesn't change okay if
1:29the bond says okay
1:31the firm can offer 10 every year that's
1:34fixed okay if you're invest if
1:37if you invest in this particular bond
1:39you get a return of 10 every year okay
1:43but on the other hand if you invest in
1:45stock or shares you don't expect
1:47periodic payments as in the case of
1:49bonds okay
1:51if you invest in shares or stock you
1:53could potentially get dividend payments
1:56which can be regular or irregular
1:58nothing is guaranteed or you could also
2:00make money if the stock appreciates in
2:02value and you could sell them but in
2:04this case of bonds they are an
2:06instrument of fixed income
2:08these coupon payments are regular but
2:10again they are not guaranteed right
2:13let's say this bond is issued by a
2:15corporation which is presumed to have
2:17high risk
2:18if at some point in time if this company
2:21goes bankrupt then the chances of you
2:23recovering the remaining coupon payments
2:25or the face value can drastically go
2:28down okay
2:30so let's start with looking at some of
2:31the terminology behind pawns okay
2:35face value or par value okay so each
2:38bond has a face value or power value
2:40which is the amount you receive
2:42when the bond matures
2:44okay this is usually a rounded value
2:46like a hundred dollars or a thousand
2:48dollars okay so if the bond is let's say
2:51for five years at the end of five years
2:53if you are a bond holder you receive
2:55this amount it can be that hundred
2:57dollars or a thousand dollars
2:59maturity date
3:01is the date at which the bond matures
3:03like i said if the bond is issued for
3:05let's say five years or ten years the
3:07maturity date would be five years from
3:09now or ten years from now
3:12coupon rate
3:14like we discussed earlier is the
3:15interest rate right so if you borrow
3:18if you buy a bond today you are entitled
3:21to a coupon payment
3:23if it's an annual bond you get it every
3:25year or if it's a semi-annual bond which
3:27is usually the case you get a coupon
3:29payment every six months okay remember
3:32this is very similar to the interest
3:34payment being made on the loan okay
3:37into maturity
3:39as the term itself implies it's the
3:41yield you make until the bond matures
3:45okay
3:46it's the return it's the expected return
3:49if you hold the bond until maturity we
3:52will see how this is different from the
3:53coupon rate later when we look at
3:55examples of how to price a bond okay
3:59when bonds are issued they are typically
4:01issued at par
4:02what i mean by at par is that if the
4:05face value of a bond is a hundred
4:06dollars
4:08the issue price is also a hundred
4:10dollars
4:11okay but bonds because they are traded
4:14in the market their price can fluctuate
4:16for a variety of reasons
4:18and if the price exceeds the face value
4:21or if the price is higher than the face
4:23value
4:24then the bond is said to be trading at
4:25premium
4:27or if the price is less than that of the
4:28face value let's say ninety dollars for
4:31a bond with the face value of a hundred
4:32dollars then the bond is said to be
4:35trading at discount okay we'll look at
4:37those in detail
4:39when we calculate how to price a bond
4:42okay we're going to start with a very
4:44simple example here
4:45with an example of a zero coupon bond
4:48okay what do i mean by zero coupon bond
4:51is a bond which does not pay coupons
4:54okay or the coupons are zero
4:57okay so what you get when the bond
4:59matures is the face value and you do not
5:02get any coupon payments in between so
5:05let's assume an example where the face
5:07value of a zero coupon bond is a hundred
5:09dollars
5:10okay
5:12and the yield to maturity is five
5:14percent okay so that's the expected
5:16return of the bond if you hold it to
5:19maturity okay
5:21the maturity so the date of maturity for
5:24the particular bond is six years from
5:26the issue date okay the price of this
5:29bond can be calculated using the present
5:32value function pv
5:34the rate is the rate of return which is
5:36five percent the number of periods is
5:39six years
5:41there are no
5:42regular payments so pmt is going to be
5:45zero
5:46every the future value is hundred which
5:48is the amount you receive at the end of
5:50six years okay
5:53i've made another video where i
5:54discussed these finance functions pv fv
5:58rate number of periods and so on in a
6:01separate video i'll link that below in
6:02the
6:03description so you can check that out if
6:05you are interested
6:06okay
6:08so the price of this bond is
6:09approximately 74
6:11okay
6:12next we are going to look at a bond with
6:14coupon payments okay we're going to
6:16continue
6:18with a similar example but in this case
6:21a bond has coupon payments
6:23okay
6:24let's assume that the bond has a face
6:26value of a hundred dollars again okay
6:29the yield to maturity is 10
6:31and the coupon payment is again
6:3310
6:34or 10 every year
6:36the maturity date is six years from now
6:39okay
6:40how do you calculate the price of this
6:42bond we use the pv function again
6:44okay so the rate
6:48is 10
6:50and the number of periods is six years
6:53now we have an annual payment of ten
6:55dollars every year
6:58which is the payment and then the future
7:00value is the face value which we get at
7:03the end of
7:04the six years okay
7:06in this case the price of the bond is
7:08exactly the same as the face value of
7:10the point
7:11this is because the yield to maturity is
7:13exactly the same as the coupon rate okay
7:16we would later look at examples to see
7:19how this changes when the intermaturity
7:21changes
7:22okay
7:23as we discussed earlier bonds provide
7:26a fixed income right so ten dollars
7:29every year is being fixed
7:31for a period of six years okay
7:34but in the market interest rates can
7:36fluctuate up or down and because of
7:39these fluctuations the effective yield
7:41you get from this particular bond can
7:44change over time
7:46now let's expand this example a little
7:48bit okay let's keep the same numbers
7:50let's assume this is a bond issued by a
7:52company called firm x okay
7:55now firm x
7:56issues a bond at par at a hundred
7:59dollars okay offering a coupon payment
8:02of ten dollars every year
8:04and the bond matures in six years
8:06okay
8:07now let's assume that two years have
8:09passed by
8:11since the issue of this bond okay so
8:13let's we're at this time point in time
8:16okay so the time left to maturity for
8:18this bond is now
8:21only four years okay i'm going to remove
8:23that first
8:24so we just have four more years to
8:26maturity
8:28in these two years let's assume that the
8:30interest rate in the market has gone up
8:32okay what do i mean by that
8:35if there are other firms in the market
8:37which are similar to firmax in in terms
8:40of their risk profile
8:42these firms
8:43offer a higher return on their bonds
8:46okay
8:47so now the bond offered by firm x
8:50is no longer attractive if it trades at
8:53a hundred dollars okay remember we
8:55mentioned that bonds can trade every day
8:57in the market
8:59and somebody who's looking to buy a bond
9:01with a similar risk profile would now
9:03prefer
9:05to invest in these other bonds let's say
9:07which offer a return of 12
9:10but firm x only offers a return of 10
9:12percent and hence it's not attractive
9:15anymore okay so what happens now is that
9:18firm x which has a similar risk profile
9:22should also offer a similar return as
9:25compared to these other firms
9:27so if the yield offered by the other
9:28bonds are 12
9:30then firm x also offers a yield of
9:3412
9:36how does this happen
9:37it happens in the market through a price
9:40adjustment okay
9:41the bond from firm x no longer trades at
9:44hundred dollars
9:45it trades at new price which can be
9:47calculated again using the same pv
9:50function
9:51the rate now is 12 instead of 10
9:55the number of periods we only have four
9:57more years to go
9:58the payment stays the same the bond
10:01still keeps offering the 10 coupon
10:03payment
10:04and the face value of a hundred dollars
10:08now we can see that the bond trades at
10:11approximately ninety four dollars
10:14okay why did the price go down
10:17so that an investor who still keeps
10:19getting the ten dollar coupon payments
10:21and the hundred dollar face value at the
10:23end of the sixth year okay would
10:25effectively
10:26get a return of 12
10:29if you look at the table here on the
10:31right this example corresponds to the
10:33last one here
10:34where the coupon rate is less than the
10:36yield to maturity so in this case 10
10:38percent was less than the 12 which is
10:40the effective return
10:42so the price adjusted itself downward as
10:45compared to the face value okay in this
10:48case the bond is said to be
10:50trading at a discount
10:52what happens if the interest rate in the
10:54market
10:55goes down okay effectively
10:58let's say
10:59the other
11:00the other bonds which are similar to
11:02firm x offer a return of
11:05eight percent
11:06instead of twelve percent okay
11:08now our bond from firm x becomes much
11:12more attractive
11:13why
11:14because offering a 10 coupon rate at a
11:17price of 100
11:19gives an effective return of 10 percent
11:21and that's very attractive so now the
11:23demand for the bond from firm x
11:26increases and this results in an upward
11:29adjustment of the price okay
11:32as you can see now the price is around
11:35107
11:37this upward adjustment in the price
11:39happened because the bond from firm x
11:42was still offering a coupon of 10
11:44percent which has been fixed
11:46but the effective return in the market
11:48is only to eight percent okay so firm x
11:52ends up offering a return which is
11:53similar to this other firms with the
11:55same risk profile in the market
11:58bonds also typically offer coupons on a
12:02semi-annual basis rather than on an
12:04annual basis okay now let's quickly see
12:06how to make these adjustments in the
12:08formula to reflect the semi-annual
12:10payments okay so we keep the same pv
12:12function
12:13okay now the rate which is eight percent
12:16is an annual rate i'm going to divide
12:18that by two to get the semi-annual rate
12:23the number of periods is four years i'm
12:25going to multiply that by two
12:27to get eight time periods
12:30the coupon payment is ten dollars per
12:32year i have to divide that by two to get
12:34to reflect five dollars every six months
12:37and the face value
12:38is at the end of
12:41the four years okay if you get
12:43semi-annual payments
12:45the price of the bond from firmax is
12:47approximately 106 dollars
12:49this price instead of using the pv
12:51function you could also calculate it
12:53using the npv function i already have
12:56another video on how to calculate npv
12:59and irr and so on i'll link that in the
13:01description below and if you're
13:03interested you can check that out
13:06thank you for watching this video cheers

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