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Bond Pricing Formula | How to Calculate Bond Pricing? - YouTube
Channel: WallStreetMojo
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this video bond pricing formula watch
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that's given below welcome everyone and
today we are going to study a
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risk-management basic basically it's a
fixed income product and we are going to
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learn the bond pricing formula something
that is a part of the fixed income
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product fixed income is a part of
investment banking under the risk
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management portion so this exactly so
this is the formula well I'm pretty much
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sure that after looking at this your
mind has gone haywire that what exactly
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CRNF is all about well don't worry we
are going to learn the nitty-gritty first
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of all we need to what we are going to
do in this whole particular session is
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that we are going to give your short
synopsis what are the topics see we are
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going to learn the bond pricing formula
okay
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was that an explanation session
explanation part will be there after an
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explanation an example will be there to
help us out to understand the formula
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and post-facto you know will have some
relevance and the use of this bond
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pricing formula well let's begin with
the formula first what is the bond price
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formula first of all see the formula for
the bond price is basically the
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calculation of the present value of the
probable future of cash flow okay cash
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flows which comprises of the coupon
payments and the par value which is the
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Redemption amount of the maturity so the
rate of the interest which is used to
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discount the future cash flow is known
as DYTM now the bond pricing formula
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for the coupon paying bonds is
mathematically represented as what I've
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shown here C divided by 1 plus or
basically you know it's a summation
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basically c upon 1 plus R raise to n
okay plus F divided by 1 plus R raised
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to n now so that
converts down to see this gets converts
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down post what we had discussed previous
formula means here F is the face value
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or the par value of the bond are over
here is basically the yield to maturity
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YTM and n over here is number to the
majority on the other hand the bond
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valuation formula for the deep discount
bonds this discount bonds or zero coupon
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bonds can be computed simply by
discounting the par value to present
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value which is mathematically
represented okay as you know the ZCV
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zero coupon bond is equal to as the name
suggests there is no coupon payments you
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know the explanation to the bond pricing
of the formula the formula for the bond
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pricing calculation by using the
following steps can be calculated first
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of all step number one is firstly the
face value or the par value of the bond
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issuance is determined as per the
funding requirement of the company the
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par value is denoted by if step number
two well now the coupon rate which is
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the analogue has to interest rate of the
bond and the frequency of the coupon
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payment is determined the coupon payment
during a period is calculated by
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multiplying the coupon rate and the par
value and dividing the result by the
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frequency of the coupon payment with you
so the coupon payment is denoted by C
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okay so C is equal to your coupon rate
into F divided by number of coupons
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payment in you know step number three
now the total number of the period still
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maturity is computed by multiplying the
number of years till the maturity and
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the frequency of the coupon payment in a
year so the number of periods till the
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maturity is denoted by n and n is equal
to number of years til maturity into
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number of coupon payments in a year
let's calculate
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step number four now the yield to
maturity is discounting factor and it is
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determined based on the current market
return from the investment with similar
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risk profile so the YTM is denoted
by R now the present value of the you
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know of the first second and the third
coupon payment and so on for the present
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value the par value to redeem n period okay is to be derived by the cash
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flow divided by one plus RS to one cash
flow of two divided by 1 plus RS to 2
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and so on and so for it goes on okay so
final step will be step number 6th that
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will be basically the bond price is
equal to your C/(1+R)
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plus R okay raise to n plus F divided by
1 plus R raised to n okay let me make
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you understand with the help of an
example here how things we settled down
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the example of the bond pricing formula
will be done something in the following
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format these are the some of the example
of the bond pricing formula example
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number 1 let us take an example of a
bond with the annual coupon payment let
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us assume that D company XYZ has issued
a bond that is having with the annual
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coupon payment and let's say XYZ has
issued a bond value of a face more bond
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having a face value of closely around 100000 having carrying an annual
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coupon rate at let's say 7% okay
and maturing in 15 years of timespan
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well in this regard the prevailing
market rate of interest is 9%
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here so given the F that is 100000 see 7%
that is the coupon amount will
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be 100000* 7% that will give us
$7000 n15 are 9% so apply
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the formula okay what will happen is
that over here we will try and calculate
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the entire value that is here 7,000
coupon okay into bracket 1 minus bracket
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1 plus the rate of interest okay that is
what your 9% close the bracket okay
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raised to now this will be in negative
raised to what it will begin number of
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years till maturity which is 15 years
we'll change it since I've written 15
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years we'll have to change it okay now
close the bracket for the timing just
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change this to 15 okay now the formula
continues again divided by you will have
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to do the rate of the interest that is
9% okay I hope you are getting
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it what we are trying to do here plus
open the bracket then again the face
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value divided by one plus this is a
formula that we have studied okay one
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plus the rate of the interest that is
9% okay raised to the number
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of years still maturity so now once we
close the bracket we have the answer a
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838 so this is the bond price we have
applied the entire formula here and then
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we have gone to Conference of 83 879 now
since the coupon rate over here is lower
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than the market interest rate the bond
price is is less than the face value and
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such bonds are trading at discount had
it been let's just change the numbers
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and see what exactly is
going to happen here
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had it been this being let's say 9%
and this be see if it is 9
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it stays at 100000 if this goes
10 it will it will trade how much will
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it be more than 100000 of will it be
worth less 100000 think about it it is
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going to be a premium so the bond price
will increase see if increase so what is
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relation
if your open rate is greater than your
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YTM then your bond will be trading at
premium and if your coupon rate is less
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than your YTM it is basically trading at
discount
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well I hope you have got a fantastic
idea how things have been operated here
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and post factor learning this I want to
make you I want to make you understand
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what is the relevance and the use of the
bond pricing formula now the concept of
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the bond pricing is very important
because bonds form an indispensable part
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of the captive market and as such
investors and analysts are required to
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understand how the different factors of
the bond behave in order to determine
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its intrinsic value so similar to the
stock valuation reprising the bond is
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helpful in understanding whether it is
suitable for investment for a portfolio
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and consequently forms an integral part
of the bond investing well that's it for
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this particular topic if you have
learned and enjoyed watching this video
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