• # Calculation of the Issue Price and Market Price

As we know, the issue price is the present value of all the future coupon payments and principal payment of the bond discounted at the bond’s yield to maturity at the time of issuing the bond.

So the present value calculation method when coupon paid annually

PV = C1 / ((1+ YTM)^1) + C2 / ((1+ YTM)^2) + C3 / ((1+ YTM)^3) + …..+ Cn / ((1+ YTM)^n) + FV / ((1+ YTM)^n)

Where:

PV = Present Value or the issue price (at the time of issue)

Ct = Coupon payment at the end of tth year (paid annually)

YTM = Annual rate of Yield to Maturity

n = Tenure (in years)

FV = Future value or Par Value (paid at the time of maturity)

Using this formula, Issue Price of a bond can be calculated.

For zero-coupon bond the formula will be

PV = FV / ((1+ YTM)^n)

If coupon will be paid semi-annually

PV = C1 / ((1+ YTM/2)^1) + C2 / ((1+ YTM/2)^2) + C3 / ((1+ YTM/2)^3) + …..+ C2n / ((1+ YTM/2)^2n) + FV / ((1+ YTM/2)^2n)

Where:

PV = Present Value or the issue price (at the time of issue)

Ct = Coupon payment at the end of every t-th period (paid semi-annually)

YTM = Annual rate of Yield to Maturity (YTM/2 is used for semiannual calculation)

n = Tenure (in years) (2n will be used for semiannual calculation)

FV = Future value or Par Value (paid at the time of maturity)

Using this formula, Issue Price of a bond can be calculated.

Now let us see the calculation formula at any time during the tenure of the bond. If the time of trading is 2 months after the third semiannual coupon payment (means the fourth coupon payment is 4 months away) then the formula will be

PV = C4 / ((1+ CY/2)^(4/12)) + C5 / ((1+ CY /2)^2) + C6 / ((1+ CY /2)^3) + …..+ C2n / ((1+ CY /2)^(2n-20/12)) + FV / ((1+ CY /2)^(2n-20/12))

Where:

PV = Present Value or the market price (at the time of trading)

Ct = Coupon payment at the end of every t-th period (paid semi-annually)

CY = Annual rate of Current Yield (CY /2 is used for semiannual calculation)

n = Tenure (in years) (2n will be used for semiannual calculation)

FV = Future value or Par Value (paid at the time of maturity)

Using this formula, Market Price of a bond can be calculated. Check the below difference.

• Only the expected future payments are considered for present value calculation. First three coupon payments are paid and from fourth coupon payment, all the payments are pending.
• To get the present value of the first coupon payment (here fourth one) 4 months are considered to get the discounted factor because the next coupon payment is due only after 4 months.
• (2n-20/12) factor is used to calculate the present value of the final coupon payment and par value as already 20 months (1 year 8 months) are passed after the issuance of the bond. So the time left to receive the final coupon payment and the par value is (2n-20/12) years.

The Relationship among all the features

Let us consider the simplest form to analyze the relationship among all the features and terms used

PV = C1 / ((1+ YTM/2)^1) + C2 / ((1+ YTM/2)^2) + C3 / ((1+ YTM/2)^3) + …..+ C2n / ((1+ YTM/2)^2n) + FV / ((1+ YTM/2)^2n)

• If YTM or interest rate increases, the issue price or market price decreases. The converse is also true.
• Higher coupon rate results in higher issue/market price.
• If coupon rate > Interest rate, then issue/market price will be higher than par value.
• If coupon rate < Interest rate, then issue/market price will be lower than par value.

From the relationship we can say that when the interest goes up, the issue price or market price falls significantly. As the yield rate follows the market interest rate, in a high interest environment it has become always tough for the companies or government to raise money through bonds. Though bonds and debts are considered to be the cheap source of money, it does not work like that during that time. That is the main reason, high interest rate or borrowing rate slows the industrial activity and expansion plans of the companies.

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