Fixed Income

Calculate the Value of a Coupon Paying Bond

The value of a coupon paying bond is calculated by discounting the future payments (coupon and principal) by an appropriate discount rate.

Suppose you have a bond with a $1,000 face value that matures 1 year from today. The coupon rate is 12% and the bond makes semi-annual coupon payments of $60. The bond yield is 13%. The cash flows from the bond are depicted below:

 The bond characteristics are summarized below:

  • Par Value =     $1,000
  • Yield        =      13% annual (13/2 =6.5% semi-annual)
  • Coupon   =      12% with semi-annual payment of $60
  • Maturity   =      1 year

The value of the bond is calculated as follows:

Note that the coupon is paid semi-annually, i.e., $60 per 6 months. The discounting is also done semi-annually.

 The general bond pricing formula for all bonds can be stated as:

 

Where:

  • Pi \=  the price of the bond i
  • Ct \= cash flow from the bond i at time t
  • ri \= the annualized yield to maturity on bond i
  • M = the time in years until the bond matures
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