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:
- 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