Yield to maturity of a bond
Examples for the financial calculators
Tuesday, 10 June 2008 05:32
This is an example for the bond calculator. See also the usage notes and the market value example.
Suppose the government issues a thousand dollar bond on January 15, 2000, with a bi-annual coupon of 3%. The bond will be repaid in 2015 at January 15. On May 2, 2008 the bond is traded for $1008, This is the clean price which means that any accrued interest has to be paid on top of this $ 1008. The question is how to compute the yield to maturity of this bond.
Enter the following values into the fields of the calculator:
|Nominal interest||6||A coupon rate of 3% twice a year makes 6% per year.|
|Coupon period||6 months||Interest is paid every 6 months.|
|Date computation||2008-05-02||The date on which the Yield to Maturity is computed. The date format is YYYY-MM-DD.|
|Maturity date||2015-01-15||Date on which the principal amount ($1000) is back back. The date format is YYYY-MM-DD. From the Maturity Date and the Coupon Period the coupon dates are computed.|
|Interest in advance or afterwards||afterwards||For almost all bonds the coupons are paid at the end of each period.|
|Nominal value||1000||Amount that is paid at the end of the last period, on top of the coupon.|
|Compute Yield to Maturity or Value||Yield||Select the type of computation|
|Market value||1008||Value of the bond on the date of the computation.|
|Add coupon to market value:||checked||If this is checked then the field Market Value refers to the Clean Price otherwise the field Market Value refers to the Dirty Price, which includes accrued interest of the current coupon.|
For the values above the calculator computes a Yield to Maturity of 5.94% per year. Furthermore the accrued interest of the current coupon period is equal to $17.64. This means that the Dirty Price of the bond is $1025.63.
The computation finally shows that the Modified Duration is equal to 5.22. So if the interest goes up by one percent then the Clean Price of the bond goes down by approximately 5%.