Overview
Bonds are financial instruments that pay regular coupons, At the maturity date the face value of the bond is paid to the holder of the bond.
The value or price of a bond depends on the current market rate:
- if interest rates increase, the coupon rate is less than the current rate, so the bond will trade below par.
- if interest rates decrease, the coupon rate is higher than the current rate, so the bond will trade above par.
In both cases the holder of the bond will receive the full face value of the bond on the maturity date, regardless whether they paid less than the face value.
To calculate the price of a bond for a given market rate, the present value of the expected coupons is added to the present value of the face value of the bond.
The yield to maturity of a bond (usually referred to as "yield") is closely related to the price of a bond, a higher price will result in a lower yield and vice versa. This metric can be used to compare bonds with different maturities and coupons.
Examples
A company sells $1,000 bonds with a nominal annual rate of 5 % which will pay semiannual coupons of $25 and will mature in 2 years.
Bond price
What is the price if the market rate is 4 %, and 6 % respectively?
Set up the following cashflow or select the Bond price and yield example in the Help > Examples menu.
| Date | Type | Value | Occurs | # | Comment |
| 1-1-2025 | unknown | 1 | once | Settlement | |
| 1-7-2025 | inflow | 25 | semiannually | 4 | Coupons |
| 1-1-2027 | inflow | 1,000 | once | Maturity |
Make sure that semiannual compounding is selected and that Auto update is checked.
As you would expect, at a rate of 5 % the x Value field displays -1,000.00.
For a rate of 4 % the x Value becomes -1,019.04, or a $1,019.04 price.
For a rate of 6 % the x Value becomes -981.42, or a $981.42 price.
Bond yield
If the bond in the previous example is priced at $1,025.00, what is its yield to maturity?
Enter -1,025 in the x Value field. Doing this will deselect Auto update and calculate with the given value.
The yield at this price can be found by checking the IRR result which shows 3.6917 %.
Calculating for dates other than the issue date
The previous examples all use the issue date.
If you want to know the value on a later date, you will need to change the date of purchase (the Unknown event) and adjust the date of the first coupon payment and the number remaining coupons accordingly.
What if the bond is a zero-coupon bond?
As zero-coupon bonds do not pay coupons, only the present value of the face value is calculated.
In the previous example, check Auto update and delete the event for the coupons.
For rates of 4, 5 and 6 %, prices will be $923.85, $905.95 and $888.49 respectively.
If it is offered at $900, its yield to maturity will be 5.3379 %
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