Bond pricing issues
Purchase price and required yield
The purchase price of a bond is calculated as the present value of the remaining coupon payments and the redemption value, using the required yield as the interest rate.
If interest rates didn't change, calculating this present value could easily be done with the Periodic Payment and the Single Payment calculations that FinKit provides.
Unfortunately, this isn't the case: the price of a typical bond will change in the opposite direction from a change in interest rates. As interest rates rise, the price of a bond will fall. As interest rates fall, the price of a bond will rise...
Accrued interest
To complicate things further, there's the problem of pricing a bond between interest dates.
When a bond is sold between the previous and the next coupon date, the buyer will have to compensate the seller for the accrued interest on the settlement date.
Theoretically, this accrued interest should be calculated as compound interest using an equivalent daily compounded rate.
In reality however, a practical method is used: the fractional part of the coupon is calculated using the effective periodic yield rate multiplied by the exact number of days since the previous coupon day and divided by the exact number of days between the previous coupon day and the next coupon day.
To determine the previous and next coupon days, FinKit assumes that if the redemption date is the last day of a month, all coupon days are also the last day of the month.
If the day number of the redemption date (e.g. 29, 30 or 31) isn't available in the target month (usually February), the last valid date in the target month will be used as the coupon date.
To view the coupon dates that FinKit uses, switch to the Bond Book Value calculation and have a look at the details.
Premium and discount
A bond is said to be purchased at a premium if its purchase price exceeds its redemption value.
If the purchase price of a bond is less than its redemption value, it is said to be purchased at a discount.
Book value
The book value of a bond is the present value of the sum being invested in a bond. It is adjusted to market value.
On the redemption date, the book value of a bond equals the redemption value of the bond.
When a bond is purchased at a premium, the book value of the bond will be written down at each coupon date, so that at the time of redemption its book value equals the redemption value.
When it is puchased at a discount, the book value of the bond will be written up at each coupon date.
The book value of a bond on the settlement date is obtained by linear interpolation between its book value on the previous coupon day and the next coupon day.
Market price and market quote
The purchase price of a bond can be considered as being composed of two parts:
| • | the market price of the bond, which is the book value of the bond on the settlement day |
| • | the accrued interest of the next coupon payment |
If actual purchase prices were quoted, there would be a steep drop in price at each coupon day, when the accrued interest would abruptly change to zero.
Therefore, the market price of the bond is quoted, or rather the market price of a $100 bond, called the market quote. It is rounded to the nearest eight.
Related topics
| Bond features |
| Bond yield measures |
| Bond Price |
| Zero-Coupon Bond Price |