How to calculate the invoice price of a bond
About this lesson
In this video, I will discuss a bond’s invoice price and show you the calculation of invoice price with a numerical example.
Quoted price vs invoice price
Bond prices are quoted without the interest that has built up since the last coupon payment. That’s the flat or clean price.
When you buy a bond between coupon dates, you also pay the seller the interest they’ve earned so far, the accrued interest. The total you pay is the invoice (or dirty) price:
Invoice price = Quoted price + Accrued interest
Accrued interest
Accrued interest = Coupon payment × (Days since the last coupon ÷ Days in the coupon period)
Example
- Face value: $1,000
- Coupon: 8%, paid semi-annually, so each payment is $40
- Days since the last coupon: 40
- Days in this coupon period: 182
- Quoted price: $990
Accrued interest = 40 × 40 ÷ 182 = $8.79
Invoice price = 990 + 8.79 = $998.79
At the next coupon date, you receive the full $40, which repays the $8.79 you gave the seller, plus the interest you earned yourself.
Why bonds are quoted “clean”
If prices included accrued interest, they would creep up between coupon dates and drop on each payment date, even if nothing changed in the market. Quoting the clean price makes real price changes easier to see.
Next: the zero-coupon bond.