A “Clean price” is the price of a bond that does not include Accrued interest. On the other hand, A “Dirty price” is the price of a bond that consists of Accrued interest and a clean price. The Exact calculation of Accrued interest depends upon the “Day Count Conventions”.
In Clean price, the price quotes the percentage of the face value and it fluctuates with interest rates and bond market conditions. The Clean Price is applied to compare different bonds. In Dirty price, the price is based on clean price and interest accrued and it changes each day that interest accrues. The Dirty Price is applied to determine the total cost of a bond.
Now, Let’s take an example to understand these terms. If company XYZ issues a bond at $1000 face value and it’s quoted at 900. The clean price of the bond is $900. If company XYZ pays an 8% coupon annually, the “clean price” of the bond is still the same,i.e., $900. Also, A Clean price is applied to calculate the Dirty price. Suppose Company XYZ issues its coupon payments on January 1 each year. In the US, Corporate bonds usually follow a 30/360-day count convention. The Accrued interest is calculated as follows:
Accrued interest = FV x C/P x D/T
FV: Face value.
C: Coupon rate.
P: Number of coupon payments per year.
D: Days Since the last coupon payment was made.
T: Days between Payments or accrual period.
I am assuming the date of selling the bond is July 1. Now, we will use the above formula to calculate the accrued interest. The accrued interest is $40. So, The Dirty price is an addition of $900(clean price) and $40(accrued interest), i.e., $940.
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