Entering the world of bonds? Understanding the difference between clean and dirty prices is crucial to navigating bond purchases and true value.
What is the Clean Price?
The clean price of a bond is the price of the bond excluding any accrued interest. This is the price that is quoted in the bond market. The clean price focuses purely on the capital value of the bond and does not take into account any interest that has accrued since the last coupon payment.
To calculate the clean price, you would typically take the bond's quoted price and subtract the accrued interest. The accrued interest is calculated based on the bond's coupon rate, the face value, and the number of days since the last coupon payment.
Example of the Clean Price
As an example, let us imagine that a company like Tesla Inc.; (TSLA), issued a bond at a face value of $1,000 and is currently trading at $970 in the financial market. The bond has a Semi-annual coupon rate of 5% with Annual Coupon rate on the bond. This means, for the bond, investors would get $25 every six months, or $50 per year.
The clean price of the bond is $970 from which the cost of the bond is subtracted to get the present values of its cash flows. If any interest has accrued on the bond and if this is to be quoted to the investors, the price would include this amount. This work is done by the broker through establishment of the daily accrued interest and then it is added to clean price. The total price, or the dirty price, is related to the number of days that have passed since the last coupon paying date, because interest starts accumulating as soon as the previous payment has been made.
Let's consider two scenarios using our Tesla example:
1. Suppose an investor purchases the bond one day before the next $25 coupon payment; he gets approximately $24.86 of interest would have been accumulated to the credit of the account up to that date. Thus, the bond price for the investor would be approximately $994.86, which is the clean price of $970 plus $24.
2. If the investor buys the bond at the date of coupon payment when interest is paid, then the dirty price will be equal to the said clean price which is $970.
Right after the coupon payment, the bond's price resets to the clean price, and the dirty price equals the clean price. Interest begins to accrue again immediately after the coupon payment until the next one.
What is a dirty price?
The dirty price of a bond, also known as the "full price" or "invoice price," is the total price an investor pays for the bond, which includes both the clean price and any accrued interest since the last coupon payment. The dirty price is important for bond transactions because it reflects the actual amount the buyer needs to pay to the seller.
To understand the dirty price, let's break down its components:
- Clean Price: This is the bond's price excluding any accrued interest. It reflects the bond's intrinsic value based solely on its coupon payments and maturity value.
- Accrued Interest: This is the interest that has accumulated on the bond since the last coupon payment date. It is calculated based on the bond's coupon rate, the face value, and the number of days since the last coupon payment.
Example of the Dirty Price
Imagine Google Inc. issued a bond with a face value of $1,000, and the market price is quoted at $950. The bond has a coupon rate of 5% annually, with interest payments made semiannually. This means investors receive $25 every six months for holding the bond.
The $950 is the clean price, or the market price without considering accrued interest. However, an investor wanting to buy the bond would get a quote from a broker that includes the clean price plus any accrued interest. The broker calculates the daily accrued interest to add to the clean price. Let's assume no broker commission is involved. The amount of accrued interest will depend on the number of days since the last coupon payment.
For instance, if the investor buys the bond one day before the next $25 coupon payment, $24 in interest would have accrued. Thus, the bond's total price for the investor would be $974, which is the clean price of $950 plus $24 in accrued interest.
Dirty Vs. Clean Pricing
The dirty price is commonly quoted in transactions between brokers and investors, while the clean price, which excludes accrued interest, is generally the published price. This clean price, also known as the flat bond price, is typically listed in newspapers and financial resources that track bond prices. Despite the dirty price encompassing accrued interest, the clean price is often regarded as the bond's current market value.
Bottom line
Understanding the difference between clean price (bond's value) and dirty price (total cost including accrued interest) is essential for bond investors. The clean price is typically quoted and reflects the bond's market value, while the dirty price reflects the actual amount an investor pays, considering accrued interest since the last coupon payment.
