Dirty Price

The dirty price depicts a bond's actual price. It includes accrued interests. Therefore, it is the price paid by an investor when they purchase a bond. Accrued interests are a culmination of interests between two coupon dates.

The dirty price always remains equal to or higher than the clean price as interest is added to the market price. On the date of coupon payment, both prices are the same. In secondary markets, it is also referred to as an invoice price.

• The dirty price of a bond includes interests. Interests are accumulated between two coupon payments; it increases every day.
• US corporations calculate the bond interest accrued over 30 days or 360 days. It is referred to as the 30/360 day-count convention.
• The actual amount paid by a buyer is called ‘dirty’ because the seller charges extra. Hence, this difference in prices becomes an income for the bond issuer.

Dirty price is the present value of a bond; specifically, it is the bond’s discounted future cash flows. The dirty price of a bond includes accrued interests.

To comprehend the meaning of bond price, we must first define a bond. Bonds are debt instruments issued by governments or corporations. Bonds are fixed-income securities that allow the bondholders to earn periodic interest—in the form of coupon payments. Thus, bond issuers are borrowers, and bondholders are the lenders (or investors).

Every bond is issued at a specific coupon rate and an interest rate. Investors receive periodic repayments based on a fixed schedule. Based on the particular schedule, bondholders receive payments every month, every quarter, twice a year, or once a year. Most US bonds repay investors twice a year.

Typically, bonds are priced according to their present value. Once the coupon payment is made, investors do not receive any amount till the next scheduled repayment. The fund accumulates interest between two scheduled payments—accrued interest. Thus, accrued interest is reset on the payment date and starts back at zero.

Therefore, if an investor purchases a bond after the scheduled payment, they do not receive any coupon payment till the next repayment date. Thus, when accrued interests are added to the bond price, it becomes the dirty price.

It is called a dirty price because when an investor purchases a bond between two repayment dates, the accrued interest gets added to the bond’s price. Thus, the bond issuer is earning an interest-added price. Meanwhile, the buyer doesn't receive any payment till the next scheduled payment, which could take as long as a month, a quarter, six months, or even a year.

Again, the investor ends up waiting a long time to receive repayment, despite paying extra for the bond. So, naturally, there is a term called clean price. Clean price is the opposite; it does not include any interest in it and is used to compare two or more bonds in the market. In other words, the clean price is the present value of a bond's discounted future cash flows, excluding the interest payments.

Investors need not hold a bond till maturity. Then, they can sell it in the secondary market. A secondary market or an aftermarket is a platform where investors can buy or sell securities issued by an original issuer (bank, corporation, or government entity).

Usually, bonds are traded OTC (over the counter), and the transaction costs are not standardized. Dealers have an inventory of corporate bonds. Markups and markdowns are associated with different types of bonds. Markups significantly affect the market price of a bond. Due to price fluctuations, investors struggle to ascertain the bond price.

The dirty price formula is as follows

Dirty Price = Clean Price + Accrued Interest

Here,

Accrued interest = F x C/M x D/T

• Here, F is the face value.
• C is the annual coupon rate.
• M denotes coupon payments per year.
• D stands for days since the last payment.
• T denotes the accrual period.

Let us look at a dirty price example to understand the concept better.

Kate bought a government bond with a coupon rate of 5%; it will mature in 2023. The bond offers semiannual payments—one on December 1 and another on June 1. Kate bought the bond on January 1, 2021, for a quoted clean price of $1,800.

Now let us determine the accrued interest. The accrued interest is a culmination of interest since the last payment date. Since Kate purchased the bond on January 1, 2022, 31 days have elapsed (December 1 to January 1).

Based on the given values, accrued interest. Is as follows:

• Accrued interest = F x C/M x D/T
• Accrued interest = 1800 x 0.05/2 x 31/182.5
• Accrued Interest = 1800 x 0.025 x 0.169
• Accrued Interest = $7.60

Now let us calculate the actual price paid by Kate (including accrued interests).

• Dirty Price = Clean Price + Accrued Interest
• Dirty Price = 1800 + 7.60
• Dirty Price = $1807.60

Therefore, on January 1, 2022, the bond's dirty price was $1807.60. Here, the bond issuer nets the extra $7.60 paid by Kate as a profit.

Let us look at dirty price vs clean price comparisons to distinguish between the two.

• Dirty price is the present value of a bond; specifically, it is the bond’s discounted future cash flows. It includes accrued interests. In contrast, the clean price of a coupon bond does not include accrued interests. Clean price is the present value of the bond’s discounted future cash flows, excluding interest payments.
• The former fluctuates daily, but the latter fluctuates concerning market conditions and interest rates.
• The former showcases a bond's actual market value, whereas the latter is the quoted price (bond issuers quote the clean price).
• The former gives an idea of the actual amount paid by a buyer. The latter is used to compare different bonds.

This has been a guide to what is Dirty Price of a Bond. Here, we explain it with its formula: Example, and comparison with the clean price. You can learn more about it from the following articles -

• Bond Quote
• Money Laundering
• Corporate Finance Interview Questions