Before knowing about the Dirty price, we have to know about some basic terminology. Let’s look into that –

Dirty Price Explained

Investment

When a private company starts an entrepreneurial business or wants to enlarge the boundary or government takes an initiative, they need a certain amount of start-up money. For this money, when a man or the bank lends money for a definite time, it is known as investment.

Interest

Why would anyone give anyone money without any profit reason? But, if you borrow money from him for some time, and when you giving back that money, you gave some extra money, then definitely they will lend you money.

Let us assume, I give you $1000 for 1 year. The condition is, after 1 year, you have to give me back $1100. So, interest for 1 year is 10%.

Bond

To know about the dirty price, the essential term is a bond. As we discussed earlier that there are two ways to borrow money.

When a company decides to borrow money from people instead of a bank, they sell bonds. One can buy one or more than one bond as per ability.

Let’s say, a company needs 5 million dollars to expand its business. Now, they can make 5000 bonds each of 1000 dollars with an annual coupon of 10%. Simply, each year the bondholders will get 100 dollars as the interest and after maturity, they also get back the lended money or we can say the principal amount. So, the next question is what is maturity?

Maturity

Maturity simply denotes the longevity of a bond. That is, for how many months or years, the bond will be applicable.

Note: Bond’s maturity can be any number of years

If the maturity of the aforementioned bond is two years, that means for two years, the lender will get 10% interest on 1000 dollars (i.e. 100 dollars annually) and after two years the company has to give back the original amount to the lender or the bondholder.

Now as the terms are clear we can finally know the meaning of Dirty price.

What is Dirty price

The dirty price is a bond pricing quote, which refers to the cost of a bond that includes accrued interest based on the coupon rate. If a bond quotes between coupon payment dates, the price cited includes accrued interest up to the day of the quote.

The interest increases at a steady rate on a bond and calculation of the earned amount happen each day. As a result, the dirty price will change daily until the payout, or coupon payment date.
The dirty price compensates the seller for the accrued interest he’s earned but not yet received.

Let’s know about Accrued Interest

In the financial world, it might happen that a bondholder sells his/her bond to another one in between the period. It that case, the previous holder must be paid the interest that accrued (accumulated) prior to the sale.

Accrued interest is the amount which has been incurred, as of a specific date, on a loan or other financial obligation but has not yet been paid out.

In the case of bonds offering semi-annual payments, the dirty price would rise slightly higher every day over the course of six months. Once the six-month mark arrives, and the coupon payment is made, the accrued interest resets to zero to begin the cycle again.

The dirty-to-clean process continues until the bond reaches maturity.

So, as a conclusion, we can say, dirty price is the amount which includes both the principal amount and the allotted interest on that amount.

Dirty price V/s Clean price

The clean price is the amount excluding any type of interest.

  • The clean price is the price of a coupon bond not including accrued interest.
  • Clean quotes are typical in the United States, and dirty quotes are standard in Europe.
  • Once the pay-out is complete, and the accrued interest resets to zero, the dirty and clean prices are the same.

In a mathematical formula, we can easily understand –

Dirty price= Clean price + Accrued interest
Clean price = Dirty price – Accrued interest
Accrued interest = Dirty price – Clean price

Example of Dirty Price

Q. A corporate bond has a price of 97.534, a $1,000 par value and a 6 percent annual coupon rate. Assume it’s been 15 days since its last interest payment.

Ans. Divide 97.534 by 100 to get 0.97534. Multiply 0.97534 by $1,000 to get a clean price of $975.34. Multiply the bond’s annual coupon rate by its face value to figure its annual coupon or interest payment. Multiply 6%, or 0.06, by $1,000 to get $60 in annual interest.

Divide 15 by 360 to get 0.0417. Multiply the result by the annual interest payment to determine the accrued interest. In this example, multiply 0.0417 by $60 to get $2.50 in accrued interest.

Add accrued interest to the bond’s clean price to calculate its dirty price. Concluding the example, add $2.50 and $975.34 to get a dirty price of $977.84.

Final Words

Both Clean price and the dirty price has its significance in the financial market and none of them can be ignored.

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