# What Is Dirty Price?

DEFINITION
The dirty price of a bond is the price of the bond that factors in accrued interest. The dirty price is what you pay when you buy a bond, and is helpful in understanding its true value. When you buy a bond between coupon dates, you need to account for any interest that has accrued

The dirty price of a bond is the price of the bond that factors in accrued interest. The dirty price is what you pay when you buy a bond, and is helpful in understanding its true value. When you buy a bond between coupon dates, you need to account for any interest that has accrued.

## Definition and Examples of a Dirty Price

The dirty price is the price of a bond that factors in any interest that’s accumulated.

Many people invest in bonds because they’re seeking regular interest payments called coupons for fixed income. When you sell a bond between coupon payment dates, you’re entitled to the price of the bond in addition to the interest that accrued between payment dates.

To calculate the dirty price, you need to know the clean price along with the amount of interest that accrued.

The dirty price is calculated as follows:

Dirty price = Clean price + Accrued interest

You’ll typically see a bond price quoted as a percentage of its face value, also known as par value. For example, if Corporation ABC issues bonds with a \$1,000 face value that are quoted at 97, the price of the bond is \$970. This is referred to as the clean price.

## How Does Dirty Price Work?

Interest payments aren’t factored into the clean price. You need to calculate the amount of interest accrued to calculate the dirty price.

In the above example, suppose ABC offers bond investors a 5% coupon and makes its payments semiannually. To calculate accrued interest, use the following formula:

Accrued interest = FV x C/P x D/T

FV: Face value

C: Coupon rate

P: Number of coupon payments made in a year

D: Number of days since the last coupon payment

T: Number of days between coupon payments

Corporations in the U.S. often calculate bond interest as accruing over 30 days in a month and 360 days in a year, which is known as a 30/360 day-count convention.

Suppose ABC makes coupon payments on March 1 and Sept. 1 each year, and you buy ABC’s bonds on April 1. Let’s assume ABC follows a 30/360 day-count convention. That means that even though there are 31 days in March, you’d use 30 for “D,” or the number of days since the last coupon payment. You’d use 180 (i.e., 360 divided by two) for “T,” or days between coupon payments, even though the coupon is semiannual and there are 365 days in a year.

You’d calculate accrued interest as follows:

Accrued interest = \$1,000 x 0.05/2 x 30/180 = \$4.16

To calculate the dirty price, add the clean price and the accrued interest:

Dirty price = \$970 clean price + \$4.16 accrued interest = \$974.16

Each day that passes, an additional 13.88 cents of interest will accrue for Company ABC’s bonds, which means the dirty price will increase by this amount daily.

## Dirty Price vs. Clean Price

The big difference between the dirty price and clean price of a bond is that the dirty price accounts for accrued interest, while the clean price does not.

However, the dirty price will increase for each day that interest accrues until the next coupon payment is made. The dirty price will always be equal to or higher than the clean price since it includes interest on top of the market price.

The day that coupon payments are made, the dirty price and the clean price will be the same.

## What It Means for Individual Investors

The dirty price is the price an investor will actually pay when they buy a bond. However, the clean price is a better benchmark for investors seeking to compare different bonds. Excluding accrued interest makes it easier to compare bonds based on market factors and the level of credit risk, both of which affect a bond’s price.

A zero-coupon bond is a bond that doesn’t pay a coupon. Instead, it trades at a deep discount and pays investors a lump sum when the bond reaches maturity. Because there’s no interest accruing for a zero-coupon bond, the clean price and dirty price are the same.

Accrued interest is typically calculated after the transaction is completed. Because the seller is entitled to interest that accrued between the most recent coupon payment and the sale date, the dirty price reflects the bond’s true market value.

### Key Takeaways

• The dirty price of a bond includes interest that’s accumulated between coupon payments, while the clean price excludes accrued interest.
• The dirty price will increase for each day that interest accrues until the next coupon payment is made
• Because a bond seller typically receives the interest that accrued between coupon payments, the dirty price represents the true market value of the bond.

### Article Sources

1. M. Choudhry, D. Joannas, G. Landuyt, R. Pereira and R. Pienaar. "Capital Market Instruments Analysis and Valuation," Third Edition, Page 74. Palgrave Macmillan UK, 2010.

2. PIMCO. "Everything You Need To Know About Bonds."