Clean price 

Clean price 

A critical factor that investors must consider while choosing their investment is the bond’s pricing. It stands for the price at which the bond is purchased or sold. However, figuring out this price is more complicated. Several variables determine the cost of bonds. One of these consists of interest rates, payments, and accumulated interest.  

 Companies may encounter varying costs while buying bonds. Each might stand in for different facets of the bond and its value. The prices for clean and unclean are two of these. The cost of a coupon bond that does not include the interest accumulated between coupon payment dates is called the “clean price.” 

 

What is the clean price? 

The price of a bond that does not include any accumulated interest is the clean price. Coupons, which are fixed-interest payments, are frequently given to bond investors. Payments for vouchers are made regularly.  

 Although some bonds offer annual, quarterly, or even monthly costs, they are most commonly made twice a year. A bond’s advertised price is known as the clean price. It varies in response to changes in monetary policy, interest rates, and even the issuer’s creditworthiness. 

Understanding clean price 

Bond prices can be either clean price or filthy price when being quoted. The term “dirty” describes the cost of a bond that takes accumulated interest depending on the coupon rate into account. When a bond quotes between coupon payment periods, the price includes the goods accrued up to that point.  

A clean bond price excludes accumulated interest, but a dirty bond price is all-inclusive it. While the dirty price is more frequently given in Europe, the clean price is more commonly quoted in the United States. Bond coupons, or interest payments, are typically made twice a year, although depending on the issuer, some bonds may pay a coupon every year, every three months, or even every day. 

Formula of clean price 

The clean price formula is as follows: clean price = dirty price – accrued interest. 

Clean Price 

 

Calculating clean price 

The following elaborates on the calculation of the clean price of a bond. The 2023 maturity date of the government bond Yoko purchased has a 5% coupon rate. The semi-annual payments for the bond are due on December 1 and June 1 of each year. Yoko purchased it in January 2021 for 1,800 US$.  

 The advertised price of a bond is often the clean price; there is no specific need to compute it. However, a bond issuer might provide an investor with a misleading price. Therefore, we must calculate the accrued interest to establish whether or not the given price is filthy.  

 From the final payment date to the date of purchase, interest has accrued. Yoko purchased the bond on January 1, 2022. As a result, from December 1, 2020, to January 1, 2021, interest was accumulated. 

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

 Now, applying the dirty price formula: 

Dirty price = clean price + accrued interest = 1800 + 7.60 = US$1807.60  

 As a result, the bond’s dirty price was US$1807.60 US on January 1, 2022. This demonstrates that Yoko got a straight quote from the broker. A clean quote can also be obtained by deducting accumulated interest from the filthy price. 

 Clean quote = Dirty price – accrued interest = 1807.60 – 7.60 = 1800 US$  

 Investors receive a precise price from a broker. But it’s crucial to remember that investors still have to pay the price. As a result, Yoko pays US$7.60 more than the clean quote, which benefits the bond issuer. 

Examples of clean rice 

The following elaborates on an example of the clean price of a bond. Bonds from XYZ Ltd. have a face value of US$1,000 and a publicised price of US$980. They have a five-year maturity date and a 5% coupon rate paid semi-annually.  

 A 5% US$1000(or US$50) annual coupon payment is required. Up to maturity, the investor will get a US$25 coupon payment every six months. The clean price of the bond in this instance is US$980. Investors are given a price quote for the bond of US$980 plus interest.  

 Brokers cite the filthy price, calculated by multiplying the clean price by the accumulated interest since that day. The dirty price for a bond whose last coupon payment was made on June 1 is calculated as clean price + accrued interest, where accrued interest is the interest earned on the bond from June 1 to August 31 based on its coupon rate. The price constantly fluctuates based on how long it has been since the bond’s last coupon payment. 

Frequently Asked Questions

Brokers and investors frequently exchange dirty prices, but the clean price or the price before interest has been charged, is typically considered the advertised price. Although accumulated interest is included in the dirty price, the clean price is frequently thought of as the bond’s worth in the current market. 

The clean price is frequently used by individual investors as a benchmark when contrasting various bonds. Changes in accumulated interest do not influence changes in yield for dirty prices, making it a superior comparison object. The filthy price is employed to determine the expected return from purchasing or selling a specific bond. 

The clean price of a bond is its face value less the most recent coupon payment and any interest that has accumulated since the bond’s issue. 

The clean price is the discounted future cash flow of a bond’s current value, with fewer interest payments. 

The dirty price always remains at or above the clean price as interest is added to the market price. 

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