Please enter any four values into the fields below to calculate the remaining value of a bond. This calculator is for bonds issued/traded at the coupon date.
Given the face value, yield, time to maturity, and annual coupon, the price is: $97.3270 .
Use this calculator to value the price of bonds not traded at the coupon date. It provides the dirty price, clean price, accrued interest, and the days since the last coupon payment.
| Dirty price: | $97.3743 |
| Clean price: | $97.3326 |
| Accrued interest: | $0.0417 |
| Interest accrued days: | 3 |
The first calculator above is designed to compute various parameters of a fixed-rate coupon bond issued or traded on the coupon date. The second calculator is used to determine the prices and accrued interest of fixed-rate bonds not traded on the coupon date, employing common day-count conventions. It is important to note that these calculators are specifically intended for use with fixed-rate coupon bonds, which represent the majority of bond types. Additionally, it should be mentioned that in pricing bonds, these calculators do not account for other factors that can influence bond prices, such as credit quality, supply and demand, and numerous other factors.
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically a corporation or governmental entity). It serves as a means for organizations or governments to raise funds by borrowing from investors. A bond specifies the terms of the loan and the payments to be made to the bondholder.
Bonds come in various types, each with its unique characteristics, risks, and benefits, catering to the diverse needs of both investors and issuers. The most common types include government bonds, municipal bonds, corporate bonds, and high-yield (junk) bonds, among others.
Bonds are considered a lower-risk investment compared to stocks, making them a popular choice among investors seeking a stable income stream and the preservation of capital. However, the risk and return on bonds can vary widely, depending on the creditworthiness of the issuer and the bond's duration. High-quality government bonds (such as U.S. Treasury bonds) are typically viewed as safe investments, while high-yield corporate bonds (also known as junk bonds) carry higher risk.
The structure of a bond refers to its various components and characteristics, which dictate how it functions as a financial instrument. Here's a breakdown of the key elements in the structure of a bond:
Beyond these core components, features such as the issuer, call and put options, credit rating, covenants, and marketability also play important roles in a bond's valuation.
Calculating the bond price involves discounting the future cash flows, which include interest payments and the principal repayment, to their present value using the required yield or discount rate. The bond price is the sum of the present values of all these cash flows. The basic formula for calculating the price of a bond is as follows:
C = the coupon payment per period,
N = number of periods until maturity,
r = the discount rate or yield per period,
F = the face value of the bond.
Let's say we have a bond with a face value of $1,000, a coupon rate of 5%, semi-annual payments, a maturity of 10 years, and we require a yield of 6%.
Coupon payment per period (C) = 5% of $1,000 / 2 = $25
Number of periods (N) = 10 years × 2 = 20 periods
Discount rate per period (r) = 6% / 2 = 3% or 0.03
The bond price is calculated by discounting each semi-annual payment and the face value at maturity back to their present value, using a 3% per period rate. For this case, the calculated bond price is $925.61. This process involves performing calculations for each payment and then summing them up, a task that can be complex without the aid of a financial calculator or software. Our calculators above are designed to facilitate this purpose.
When calculating the price or present value of a bond, it is often assumed that the bond trades or is issued on the coupon date. However, in reality, bonds are mostly traded outside of the coupon dates. In the bond market, the terms 'clean price' and 'dirty price' are used to distinguish between two ways of quoting the price of a bond outside the coupon date. These concepts are crucial for understanding how bonds are traded and priced.
Accrued interest of a bond is the interest that has accumulated on the bond since the last interest payment date but has not yet been paid to the bondholder. The accrued interest can be calculated using the formula:
The clean price of a bond is the price that excludes any accrued interest since the last coupon payment. When bonds are quoted in financial markets and to the public, the clean price is typically used. This price reflects the market value of the bond itself, without considering any accrued interest. The clean price is useful because it provides a standard way to compare the prices of different bonds without the variability introduced by differing interest accrual periods.
The dirty price of a bond, also known as the invoice price, is the price that includes the accrued interest on top of the clean price. The dirty price is the actual amount paid by a buyer to the seller of the bond. Since bondholders earn interest on a daily basis, if a bond is bought or sold between coupon payment dates, the buyer compensates the seller for the interest income earned from the last coupon date up to the purchase date. This makes the dirty price a more accurate reflection of the bond's total value at any given point in time between coupon payments.
Based on the definitions above, the relationship between clean and dirty prices can be summarized as:
dirty price = clean price + accrued interest
This formula highlights that the dirty price, which is the total price paid by the buyer, includes both the clean price of the bond (its market value excluding accrued interest) and the accrued interest earned on the bond from the last coupon payment date up to the purchase date.
As seen in the accrued interest calculation formula above, the accrued interest is closely related to the methods of counting the number of days since the last coupon payment and the total days in a year. Day-count conventions in the bond market are rules that determine how days are counted for the calculation of interest that accrues over time on bonds. The main day-count conventions used in the bond market include:
Different bonds may use different day-count conventions. The choice of day-count convention affects the calculation of accrued interest and, therefore, the price of the bond when it is traded between coupon dates. The second calculator above gives the option to select the day-count convention to use in the calculation. The accrued interest differences between different day-count conventions are normally very small. In extreme cases, it can have a difference of up to 6 days of accrued interest.