Price of coupon bearing bond calculation

What is the accrued interest?

Global Financial Management

The buyer must compensate the seller for the portion of interest between the settlement date and the next coupon payment. This is because the seller will then send the next payment to the buyer. This interest is called accrued interest.

The price of a bond which includes the accrued interest is called the dirty price. A bond priced at the settlement date no accrued interest is called the clean price. When the dirty price is calculated, the next coupon payment is a discounted value.

However, accrued interest is not discounted. Therefore, if a bond is selling at par and the settlement date is not a coupon date, the yield will be slightly less than the coupon rate. Only when the coupon date and settlement date coincide is the yield equal to the coupon rate for a bond selling at par. The convention is to quote a bond's clean price, but the buyer will pay the dirty price.

As the interest accumulates in-between coupon periods, the price acquires a saw-tooth shape when the accumulated interest drops to zero at the next coupon payment.

Bonds have an ex-coupon ex-dividend date, which is a date in which the trade must occur in order for the buyer to receive the next coupon. If the trade occurs after that date, the accrued interest must be subtracted from the price. This is known as negative accrued interest. When the buyer receives the next coupon, the bond is said to be traded cum-coupon cum-dividend.

The number of days between coupon periods vary by bond issuer. The notations have been standardized in the form of:. Some example conventions: [24]. See the Excel help file to understand how it works. From Bogleheads. Jump to: navigation , search. This article builds on the basic financial principles from Comparing investments to show how bond prices are calculated. It does not discuss why prices change, nor should it be used to predict future performance.

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For example PV rate; numperiods; payment; futurevalue; type is identical. Note: The graphs on this page are not from this text derived by the wiki author. There are no spreadsheet programs used in this book- the examples are used to verify results from Excel. See Periodic Interest Rate in the wiki. Used to confirm results with Excel only. Also Bond Accrued Interest. Municipal bonds. Vanguard bond ETFs. Financial theory.

It is possible to get an approximate YTM for a bond using a bond yield table. The best way to compute the YTM for a bond is to use a financial calculator. Using a financial calculator, punching in four out of five of the relevant variables price , par value, maturity, coupon payment, YTM will give you the fifth variable.

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By lending P , you will receive the stream of cash flows:. You wish to value this stream. To do so, you need to discount this stream at a rate that makes the price paid for the bond, P , just equal to the present value of this stream of cash flows. That is, r , which is the bond yield, or yield to maturity, solves. Since this is a constant coupon, then and so , or more compactly as.