Subject 3. Flat Price, Accrued Interest, and the Full Price

Coupon interest is paid not daily, but monthly, semi-annually or annually. If an investor sells a bond between coupon payments and the buyer holds it until the next coupon payment, the entire coupon interest earned for the period will be paid to the buyer. The seller gives up the interest from the time of the last coupon payment to the time until the bond is sold. The amount of interest over this period that will be received by the buyer (even though it was earned by the seller) is called accrued interest.

Accrued interest is calculated as a proportional share of the next coupon payment using either the actual/actual or 30/360 method to count days.

The amount that the buyer pays the seller the agreed upon price for the bond plus accrued interest is called the full price (dirty price). The agreed-upon bond price without accrued interest is simply referred to as the flat price (clean price). Flat prices are quoted in order to not to misrepresent the daily increase in the full price as a result of interest accruals.

Here is how to calculate the full price:

Note that the next coupon payment is discounted for the remainder of the coupon period.

An easier formula is used to to get the present value of the bond at the last coupon payment date and find its (future) value on the settlement date.

User Contributed Comments 10

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amamed213: Can we say that clean price = the agreed upon price ?
yu0825: If this agreed upon price does not include the accrued interest, then yes. Just note that the difference if there is inclusion of ACCRUED INTERESTS.
amamed213: Thanks yu0825
Jilany: Hi amamed213, we actually can't say clean price = agreed upon price. This is because the agreed upon price may or may not include accrued interest. Only when the agreed upon price excludes accrued interest, in that case we can say it clean price.
freyalam: so the agreed upon price can be either the clean or dirty price, depending on what was ... agreed upon, right?
Leonie: Correct. Think of it this way, agreed upon price one concept, dirty or clean another concept.
johntan1979: Enough of all this dirty talk. Time for me to wash up.
johntan1979: One fundamental concept that AnalystNotes did not include here in the notes is about trading cum coupon vs trading ex coupon.

Just like dividends, bonds have ex coupon dates. Traded ex coupon, means buyer trade on ex coupon date and has to forgo and not receive the next coupon payment, so ex coupon price = full price ? accrued interest

If traded cum coupon, buyer trade before ex coupon date and receives the next coupon payment BUT must pay the seller the accrued interest. Cum coupon price = full price ? accrued interest

Technically, ex coupon price = cum coupon price, but essentially, they mean different things due to the ex coupon date. In the US, Treasury coupon securities ALWAYS trade cum coupon.
CFAToad: So you price out the Cum Coupon as though the buyer will take the next coupon. So the Buyer pays the Seller for the accrued interest. The Ex Coupon Buyer does not take the next coupon. So the Buyer pays the Seller for the price from the next coupon date.

Johntan, you may be too smart for OUR own good.
Thanks for the heads up.
Rohule: what if we use Bond ( number 9) calculation on the ba ii?