Prof. Haluk Unal Fixed Income Analysis 1
Flat - Full Price
BUFN 732 Fixed Income Analysis
Prof. Haluk Unal Fixed Income Analysis 2
Bond price calculation
In the following set up for the bond price:
P is calculated as if the date of the cash exchange for the bond is t=0. In other words, we find the
price of the bond as the PV of future cash flows as of t=0.
However, the settlement date, the time when cash is exchanged for the bond, may not be at t = 0.
The settlement date can be some time between t = 0 and t = 1.
This real-life complication has implication for valuation.
P
t=0
C
1
C
2
C
3
C+F
4
Prof. Haluk Unal Fixed Income Analysis 3
An example for bond price calculation
Consider the example,
This 5% bond makes coupon payments semiannually on June 15 and December 15. Suppose its YTM
is 4% and this bond is purchased on June 15 (excluding the June coupon), but will settle on August
21. At that time, four coupon payments remain for the rest of the bond.
June 15 Dec 15 June 15 Dec 15 June 15
$25 $25 $25 $25+$1000
Prof. Haluk Unal Fixed Income Analysis 4
An example for bond price calculation (cont’d)
If the bond were to be exchanged for cash on June 15, the valuation would have been:
However, the cash settlement is on August 21 (67 days after June 15):
June 15 June 15
25+1000
Dec 15Dec 15June 15
August 21
183 days
67 days
P =
25
1.02
+
25
1.02 2
+
25
1.02 3
+
25 + 1000
1.02 4
= $1019.04
Prof. Haluk Unal Fixed Income Analysis 5
An example for bond price calculation (cont’d)
The value at settlement date ( the full price of the bond) is:
Note that, this full price includes accrued interest between last coupon and settlement date. To
figure out this accrued interest:
In other words, the seller is entitled to this $9.15 interest because he/she has not received the cash till August 21.
Full Price = 1019.04 ∗ 1.02 67
/183 = $1026.46
Accrued Interest = $25 ∗ (
67
183
) = $9.15
Prof. Haluk Unal Fixed Income Analysis 6
Calculation for full price
Hence, the full price has two components:
Full Price = Accrued Interest + Flat Price.
Flat Price = Full Price - Accrued Interest = 1026.46 - 9.15 =$1017.31
Flat price is also called “clean” price meaning value that is free of accrued interest; Full price is also
called “dirty” price because it includes elements of accrued interest.
1019.04
1026.46 = Full Price.
Accrued Int
= 9.15
25 25 25 25+1000
(This price includes the accrued interest on principal and the coupon.)
1017.31
Flat price
9.15
Accrued Interest on coupon
Prof. Haluk Unal Fixed Income Analysis 7
Calculation for accrued interest
In calculating accrued interest, note that we used actual number days between coupon
payments (183 days) and the actual number of days between the last coupon date and
the settlement date (67 days).
This actual/actual method is used most often with government bonds.
Prof. Haluk Unal Fixed Income Analysis 8
Calculation for accrued interest (cont’d)
There is another method that assumes there are 30 days in each month and 360 days in a year. In this
method:
June 15 Dec 15
25 25 25 25+1000
August 21
August 15
2*30 =
60 days
6 days
66 days
180 days
Accrued interest = 25*(66/180) = $9.166
*Note that under the 30/360 method the accrued
interest is slightly more.
Prof. Haluk Unal Fixed Income Analysis 9
Quotation conventions
If the bond price is quoted clean price (flat price), this is not the price what you actually pay to buy
the bond. You have to include the accrued interest in the price you pay, which is the dirty price (full
price).
Corporate and municipal bond issuers assume a 30/360 method. However, government bonds use
actual/actual method.
When the price of coupon bonds are quoted, they are either quoted at a full price or flat price.
Bonds may trade at flat price if the bond settles on the same date as interest paid, so no accrued
interest exist. Alternatively, bonds in default may trade at flat price.