Question

A 6% German corporate bond is priced for settlement on 18 June 2015 at a yield (YTM) of 6%. The bond makes semi-annual coupon payments on 19 March and 19 September each year and matures on 19 September 2016. Assume the market uses an actual/actual convention to price this bond.

a. What is the full price of this bond? (Hint: based on an actual/actual day-count convention there are 91 days between the last coupon date and the settlement date, and 184 days between the last coupon period and the next coupon period).

b. What is the accrued interest (AI) owed to the seller of the bond on the settlement date?

c. What is the clean price of the bond on settlement date?

Answer 1

Assuming par value of the bond is $1000.

Value of coupon will be 3% (6/2) as semi annual coupon payment I.e. $30. Calculation for present value of the bond par value $1000*(1/1.03)^3=915.142 Period 19 march to 18 sep=181 days Period 19 sep to 18 march=184days Period 18 June 2015 to 19 sep 2015 (93days){30/1.03×93/184}=14.72 Period 19 sep 2015 to 19 march 2016 (181 days) ={30/1.03×181/181}=29.126 Period 19 march 2016 to 19 sep 2016 (184 days) ={30/1.03×184/184}=29.126 Value of the bond (present value of accrued interest and present value bond) (accrued interest=15.126+29.126+29.126=73.378 + present value of bond 915.142) =988.52 B)Interest accrued on settlement date =($1000*3/100)93/184=15.163 C) clean price = dirty price - accrued interest Dirty price = 988.52× ( 1+ .06/2) = 1018.167 Clean price = 1018.167-15.163 =1003.004