Question

Consider a T-bond maturing in March 2020 with coupon payments on September 1st and March 1st. Assume that the bond has $1000 par value, 10% coupon rate, and YTM = 12.5%. The bond is traded on December 13, 2013. What is the Accrued Interest? What is the full price? What is the flat price?

Answer 1

Full price (or purchase price) = flat price (quoted price) + accrued interest

From the trading date of Dec. 13, 2013, there are 13 coupon payments left to be made.

So, bond price with 13 coupons pending:

FV (par value) = 1,000; PMT (semi-annual coupon) = annual coupon rate*par value/2 = 10%*1,000/2 = 50; N = 13; rate (semi-annual YTM) = 12.5%/2 = 6.25%, solve for PV.

Bond price = 890.94 (price as on Sep. 1, 2013)

Now, number of days from Sep. 1, 2013 to Dec. 13, 2013 = 103 (number of days for calculating accrued interest)

Number of days from Sep. 1 2013 to Mar. 1, 2014 = 181 (semi-annual period)

Time fraction (t) = 103/181 = 0.5691

Purchase price of the bond (as of Dec. 13, 2013) = bond price*(1+ semi-annual YTM)^t

= 890.94*(1+6.25%)^0.5691 = 922.21 (Full price)

Accrued interest = semi-annual coupon*t = 50*0.5691 = 28.4530

Flat price = full price - accrued price = 922.21 - 28.4530 = 893.76