Question

In: Accounting

Consider a T-bond maturing in March 2020 with coupon payments on September 1st and March 1st....

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?

Solutions

Expert Solution

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


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