Question

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

The purchase price = flat price + accrued interest

Consequently, bond price with 13 coupons pending can be obtained by:

FV which is the par value = 1,000;

PMT or the semi-annual coupon

= annual coupon rate x par value/2

= 10% x1,000/2 = 50;

Where N is 13; and the rate (semi-annual YTM) is 12.5%/2 = 6.25%,

As to solve for PV we take.

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

Or the price can be calculated using below way also

The number of days from Sep. 1, 2013 to Dec. 13, 2013 will be 103 where we obtain the number of days for calculating accrued interest

The No of days from Sep. 1 2013 to Mar. 1, 2014 = 181 (semi-annual period)

Time fraction is = 103/181

= 0.5691

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

= 890.94 * (1+6.25%) ^0.5691

= 922.2151 and this is the full price

Accrued interest = semi-annual coupon x t

= 50 x 0.5691

= 28.4530

The flat price = full price - accrued price

= 922.2151 - 28.4530

= 893.7621