Question

An investor buys a corporate bond with a coupon rate of 7.6%. The transaction is settled on July 5, 2020. The bond makes semiannual coupon payments on April 28 and October 28 each year and matures on April 28, 2026. Assume the 30/360 day-count convention and $100 par value. The yield to maturity of the bond is 6.3%. Keep four decimal places for all calculations. 1) (7 points) Calculate the dirty (full) price of this bond on the settlement day. $Answer 2) (4 points) Calculate the accrued interest of this bond on the settlement day. $Answer 3) (2 points) Calculate the clean (flat) price of this bond on the settlement day. $Answer

Answer 1

Settlement date: July 5, 2020; Last coupon date: April 28, 2020; Next coupon rate: October 28, 2020

Number of days from last coupon date to settlement date (m) = July 5, 2020 - April 28, 2020 = 68 days

Number of days during one semi-annual period (n) = October 28, 2020 - April 28, 2020 = 183 days

Price of the bond at the last coupon date of April 28, 2020: FV (par value) = 100; PMT (semi-annual coupon) = annual coupon*par value/2 = 7.6%*100/2 = 3.80; N (number of coupons left) = 12; rate (semi-annual rate) = APR/2 = 6.30%/2 = 3.15%, solve for PV.

Price = 106.41

Price as on settlement date = last coupon price*(1+yield/2)^(m/n) = 106.41*(1+6.30%/2)^(68/183) = 107.65 (Dirty price)

Accrued interest = semi-annual coupon*(m/n) = 3.80*68/183 = 1.41

Clean price = dirty price - accrued interest = 107.65-1.41 = 106.23