Question

Suppose that there are 4 semi-annual coupons remaining for a 7% coupon bond. There are 104 days until the next coupon payment date and there are 182 days in a coupon period. Assuming that the annualized discount rate on a bond-equivalent yield basis is 10%, what is the clean price of this bond? Par value is $100.

Answer 1

Time left to maturity = 182*3+104 days = 650 days

Time to maturity since last coupon payment = 182*4 = 728

Bond price at the last coupon date is found by discounting 100 after 728 days at the bond equivalent yield basis of 10%

Bond price at the last coupon date= 100 / (((0.1)*728/360) +1)

Bond price today = 83.179

We now find the ytm on the bond, using a financial calculator

PV = -83.179

FV = 100

PMT = 3.5

N = 4

cpt I/Y, we get I/Y = 8.652%

Annualised YTM = 8.652*2 = 17.30%

Days from last coupon payment = 182-104 = 78 days

Adjust for number of days since last coupon payment

Full price = 83.179*(1.08652)^(78/182) = $86.19

Semi-annual coupon = 7%*100/2 = 3.5

Accrued interest = 3.5*78/182 = $1.5

Clean price = Full price - Accrued interest

Clean price = $86.19-$1.5 = $84.69