A $1,000 par corporate bond carries a coupon rate of 6%, pays coupons semiannually, and has ten coupon payments remaining to maturity. Market rates are currently 5%. There are 90 days between settlement and the next coupon payment. The dirty and clean prices of the bond, respectively, are closest to:
A. $1,043.76, $1,013.76
B. $1,043.76, $1,028.76
C. $1,056.73, $1,041.73
D. $1,069.70, $1,054.70
Answer:C
The dirty price of the bond 90 days ago is calculated as N = 10, I/Y = 2.5, PMT = 30, FV = 1,000;
CPT→PV = 1,043.76.
Adjusting the PV for the fact that there are only 90 days until the receipt of the first coupon, then the dirty price now is 1,043.76×1.025(90/180) = 1054.73. Clean price = dirty price – accrued interest = 1056.73 – 30× (90/180) = 1041.73