Question

Bond A with a $1000$1000 par value pays coupons semi-annually at 4.44.4% and matures in 55 years and 44 months. Bond B is a zero coupon bond with the same face value, time to maturity, and similar risk as Bond A and trades at $$788788.

What is the dirty (or actual) price of Bond A, the coupon paying bond?

$$ (Give answer to 2 decimal places)

Answer 1

WE ARE STANDING AT THE POSITION WHERE THE TIME REMAINING IS 5 YEARS AND 4 MONTHS SO TOTAL NUMBER OF THE REMAINING PAYMENTS ARE 5*2+ 1 THAT MEANS 11 COUPON PAYMENTS WILL BE RECIEVED

NOW WE HAVE TO CALCULATE THE MARKET YIELD USING THE ZERO COUPON BONDS SINCE BOTH HAVE THE SAME RISK

1000= 788( 1+ R)^5.33

R =.0457 OR 4.57%

NOW MARKET PRICE AFTER 4 MONTHS

MARKET PRICE = 4.44%/2 * 1000 * PVAF ( 10, 2.28%) + 1000* PVIF( 10, 2.28%)

= 22.2* 8.8525 + 0.7982*1000

=196.5255+ 798.2

=994.72

ALSO WE WILL RECIEVE THE COUPON AFTER FOUR MONTHS THAT WOULD BE ADDED TO VALUE

= 994.72+ 22.2

= 1016.92

BUT THIS PRICE IS AFTER FOUR MONTHS SO WE HAVE TO DISCOUNT IT TO THE CURRENT DATE

= 1016.92/ (1+ 0.0229)^4/6

=1016.92/ 1.0345

= 983. 01 APPROX IS THE DIRTY PRICE