Question

A $50,000 bond bearing interest at 5.5% payable semi-annually is redeemable at par on August 10, 2033. The bond is sold on the primary market on December 10, 2013, to yield 5% compounded semi-annually. Determine the amount of discount or premium on the sale of the bond.

Answer 1

Face Value (FP) or Redemption value = $50000

YTM = 5% semiannually =5/2= 2.5%

Coupon Rate =5.5 semiannually =5.5/2 =2.75%

Maturity life =20Year as semianually 20*2 =40 ... Dec 2013 - August 2033

Bond value = I* PVAF (YTM,yr) +Redemption value or Face value * PVF (TYM,yr)

PVAF for 40year at 2.5% discounting rate

Pvf of 40th year at 2.5% of discounting rate

where I is interest on bond , YTM is yield , PVAF present value annuity factor , PVF present value factor

BV or MP Market Price

=( 50000*2.75%) * 25.10 + 50000*0.372

=34512.5+ 18600

=$53112.5

Premium on Sale of bond is 53112.5-50000 = $3112.5