Question

A $100 par value non-callable bond has 4% semiannual coupons and is redeemable at $103 after 20 years. The bond is currently selling at $105.

a.) Find the yield to maturity of the bond convertible yearly.

b.) If coupons can be reinvested at 4.5% compounded semiannually, find the 20-year holding-period yield convertible yearly. Compare this with the answer obtained in a.

PLEASE SHOW ALL WORK BY HAND, WITHOUT USING A FINANCE CALCULATOR OR EXCEL. THANK YOU.

Answer 1

a)

ytm of the bond = [ coupon + ( redemption price - price) / no of coupons ] / ( redemption price + price) / 2

= [ 2 + ( 103-105) / 40 ] / ( 103+105) / 2 = 1.95 /104 = 1.875 for 6 months

yearly ytm = 1.875*2 = 3.75%

b)

Future value of coupon = coupon * [ ( 1 + int rate )^no of years - 1 ] / int rate

= 2 * [ ( 1+0.045/2^20*2] /0.045/2

= 127.57

holding period return = ( future value of coupons + redemption value ) / purcahse price

= [( 127.57 + 105 ) / 103 ] ^ 1/20 - 1

= 4.16 %