Question

Callable bond. Corso Books has just sold a callable bond. It is a thirty-year semiannual bond with an annual coupon rate of 12% and $1,000 par value. The issuer, however, can call the bond starting at the end of 10 years. If the yield to call on this bond is 5% and the call requires Corso Books to pay one year of additional interest at the call (2 coupon payments), what is the bond price if priced with the assumption that the call will be on the first available call date?

It is a​ thirty-year

semiannualsemiannual

bond with an annual

coupon rate

LOADING...

of

1212​%

and

​$1 comma 0001,000

par value. The​ issuer, however, can call the bond starting at the end of

1010

years. If the

yield to call

LOADING...

on this bond is

55​%

and the call requires Corso Books to pay one year of additional interest at the call

​(22

coupon​ payments), what is the bond price if priced with the assumption that the call will be on the first available call​ date?

Answer 1

Coupon payment = Periodic Coupon Rate * Face Value = (12%/2) * $1,000 = $60

Call Price = Face Value + [2 * Coupon Payment] = $1,000 + [2 * $60] = $1,000 + $120 = $1,120

Bond's Market Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(12%/2)*$1,000} * {(1 - (1 + 0.05/2)^-(10*2)) / (0.05/2)}] + [$1,120 / {1 + (0.05/2)}^(10*2)]

= [$60 * {0.3897 / 0.025}] + [$1,120 / 1.6386]

= [$60 * 15.5892] + $683.50

= $935.35 + $610.27 = $1,618.85