Question

A convertible bond is sold with a coupon rate of 7%. Straight bonds are yielding 10% now and the bond has a 30 year life. Find the bond or investment value of this convertible security.

a) $820

b) $1100

c) $650

d) $716

Answer 1

d.$716.

straight bond value = [present value of annuity* interest payment] + [present value factor * face value]

present value of annuity =[1-(1+r)^(-n)] / r

here,

r = 10% per annum =>5% =>0.05.

n = 30 years * 2 semi annual period =>60 periods.

=>annuity factor = [1-(1.05)^(-60)] / 0.05

=>0.9464645/0.05

=>18.92929.

interest payment = $1,000 * 7% *6/12=>$35

present value factor = 1/(1+r)^n =>1/(1.05)^60

=>0.05353552

face value = $1000....(default value).

bond value =[18.92929*$35]+[0.05353552*$1,000]

=>662.52515+53.53552

=>$716.06