Question

A 20 year, 4%, $1000 face value bond paying annual coupons is callable at par at the end of any year from 15 on.

a) How much should an investor pay if they want to earn at least 6% until the bond is called (or matures).

b) How much should an investor pay if they want to earn at least 3% until the bond is called (or matures).

explain fully please

Answer 1

Price of the bond=Coupon rate*Face Value/return*(1-1/(1+return)^t)+Face Value/(1+return)^t

The return of at least will be guaranteed if one considers call at the time of first allowed date

1.
=4%*1000/6%*(1-1/1.06^15)+1000/1.06^15=805.75502024518

2.
=4%*1000/3%*(1-1/1.03^15)+1000/1.03^15=1119.37935086776