Suppose there are three fixed income securities issued by Foxtrot Capital currently outstanding on the Australian Securities Exchange: a semi-annual coupon bearing bond, a zero-coupon bond, and a perpetual bond. The coupon bearing bond has a coupon rate of 4% per annum, with semi-annual coupons, and a par value of $1,000. The zero-coupon bond has a par value of $1,000, with interest compounding annually. The perpetual bond has no maturity value and pays bondholders an annual coupon of $16. These three securities were originally issued on 19 November 2021, with the coupon bearing bond and zero-coupon bond scheduled to mature on 19 November 2046.
a) Determine the value of the semi-annual coupon bearing bond, as of when it was first issued, assuming investors at the time required a return of 5% per annum, compounding semi-annually, for securities issued of similar risk.
b) Determine the value of the zero-coupon bond and the perpetual bond, as of when they were first issued, assuming investors at the time required a return of 5% per annum, compounding annually, for these two securities.
c) Seven years after issuance, the coupon bearing bond is currently trading at $1,129, the zero-coupon bond is trading at $571, and the perpetual bond is trading at $546. If you now require a return of 3% per annum on all corporate bonds issued by Foxtrot Capital, assess only one of the three available bonds and determine whether you should buy it as of 19 November 2028.
A fast response would be appreciated.