Question

1. Set up the calculation to arrive at the market value of a new bond having a face amount of $1,000, the annual interest rate of 7% payable semiannually, callable at the end of five years (call price of 106) and 25 years remaining maturity at a 6% yield to call. (Do not use a calculator. Show the appropriate equation and data substitution.) At this yield will the bond trade at par, a discount or a premium?

Answer 1

Price of bond is $ 1087.30 and it trades at premium.

Present Value of coupon	$     298.56
Present Value of maturity Value	$     788.74
Price of Bond	$ 1,087.30
Working:
Semi annual coupon	=	Face Value	*	Semi annual coupon rate
	=	$ 1,000.00	*	3.50%
	=	$       35.00
Present Value of annuity of 1	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.03)^-10)/0.03	i	=	3%
	=	8.5302028		n	=	10
Present Value of 1	=	(1+i)^-n
	=	(1+0.03)^-10
	=	0.7440939
Present Value of coupon	=	Coupon	*	Present Value of annuity of 1
	=	$       35.00	*	8.530203
	=	$     298.56
Present Value of Call Price	=	Call Price	*	Present Value of 1
	=	$ 1,060.00		0.744094
	=	$     788.74