Question

An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.3%. Bond C pays a 12% annual coupon, while Bond Z is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 9.3% over the next 4 years, calculate the price of the bonds at each of the following years to maturity. Round your answer to the nearest cent. Years to Maturity Price of Bond C Price of Bond Z

4    Price of bond c Price of bond z

3   

2   

1   

0

Answer 1

	Years to maturity		Price of Bond C		Price of bond Z
	4		$ 1,086.90		$     700.68
	3		$ 1,067.98		$     765.84
	2		$ 1,047.30		$     837.07
	1		$ 1,024.70		$     914.91
	0		$ 1,000.00		$ 1,000.00
	Working:
	Bond C:
a.	4 years to Maturity
	Par Value		$       1,000
	Annual Coupon		$       1,000	x	12%	=	$        120
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.093)^-4)/0.093			i	9.3%
				=	3.2185			n	4
	Present Value of single 1			=	(1+i)^-n			Where,
				=	(1+0.093)^-4			i	9.3%
				=	0.7007			n	4
	Present Value of coupon			$        120	x	3.2185	=	$     386.22
	Present Value of Par value			$    1,000	x	0.7007	=	$     700.68
	Current Price							$ 1,086.90
b.	3 years to maturity
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.093)^-3)/0.093			i	9.3%
				=	2.518			n	3
	Present Value of single 1			=	(1+i)^-n			Where,
				=	(1+0.093)^-3			i	9.3%
				=	0.766			n	3
	Present Value of coupon			$        120	x	2.5178	=	$     302.14
	Present Value of Par value			$    1,000	x	0.7658	=	$     765.84
	Current Price							$ 1,067.98
c.	2 years to maturity
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.093)^-2)/0.093			i	9.3%
				=	1.7520			n	2
	Present Value of single 1			=	(1+i)^-n			Where,
				=	(1+0.093)^-2			i	9.3%
				=	0.8371			n	2
	Present Value of coupon			$        120	x	1.7520	=	$     210.24
	Present Value of Par value			$    1,000	x	0.8371	=	$     837.07
	Current Price							$ 1,047.30
d.	1 year to maturity
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.093)^-1)/0.093			i	9.3%
				=	0.9149			n	1
	Present Value of single 1			=	(1+i)^-n			Where,
				=	(1+0.093)^-1			i	9.3%
				=	0.9149			n	1
	Present Value of coupon			$        120	x	0.9149	=	$     109.79
	Present Value of Par value			$    1,000	x	0.9149	=	$     914.91
	Current Price							$ 1,024.70
e.	0 year to maturity
	Present Value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.093)^-0)/0.093			i	9.3%
				=	0			n	0
	Present Value of single 1			=	(1+i)^-n			Where,
				=	(1+0.093)^-0			i	9.3%
				=	1			n	0
	Present Value of coupon			$        120	x	0	=	0
	Present Value of Par value			$    1,000	x	1.0000	=	$ 1,000.00
	Current Price							$ 1,000.00
	Bond Z
a.	4 Years to maturity
	Price of Bond			1000	x (1.093^-4)		=	$     700.68
b.	3 Years to maturity
	Price of Bond			1000	x (1.093^-3)		=	$     765.84
c.	2 Years to Maturity
	Price of Bond			1000	x (1.093^-2)		=	$     837.07
d.	1 Year to maturty
	Price of Bond			1000	x (1.093^-1)		=	$     914.91
e.	0 year to maturity
	Price of Bond			1000	x (1.093^-0)		=	$ 1,000.00