Question

1. The only investments available are one-year zero coupon bonds and two-year 5% annual coupon bonds maturing at par. These bonds can be bought in any quantity, including fractional units. A company expects to pay a benefit of $600 in one year and $900 in two years. How much of each bond (in terms of maturity values) should the company buy in order to exactly match the assets and liabilities? If the current market interest rate is 7%, what is the cost of buying this portfolio?

Answer 1

		One year Zero Coupon Bond:
		Assume Face value of one Bond	$100
		Maturity Value =Face value	$100
		Number of bonds required =600/100=	6
		Market Interest rate	7%
		Current Market Value of Each Bond	$93.46	(100/1.07)
		Price for 6 bonds=93.46*6=	$560.75
		Maturity Value =6*100	$600
	A	Cost of buying	$560.75
		Two year 5% annual coupon Bonds;
		Assume Face value of one Bond	$100
		Maturity Value =Face value	$100
		Annual Coupon	$5	(100*5%)
		Present Value of Year 1 Coupon	$4.67	(5/1.07)
		Present Value of Year 2 Coupon	$4.37	(5/(1.07^2)
		Present Value of maturity payment	$87.34	(100/(1.07^2)
		Current market value of each Bond	$96.38	(4.67+4.37+87.34)
		Assuming Coupons is reinvested at market Rate:
		Future Value of year 1 Coupon=5*1.07=	$5.35
		Amount received on maturity per bond	$105.00	(100+5)
		Total Future Value of each bond	$110.35
		Amount required to be paid	$900
		Number of Bonds tobe purchased	8.1558677	(900/110.35)
		Maturity value =100*8.155868	$815.59
	B	Cost of buying =8.155868*96.38	$786.09
	C=A+B	COST OF BUYING THE PORTFOLIO	$1,346.84	(560.75+786.09)