Question

The following liabilities are due in the next four years:

Due Date	Amount
May 1st 2019	$3,710,000
May 1st 2020	$6,620,000
May 1st 2021	$4,410,000
May 1st 2022	$5,250,000

The following US Treasuy Bonds have been selected to pay the obligations. Interest is paid annually on April 30th of each year. Assume we are purchasing in April 2018.

Maturity Date	Coupon Rate
April 30th, 2019	2.75%
April 30th, 2020	3.50%
April 30th, 2021	4.75%
April 30th, 2022	5.50%

How much in par value should be bought of each bond to ensure the liabilities are paid by the due date?

Assume the minimum denomination to invest in each security is $10,000 (your par value to invest in each bond needs to be rounded to $10,000)

Answer 1

No. of bonds to purchase for April 30, 2019 = (3710000/1.0275)/10000 = 362 (rounded to higher value)

Money left after 1st May, 2019 =3620000*1.0275 -3710000 = 9950

No. of bonds to purchase for April 30, 2020= (6620000/1.035^2)/10000 = 618 (rounded to higher value)

Money left after 1st May, 2020 =6180000*(1.035)^2- 6620000 +9950 (earlier) = 10,121

No. of bonds to purchase for April 30, 2021 = (4410000/1.0475^3)/10000 = 383 (rounded to lower value, we had extra $10,121)

Money left after 1st May, 2021 =3830000*(1.0475)^3- 4410000 +10121 (earlier) = 2231

No. of bonds to purchase for April 30, 2022 = (5250000/1.055^4)/10000 = 424 (rounded to higher value)