Question

Today is 1 July 2018. Matt is 30 years old today. Matt has a portfolio which consists of three Treasury bonds (henceforth referred to as bond A, bond B and bond C). There are 200 units of bond A, 300 units of bond B and 500 units of bond C. Bond A is a Treasury bond which matures on 1 January 2027. One unit of bond A has a coupon rate of j2 = 2.95% p.a. and a face value of $100. Matt purchased this Treasury bond on 15 March 2018. The purchase yield rate was j2 = 3.5% p.a. Find the purchase price of one unit of bond A. Using the formulae Price = v^(f/d) [ Co + CAn + (100V)^n ] where c = coupon amount, Co = next coupon amount, n = number of interest periods from next coupon date to maturity, d= number of days in current interest period, f = number of days from valuation date to next coupon date

Answer 1

			Face value of bond A	$100
			Annual Coupon payment	$                      2.95	(0.0295*100)
			Purchase date,15 March 2018
			Yield =3.5%	0.035
	year	Date	Cash flow:	Present Value of Cash Flow as on Jan1.2019
	0	.January 1, 2019	$2.95	$2.95
	1	.January 1, 2020	$2.95	$2.85	(2.95/1.035)
	2	.January 1, 2021	$2.95	$2.75	(2.95/(1.035^2)
	3	.January 1, 2022	$2.95	$2.66	(2.95/(1.035^3)
	4	.January 1, 2023	$2.95	$2.57	(2.95/(1.035^4)
	5	.January 1, 2024	$2.95	$2.48	(2.95/(1.035^5)
	6	.January 1, 2025	$2.95	$2.40	(2.95/(1.035^6)
	7	.January 1, 2026	$2.95	$2.32	(2.95/(1.035^7)
	8	.January 1, 2027	$2.95	$2.24	(2.95/(1.035^8)
	8	.January 1, 2027	$100(Maturity payment)	$75.94	(2.95/(1.035^8)
			SUM	$99.17
			Market Price on January 1, 2019	$99.17
	9.5 Months	March 15,2018	Market Price on March15, 2018	96.49559241	(99.17/(1+(0.035*(9.5/12)
			Purchase Price of one unit of Bond	$                    96.50