Question

A) Draw a timeline for a bullet bond, face value of $1,000, with 3 years remaining to maturity that pays a coupon rate of 5.5%/year semi-annually.

B) What is the market price of the bond in A if the current market rate is 3%/year?

Answer 1

	Solution
	Face value of Bond (FV)	1000	$
	Coupon Rate ( r)	5.50%
	Therefore, Coupon paid will be	= FV * r	55	$
	Remember this coupon is paid semi annualy i.e. every six months.
	So, semi annual coupon payment will be $55/2 = $27.5
	Nature of the bond is Bullet i.e. payment at the end of the tenure.
	Remaining tenor of the bond is three years.
A)	Time line of the bond is
		Months	0	6	12	18	24	30	36
		Period	0	1	2	3	4	5	6
		Coupon Payment		27.5	27.5	27.5	27.5	27.5	27.5
		Maturity Payment							1000
		Cash flows from Bond		27.5	27.5	27.5	27.5	27.5	1027.5
B)	Market price of the Bond
		Market price of the bond can be achieved by discounting the above cash flows with a discount rate.
		But what is the applicable discount rate?
		Given discount rate is 3% (the market rate). However it is for the year.
		Our cash flows are semi annual, so applicable dicount rate is 3/2 = 1.5% per semi annual
		Period	0	1	2	3	4	5	6
		Cash flows from Bond		27.5	27.5	27.5	27.5	27.5	1027.5
		Discount Rate		1.50%	1.50%	1.50%	1.50%	1.50%	1.50%
		Discount Factor (1/(1+r)^n)		0.985222	0.970662	0.956317	0.942184	0.92826	0.914542
		PV of cash flows (Cash flow * discount factor)		27.0936	26.6932	26.29872	25.91007	25.52716	939.6921
		Market price of bond = sum of pv of cash flows
			1071.215	$
		(Note : As market rate is less that coupon rate, value of bond is higher than face value of bond)
		(Note : market price also be calculated using direct formulas = 27.5 * Annuity Factor(1.5%,6) + 1000$/(1.015)^6)