Question

Both Bond A and Bond B have 10 percent coupons, make semiannual payments, and are priced at par value. Bond A has 5 years to maturity, whereas Bond B has 10 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond A and Bond B? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond A and Bond B?

Please shows all the formula and steps. Don't round off until you get to the end.

Answer 1

	Price of a bond is the sum of the PV of the expected cash flows
	from the bond if, it is held till maturity.
	The expected cash flows are:
	*The maturity value of $1000 receivable at maturity.
	*The interest payments, which constitute an ordinary annuity.
	The discount rate to be used is the market rate of interest.
	If the interest payments are semi-annual, the discounting is to be
	done semi-annually.
1]	Price of bonds when interest rate is 10%+2% = 12.00%:
	Price of Bond A = 1000/1.06^10+50*(1.06^10-1)/(0.06*1.06^10) =	$         926.40
	% change in price of Bond A = 926.40/1000-1 =	-7.36%
	Price of Bond B = 1000/1.06^20+50*(1.06^20-1)/(0.06*1.06^20) =	$         885.30
	% change in price of Bond A = 885.30/1000-1 =	-11.47%
2]	Price of bonds when interest rate is 10%-2% = 8.00%:
	Price of Bond A = 1000/1.04^10+50*(1.04^10-1)/(0.04*1.04^10) =	$     1,081.11
	% change in price of Bond A = 1081.11/1000-1 =	8.11%
	Price of Bond B = 1000/1.04^20+50*(1.04^20-1)/(0.04*1.04^20) =	$     1,135.90
	% change in price of Bond A = 1135.90/1000-1 =	13.59%