Question

Consider a bond with a coupon of 7.2 percent, five years to maturity, and a current price of $1,027.60. Suppose the yield on the bond suddenly increases by 2 percent.

a. Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price: ______

b. Calculate the new bond price using the usual bond pricing formula. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price: _____

Answer 1

a

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

1027.6 =∑ [(7.2*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^5

k=1

YTM% = 6.54

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,027.60)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	72.00	1.07	67.58	67.58
2	72.00	1.14	63.43	126.86
3	72.00	1.21	59.54	178.61
4	72.00	1.29	55.88	223.53
5	1,072.00	1.37	780.96	3,904.82
			Total	4,501.41

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=4501.41/(1027.6*1)

=4.380512

Modified duration = Macaulay duration/(1+YTM)

=4.38/(1+0.0654)

=4.111612

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-4.11*0.02*1027.6

=-84.5

%age change in bond price=Mod.duration prediction/bond price

=-84.5/1027.6

=-8.22%

New bond price = bond price+Modified duration prediction

=1027.6-84.5

=943.1

b

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

Bond Price =∑ [(7.2*1000/100)/(1 + 8.54/100)^k]     +   1000/(1 + 8.54/100)^5

k=1

Bond Price = 947.25