Question

Consider a bond with a coupon of 6.4 percent, six years to maturity, and a current price of $1,067.10. Suppose the yield on the bond suddenly increases by 2 percent.

a. Use duration to estimate the new price of the bond.

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

Answer 1

K = N

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

k=1

K =6

1067.1 =∑ [(6.4*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^6

k=1

YTM% = 5.07

a

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,067.10)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	64.00	1.05	60.91	60.91
2	64.00	1.10	57.97	115.95
3	64.00	1.16	55.18	165.53
4	64.00	1.22	52.51	210.05
5	64.00	1.28	49.98	249.89
6	1,064.00	1.35	790.80	4,744.83
			Total	5,547.16

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

=5547.16/(1067.1*1)

=5.198347

Modified duration = Macaulay duration/(1+YTM)

=5.2/(1+0.0507)

=4.947508

Using only modified duration

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

=-4.95*0.02*1067.1

=-105.59

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

=-105.59/1067.1

=-9.9%

New bond price = bond price+Modified duration prediction

=1067.1-105.59

=961.51

b

Actual bond price change

K = N

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

k=1

K =6

Bond Price =∑ [(6.4*1000/100)/(1 + 7.07/100)^k]     +   1000/(1 + 7.07/100)^6

k=1

Bond Price = 968.13

b