Question

Problem 10-24 Using Duration (LO4, CFA6) Consider a bond with a coupon of 7.6 percent, seven years to maturity, and a current price of $1,032.20. 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 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 =7

1032.2 =∑ [(7.6*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^7

k=1

YTM% = 7

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,032.20)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	76.00	1.07	71.03	71.03
2	76.00	1.14	66.38	132.76
3	76.00	1.23	62.04	186.12
4	76.00	1.31	57.98	231.92
5	76.00	1.40	54.19	270.93
6	76.00	1.50	50.64	303.85
7	1,076.00	1.61	670.08	4,690.55
			Total	5,887.16

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

=5887.16/(1032.2*1)

=5.703512

Modified duration = Macaulay duration/(1+YTM)

=5.7/(1+0.07)

=5.330385

Using only modified duration

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

=-5.33*0.02*1032.2

=-110.04

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

=-110.04/1032.2

=-10.66%

New bond price = bond price+Modified duration prediction

=1032.2-110.04

=922.16

b

K = N

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

k=1

K =7

Bond Price =∑ [(7.6*1000/100)/(1 + 9/100)^k]     +   1000/(1 + 9/100)^7

k=1

Bond Price = 929.54