Question

Calculate the Macaulay duration of a 9%, $1,000 par bond that matures in three years if the bond's YTM is 14% and interest is paid semiannually. You may use Appendix C to answer the questions.

A. Calculate this bond's modified duration. Do not round intermediate calculations. Round your answer to two decimal places.

B. Assuming the bond's YTM goes from 14% to 13.0%, calculate an estimate of the price change. Do not round intermediate calculations. Round your answer to three decimal places. Use a minus sign to enter negative value, if any.

Answer 1

A

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =3x2

Bond Price =∑ [(9*1000/200)/(1 + 14/200)^k]     +   1000/(1 + 14/200)^3x2

k=1

Bond Price = 880.84

Period	Cash Flow	Discounting factor	PV Cash Flow
0	($880.84)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor
1	45.00	1.07	42.06
2	45.00	1.14	39.30
3	45.00	1.23	36.73
4	45.00	1.31	34.33
5	45.00	1.40	32.08
6	1,045.00	1.50	696.33
			Total

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

=4706.57/(880.84*2)

=2.67164

Modified duration = Macaulay duration/(1+YTM)

=2.67/(1+0.14)

=2.50

B

Using only modified duration

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

=-2.5*(-0.01)*880.84

=21.993