Question

Calculate the Macaulay duration of an 8%, $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(https://cnow.apps.ng.cengage.com/ilrn/books/reia11h/appendix_c.jpg) to answer the questions.

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

     years

2. 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 =∑ [(8*1000/200)/(1 + 14/200)^k]     +   1000/(1 + 14/200)^3x2

k=1

Bond Price = 857

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($857.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	40.00	1.07	37.38	37.38
2	40.00	1.14	34.94	69.88
3	40.00	1.23	32.65	97.96
4	40.00	1.31	30.52	122.06
5	40.00	1.40	28.52	142.60
6	1,040.00	1.50	693.00	4,157.98
			Total	4,627.85

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

=4627.85/(857*2)

=2.70

Modified duration = Macaulay duration/(1+YTM)

=2.7/(1+0.14)

=2.52

b

Using only modified duration

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

=-2.52*-0.01*857

=--21.63

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

=21.63/857

=2.52%

New bond price = bond price+Modified duration prediction

=857--21.63

=878.63