Question

Consider the following. a. What is the duration of a two-year bond that pays an annual coupon of 10 percent and whose current yield to maturity is 14 percent? Use $1,000 as the face value. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) b. What is the expected change in the price of the bond if interest rates are expected to decline by 0.5 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

K = N

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

k=1

K =2

Bond Price =∑ [(10*1000/100)/(1 + 14/100)^k]     +   1000/(1 + 14/100)^2

k=1

Bond Price = 934.13

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($943.13)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	100.00	1.14	87.72	87.72
2	1,100.00	1.30	846.41	1,692.83
			Total	1,780.55

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

=1780.55/(943.13*1)

=1.887914

Modified duration = Macaulay duration/(1+YTM)

=1.89/(1+0.14)

=1.656064

Using only modified duration

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

=-1.66*-0.005*943.13

=+7.81

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

=7.81/943.13

=0.83%

New bond price = bond price+Modified duration prediction

=943.13+7.81

=950.94