Question

A bond is scheduled to mature in five years. Its coupon rate is 9 percent with interest paid annually. This $1,000 par value bond carries a yield to maturity of 10 percent.

Calculate the percentage change in this bond's price if interest rates on comparable risk securities increase to 11 percent. Use the duration valuation equation.

+4.25 percent

-4.25 percent

+8.58 percent

-3.93 percent

-3.84 percent

Answer 1

K = N

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

k=1

K =5

Bond Price =∑ [(9*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^5

k=1

Bond Price = 962.09

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($962.09)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	90.00	1.10	81.82	81.82
2	90.00	1.21	74.38	148.76
3	90.00	1.33	67.62	202.85
4	90.00	1.46	61.47	245.88
5	1,090.00	1.61	676.80	3,384.02
			Total	4,063.34

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

=4063.34/(962.09*1)

=4.223451

Modified duration = Macaulay duration/(1+YTM)

=4.22/(1+0.1)

=3.839501

Using only modified duration

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

=-3.84*0.01*962.09

=-36.94

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

=-36.94/962.09

=-3.84%