Question

Consider the following.

a.	What is the duration of a two-year bond that pays an annual coupon of 9 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))

Duration of a bond

b.	What is the expected change in the price of the bond if interest rates are expected to decline by 0.2 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Expected change in the price

$

Answer 1

Time	Cashflow	PVF@14%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	90	0.877	78.95	0.0860	0.086
2	1090	0.769	838.72	0.9140	1.828

Current bond price = 78.95+838.72

= 917.67

Duration = Time*Weight

= .086+1.828

= 1.914 years

Modified Duration = Duration/(1+YTM)

= 1.914/1.14

= 1.679 years

Modified Duration measures the change in bond price with respect to change in YTM. But the direction of change is opposite. That is when YTM increases, bond price decreases. Similarly when YTM decreases, bond price increases.

Change in bond price = Modified Duration*% change in YTM

= 1.679*.2

= 0.3358%

Since YTM declines, bond price rises by .3358%

New bond price = 917.67+917.67*.3358%

= 917.67+3.08153586

= $920.75