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))
b. What is the expected change in the price of the bond if interest rates are expected to decrease 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))

Answer 1

Duration = Weight * Year

Year	CF	PVF @14%	Disc CF	Weight	Duration
1	$      90.00	0.8772	$   78.95	0.0860	0.0860
2	$      90.00	0.7695	$   69.25	0.0755	0.1509
2	$ 1,000.00	0.7695	$ 769.47	0.8385	1.6770
Duration of Bond					1.9140

Modified Duration: Duratiion / (1+YTM)

= 1.9140 / ( 1 +0.14)

= 1.9140 / 1.14

= 1.6789

i.e 1% change in YTM, will affect the price by 1.6789% in opposite direction.

0.2% decrease in YTM will lead to inc of Price by

= 1.6789% * 0.2 /1

= 0.34%

Original Price:

Year	CF	PVF @14%	Disc CF
1	$      90.00	0.8772	$   78.95
2	$      90.00	0.7695	$   69.25
2	$ 1,000.00	0.7695	$ 769.47
Price			$ 917.67

New Price = Old Price * (1+0.0034)

= 917.67 * 1.0034

= $ 920.79