Question

Calculate the Macaulay duration of an 8%, $1,000 par bond that matures in three years if the bond's YTM is 10% and interest is paid semiannually. You may use Appendix C to answer the questions.

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

  years

Assuming the bond's YTM goes from 10% to 8.5%, 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

Modified Duration = Duaration / ( 1 + YTM)

Duration in periods:

= Weight * Period

Period	CF	PVF @5%	Disc CF	Weight	Wt * Period
1	$      40.00	0.9524	$   38.10	0.0401	0.0401
2	$      40.00	0.9070	$   36.28	0.0382	0.0764
3	$      40.00	0.8638	$   34.55	0.0364	0.1092
4	$      40.00	0.8227	$   32.91	0.0347	0.1387
5	$      40.00	0.7835	$   31.34	0.0330	0.1651
6	$ 1,040.00	0.7462	$ 776.06	0.8176	4.9054
Durartion in Periods					5.4349

Duration in Years = Duration in Periods / 2

= 5.4349 / 2

= 2.72 Years

Modified Duration = Duaration / ( 1 + YTM)

= 2.72 / 1 + 0.10

= 2.72 / 1.1

= 2.47%

i.e 1% change in YTM leads to chnage in price by 2.47%

If YTM fall by 1.5%, Price change is 2.47% * 1.5

= 3.71%

Price will increased by 3.71% as there is inverse relation between YTM and Price.