Question

Calculate the Macaulay duration of a 9%, $1,000 par bond that matures in three years if the bond's YTM is 12% and interest is paid semiannually. You may use Appendix C to answer the questions.

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

   ____years

2. Assuming the bond's YTM goes from 12% to 11.5%, calculate an estimated percentage 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

Time (t)	CF	PV	PV x t
0.5	45	42.52	21.26
1	45	40.18	40.18
1.5	45	37.97	56.95
2	45	35.87	71.75
2.5	45	33.90	84.74
3	1045	743.81	2231.43
	Sum	934.25	2506.31
		Mac Dur	2.68

CF - Cash Flows = 9% x 1000 / 2 = 45 in coupon and par value of 1000 at maturity

PV - Present Value = CF / (1 + YTM)^t, YTM = 12%

Macaulay Duration = Sum of PV x t / Sum of PV = 2.68

Modified Duration = Macaulay Duration / (1 + YTM/n) = 2.68 / (1 + 12%/2) = 2.53

% Change in Price = - Mod Duration x Chg in yield = - 2.53 x -0.5% = +1.265%