Question

A bond with a coupon rate of 7 percent sells at a yield to maturity of 9 percent. If the bond matures in 12 years, what is the Macaulay duration of the bond? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

	Duration Macaulay years Modified years

Answer 1

(a)-Macaulay Duration of the Bond

Period (1)	Cash Flow (2)	Present Value Factor at 9% (3)	Present Value (4) = (3) x (2)	Weight (5)	Duration (6) = (1) x (5)
1	70	0.91743	64.22	0.0750	0.075
2	70	0.84168	58.92	0.0688	0.138
3	70	0.77218	54.05	0.0631	0.189
4	70	0.70843	49.59	0.0579	0.232
5	70	0.64993	45.50	0.0531	0.265
6	70	0.59627	41.74	0.0487	0.292
7	70	0.54703	38.29	0.0447	0.313
8	70	0.50187	35.13	0.0410	0.328
9	70	0.46043	32.23	0.0376	0.339
10	70	0.42241	29.57	0.0345	0.345
11	70	0.38753	27.13	0.0317	0.348
12	1070	0.35553	380.42	0.4440	5.328
TOTAL			856.79	1.0000	8.192

Macaulay Duration of the Bond will be 8.192 Years

(b)-Modified Duration of the Bond

Modified Duration of the Bond = Macaulay Duration / [1 + YTM]

= 8.192 Years / [1 + 0.09]

= 8.192 Years / 1.09

= 7.516 Years

The Modified Duration of the Bond will be 7.516 Years

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.