Question

What is the Macaulay duration of a bond with a coupon of 5.4 percent, nine years to maturity, and a current price of $1,055.40? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

                  

Answer 1

Step 1: YTM Calculation

Yield To Maturity(YTM) = (interest per period+ ((Redemption price - Current market price) / life remaining to maturity)) / ((.4*Redemption price)+ (.6*Current market price))

= ((1000*5.4%)+ ((1000-1055.40) / 9)) / ((.4*1000)+ (.6*1055.40))

= (54-6.15555555556) / 1033.24

= 47.8444444444 / 1033.24

= 4.63%

note: It is general practice to take $1,000 as face value when no details are given.

Prima facie, the bond will trade at Premium as YTM<coupon rate

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	54	0.956	51.61	0.0489	0.049
2	54	0.913	49.33	0.0467	0.093
3	54	0.873	47.14	0.0447	0.134
4	54	0.834	45.06	0.0427	0.171
5	54	0.797	43.06	0.0408	0.204
6	54	0.762	41.16	0.0390	0.234
7	54	0.728	39.34	0.0373	0.261
8	54	0.696	37.60	0.0356	0.285
9	1054	0.665	701.35	0.6644	5.979

Duration = Time*Weight

= 7.410

Modified Duration = Duration/(1+YTM)

= 7.410/1.0463

= 7.082