Question

a. Find the duration of a 6% coupon bond making (semiannually) coupon payments if it has three years until maturity and has a yield to maturity of 6%.

b. What is the duration if the yield to maturity is 10%?

Answer 1

a. Find the duration of a 6% coupon bond making (semiannually) coupon payments if it has three years until maturity and has a yield to maturity of 6%.

Time	Cashflow	PVF@3%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	30	0.971	29.13	0.0291	0.0291
2	30	0.943	28.28	0.0283	0.0566
3	30	0.915	27.45	0.0275	0.0824
4	30	0.888	26.65	0.0267	0.1066
5	30	0.863	25.88	0.0259	0.1294
6	1030	0.837	862.61	0.8626	5.1757

Duration of semi annual bond = Time*Weight/2

= 5.5797/2

= 2.78985

= 2.79 years

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

Prima facie, the bond will trade at par as YTM=coupon rate

Note : Since the bond makes semiannual interest payments, total no. of period is 6 (3*2), cashflow per period is 30(1000*6%/2) and cashflows are discounted at 3% (6/2).

You can use the equation (1-(1+r)^-n)/r to find PVF using calculator

b. What is the duration if the yield to maturity is 10%?

Time	Cashflow	PVF@5%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	30	0.952	28.57	0.0318	0.0318
2	30	0.907	27.21	0.0303	0.0606
3	30	0.864	25.92	0.0288	0.0865
4	30	0.823	24.68	0.0275	0.1099
5	30	0.784	23.51	0.0262	0.1308
6	1030	0.746	768.60	0.8554	5.1326

Duration of semi annual bond = Time*Weight/2

= 5.5522/2

= 2.7761

= 2.78 years

Note : Since the bond makes semiannual interest payments, total no. of period is 6 (3*2), cashflow per period is 30(1000*6%/2) and cashflows are discounted at 5% (10/2).