Question

Find the duration of a 7.6% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 12.0%? Note: The face value of the bond is $100

Answer 1

Step-by-step explanation:

What is given:

Semiannual coupon payments [7.6%*100/2 = 3.8]

n = 3*2 = 6 periods

YTM =6%; 12%

Calculations:

YTM = 6%

Cash-flows during periods 1-5 = 3.8 and pays 103.8 at the end

PV of CF1 = 3.68932

PV of CF2 = 3.581864

PV of CF3 = 3.477538

PV of CF4 = 3.376251

PV of CF5 = 3.277913

PV of CF6 = 86.93087

Price(Total of CFs) = 104.3338

Weighted CF1 =3.8

Weighted CF1 = 2*3.8 = 7.6

Weighted CF2 = 3*3.8 = 11.4

Weighted CF3 = 4*3.8 = 15.2

Weighted CF4 = 5*3.8 = 19

Weighted CF5 = 6* 103.8 = 622.8

PV of Weighted CF1 = 3.68932

PV of Weighted CF2 = 7.163729

PV of Weighted CF3 = 10.43261

PV of Weighted CF4 = 13.505

PV of Weighted CF5 = 16.38957

PV of Weighted CF6 = 521.5852

Sum of weighted CFs = 572.7654

Duration 2.744871

YTM = 12%:

PV of CF1 = 3.584906

PV of CF2 = 3.381986

PV of CF3 = 3.190553

PV of CF4 = 3.009956

PV of CF5 = 2.839581

PV of CF6 = 73.1749

Price(Total of CFs) = 89.18189

Weighted CF1 =3.8

Weighted CF1 = 2*3.8 = 7.6

Weighted CF2 = 3*3.8 = 11.4

Weighted CF3 = 4*3.8 = 15.2

Weighted CF4 = 5*3.8 = 19

Weighted CF5 = 6* 103.8 = 622.8

PV of Weighted CF1 = 3.584906

PV of Weighted CF2 = 6.763973

PV of Weighted CF3 = 9.57166

PV of Weighted CF4 = 12.03982

PV of Weighted CF5 = 14.19791

PV of Weighted CF6 = 439.0494

Sum of weighted CFs = 485.2077

Duration 2.720326