Find the duration of a 3 coupon bond making annual coupon pa

Find the duration of a 3% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6.1%. What is the duration if the yield to maturity is 10.1%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM	Duration
6.1% YTM
10.1% YTM

Solution

YTM

Duration

6.1% YTM

2.9093

10.1% YTM

2.9038

Working:

Duration at YTM 6.1%

Period

Cash Flow

Discounting factor = 1/(1+R)^Y

PV of the cash flows = Cash flow x Df

Weighted cash flow = Period x Cash flow

Present value of weighted cash flow = Weighted Cash flow x Df

Y

CF

Df = 1/(1+6.1%)^Y

PV = CF x Df

WCF = CF x Y

WPV = WCF x Df

                      1

30

0.9425

28.2752

30

28.2752

                      2

30

0.8883

26.6496

60

53.2992

                      3

1030

0.8372

862.3649

3090

2587.0947

Total = P =

917.2897

Total = WP =

2668.6691

Duration = WP/P =

2.9093

Duration at YTM of 10.1%

Period

Cash Flow

Discounting factor = 1/(1+R)^Y

PV of the cash flows = Cash flow x Df

Weighted cash flow = Period x Cash flow

Present value of weighted cash flow = Weighted Cash flow x Df

Y

CF

Df = 1/(1+10.1%)^Y

PV = CF x Df

WCF = CF x Y

WPV = WCF x Df

                      1

30

0.9083

27.2480

30

27.2480

                      2

30

0.8249

24.7484

60

49.4967

                      3

1030

0.7493

771.7476

3090

2315.2427

Total = P =

823.7439

Total = WP =

2391.9874

Duration = WP/P =

2.9038

YTM	Duration
6.1% YTM	2.9093
10.1% YTM	2.9038