Let us take the base case first of an 8% coupon bond of face value Rs.1000 when the market bond yield is 9%. Check the table below.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

Calculate Bond Duration using the Cash Flows

Period

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 1,040.00

Present Value of Cash Flow

? 38.28

? 36.63

? 35.05

? 33.54

? 32.10

? 30.72

? 29.39

? 731.31

? 967.02

Weight

4.0%

3.8%

3.6%

3.5%

3.3%

3.2%

3.0%

75.6%

100.0%

Weight * Time

0.02

0.04

0.05

0.07

0.08

0.10

0.11

3.03

3.49

Duration

3.49

Modified Duration

3.34

Now, there is a slight change in the way the issuer wants to redeem the bond. Instead of redeeming the entire bond at the end of the fourth year, the issuer redeems 50% at the end of 3^{rd} year and 50% at the end of the fourth year. How will duration change in this case? Check the table below…

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

Calculate Bond Duration using the Cash Flows

Period

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 540.00

? 20.00

? 520.00

Present Value of Cash Flow

? 38.28

? 36.63

? 35.05

? 33.54

? 32.10

? 414.66

? 14.70

? 365.66

? 970.62

Weight

3.9%

3.8%

3.6%

3.5%

3.3%

42.7%

1.5%

37.7%

100.0%

Weight * Time

0.02

0.04

0.05

0.07

0.08

1.28

0.05

1.51

3.10

Duration

3.10

Modified Duration

2.97

Why do we see a sharp fall in the duration? Due to the early redemption, the weight of the cash flows now veers more towards the year 3, which is evident from the sharp fall in the duration of the bond as well as the modified duration. Quicker the cash flow, the faster you recover your bond investment and the time value works to reduce your duration of the bond.

prachi Patwardhananswered.Let us take the base case first of an 8% coupon bond of face value Rs.1000 when the market bond yield is 9%. Check the table below.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

Calculate Bond Duration using the Cash FlowsPeriod

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 1,040.00

Present Value of Cash Flow

? 38.28

? 36.63

? 35.05

? 33.54

? 32.10

? 30.72

? 29.39

? 731.31

? 967.02

Weight

4.0%

3.8%

3.6%

3.5%

3.3%

3.2%

3.0%

75.6%

100.0%

Weight * Time

0.02

0.04

0.05

0.07

0.08

0.10

0.11

3.03

3.49

Duration

3.49

Modified Duration

3.34

Now, there is a slight change in the way the issuer wants to redeem the bond. Instead of redeeming the entire bond at the end of the fourth year, the issuer redeems 50% at the end of 3

^{rd}year and 50% at the end of the fourth year. How will duration change in this case? Check the table below…InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

Calculate Bond Duration using the Cash FlowsPeriod

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 540.00

? 20.00

? 520.00

Present Value of Cash Flow

? 38.28

? 36.63

? 35.05

? 33.54

? 32.10

? 414.66

? 14.70

? 365.66

? 970.62

Weight

3.9%

3.8%

3.6%

3.5%

3.3%

42.7%

1.5%

37.7%

100.0%

Weight * Time

0.02

0.04

0.05

0.07

0.08

1.28

0.05

1.51

3.10

Duration

3.10

Modified Duration

2.97