In the case we are considering below, the market yield on the bond has fallen by 100 bps possibly due to a dovish tone by the RBI. While the coupon rate of the bond is at 5% the yield in the market has fallen to 4%. That means the present value will be discounted at a lower rate and therefore the market price of the bond will be higher than the face value of the bond. Check the table below.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

5.0%

Yield to Maturity (Annualized) (y)

4.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

2.0%

Coupon Payment (PMT)

? 25

Calculate Bond Price 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

Cash Flows

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 1,025.00

Present Value of Cash Flow

? 24.51

? 24.03

? 23.56

? 23.10

? 22.64

? 22.20

? 21.76

? 874.83

Bond Price

? 1,036.63

In the above instance, the coupon rate is at 5% but the bond yield is at 74%. That is the reason the market price of the bond at Rs.1036.63 is higher than the face value of the bond. Look at the cash flows over 8 half yearly periods over a period of 4 years. The interest rates are being discounted at a yield that is 100 bps lower than the coupon rate. Thus the future value of the coupon is less than offset by the present value of the bonds and the sum of the present values adds up to higher than the face value of the bond. That is because the impact of higher present value of cash flow in future years is inflating the present value of the bond price. That explains the price of the bond being at a premium to the face value.

In the case we are considering below, the market yield on the bond has fallen by 100 bps possibly due to a dovish tone by the RBI. While the coupon rate of the bond is at 5% the yield in the market has fallen to 4%. That means the present value will be discounted at a lower rate and therefore the market price of the bond will be higher than the face value of the bond. Check the table below.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

5.0%

Yield to Maturity (Annualized) (y)

4.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

2.0%

Coupon Payment (PMT)

? 25

Calculate Bond Price 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

Cash Flows

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 25.00

? 1,025.00

Present Value of Cash Flow

? 24.51

? 24.03

? 23.56

? 23.10

? 22.64

? 22.20

? 21.76

? 874.83

Bond Price

? 1,036.63

In the above instance, the coupon rate is at 5% but the bond yield is at 74%. That is the reason the market price of the bond at Rs.1036.63 is higher than the face value of the bond. Look at the cash flows over 8 half yearly periods over a period of 4 years. The interest rates are being discounted at a yield that is 100 bps lower than the coupon rate. Thus the future value of the coupon is less than offset by the present value of the bonds and the sum of the present values adds up to higher than the face value of the bond. That is because the impact of higher present value of cash flow in future years is inflating the present value of the bond price. That explains the price of the bond being at a premium to the face value.