Again, the coupon flows over the 4 year period are not impacted by the yield but by the coupon rate. But what we notice here is that the yield of the bond has gone up sharply from 5% to 7% that is a rise of 200 bps. That will obviously lead to a fall in the price of the bond. Thus the bond price will be less than the par value of the bond. Let us understand through the cash flow angle.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

5.0%

Yield to Maturity (Annualized) (y)

7.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

3.5%

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

? 24.15

? 23.34

? 22.55

? 21.79

? 21.05

? 20.34

? 19.65

? 778.40

Bond Price

? 931.26

In the above instance, the coupon rate is at 5% but the bond yield is at 7%. That is the reason the market price of the bond at Rs.931.26 is lower 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 200 bps higher than the coupon rate. Thus the future value of the coupon is more than offset by the present value of the bonds and the sum of the present values adds up to lower than the face value of the bond. That is because the impact of lower present value of cash flow in future years is depressing the present value of the bond price. That explains the price of the bond being at a discount to the face value.

Again, the coupon flows over the 4 year period are not impacted by the yield but by the coupon rate. But what we notice here is that the yield of the bond has gone up sharply from 5% to 7% that is a rise of 200 bps. That will obviously lead to a fall in the price of the bond. Thus the bond price will be less than the par value of the bond. Let us understand through the cash flow angle.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

5.0%

Yield to Maturity (Annualized) (y)

7.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

3.5%

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

? 24.15

? 23.34

? 22.55

? 21.79

? 21.05

? 20.34

? 19.65

? 778.40

Bond Price

? 931.26

In the above instance, the coupon rate is at 5% but the bond yield is at 7%. That is the reason the market price of the bond at Rs.931.26 is lower 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 200 bps higher than the coupon rate. Thus the future value of the coupon is more than offset by the present value of the bonds and the sum of the present values adds up to lower than the face value of the bond. That is because the impact of lower present value of cash flow in future years is depressing the present value of the bond price. That explains the price of the bond being at a discount to the face value.