Question

Consider two bonds, both with 8% coupon rates (assume annual coupon payments) one with 10 years to maturity and the other with 20 years to maturity. Assume that current market rates of interest are 8%. Calculate the difference in the change of the price of the two bonds if interest rates decrease to 6% one year after purchasing the bond. Repeat the procedure assuming that interest rates increase to 10% one year after purchase. Explain the major bond pricing principle that is being illustrated here

Answer 1

Assuming that the face value of each bond is $100

Price of 10-year bond today is calculated using the PV function in Excel with these inputs :

rate = 8% -    market interest rate

nper = 10 -   10 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $100.00

The price of the bond today is $100.00

Price of 20-year bond today is calculated using the PV function in Excel with these inputs :

rate = 8% -    market interest rate

nper = 20 -   20 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $100.00

The price of the bond today is $100.00

If the market interest rates fall to 6% one year after purchasing the bond :

Price of 10-year bond today is calculated using the PV function in Excel with these inputs :

rate = 6% -    market interest rate

nper = 10 -   10 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $114.72

The price of the bond is $114.72

Price of 20-year bond today is calculated using the PV function in Excel with these inputs :

rate = 6% -    market interest rate

nper = 20 -   20 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $122.94

The price of the bond is $122.94

If the market interest rates rise to 10% one year after purchasing the bond :

Price of 10-year bond today is calculated using the PV function in Excel with these inputs :

rate = 10% -    market interest rate

nper = 10 -   10 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $87.71

The price of the bond is $87.71

Price of 20-year bond today is calculated using the PV function in Excel with these inputs :

rate = 10% -    market interest rate

nper = 20 -   20 years to maturity annual coupon payments each year

pmt = 100 * 8% - annual coupon payment = face value * coupon rate

fv = 100                - face value of the bond receivable on maturity

PV is calculated to be $82.97

The price of the bond is $82.97

The bond principle being illustrated is :

• If market interest rate (YTM) equals coupon rate, bonds price will be equal to its face value (bond trading at par)
• If market interest rate (YTM) is lower than coupon rate, bonds price will be higher its face value (premium bond)
• If market interest rate (YTM) is higher than coupon rate, bonds price will be lower its face value (discount bond)