Question

Consider three bonds with 5.70% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years. a. What will be the price of the 4-year bond if its yield increases to 6.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What will be the price of the 8-year bond if its yield increases to 6.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) c. What will be the price of the 30-year bond if its yield increases to 6.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. What will be the price of the 4-year bond if its yield decreases to 4.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) e. What will be the price of the 8-year bond if its yield decreases to 4.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) f. What will be the price of the 30-year bond if its yield decreases to 4.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

In the given question we are asked to calculate the Price of the bond for three categories of bonds

• Short term bond , maturity 4 years, interest rate 5.7%
• Intermediate bond , maturity 8 years, interest rate 5.7%
• Long term bond , maturity 30 years, interest rate 5.7%

Sine the face value has not been given of the respective bonds, lets assume all have the same face value of $1000 each

a) We are required to computed the price of the 4-year bond if its yield increases to 6.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate.

hence we say simplify it as follows

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

Since in the given case we have been give a 4 years bond, with coupon/ interest payments for respective years. therefore Company will pay its bondholders 4 identical interest payments of $57($1000*5.70*12/12) at the end of each of the 4 annual periods.

Moreover, maturity of Bond falls on the end of the 4^th year , therefore the single principal payment of $1000 is also payable .

to calculate the price of the bond, the market interest rate is used to discount both the bond's future interest payments and the principal payment occurring on the maturity date.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 6.7%.

Now use the Present value of the ordinary annuity (PVOA) of 6.7% for 4 periods (refer to PVOA table) = 3.41

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*3.41

=$194.38

WN2) Refer Presenr value of 1 Table , here n= 4 & i= 6.7% , hence PV factor =.7715

Present value of Bond's Maturity Amount = $1000 * PVIF OF 4th Period(6.7%, 4th period)

=1000* .7715

=$ 771.51

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$194.38 (ReferWN1)+$ 771.51(Refer WN2)

= $965.90

B) We are required to computed the price of the 8-year bond if its yield increases to 6.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate.

hence we say simplify it as follows

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

Since in the given case we have been give a 8 years bond, with coupon/ interest payments for respective years. therefore Company will pay its bondholders 8 identical interest payments of $57($1000*5.70*12/12) at the end of each of the 8 annual periods.

Moreover, maturity of Bond falls on the end of the 8^th year , therefore the single principal payment of $1000 is also payable .

to calculate the price of the bond, the market interest rate is used to discount both the bond's future interest payments and the principal payment occurring on the maturity date.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 6.7%.

Now use the Present value of the ordinary annuity (PVOA) of 6.7% for 8 periods (refer to PVOA table) = 6.04

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*6.04

=$344.35

WN2) Refer Presenr value of 1 Table , here n= 8 & i= 6.7% , hence PV factor =.7715

Present value of Bond's Maturity Amount = $1000 * PVIF OF 8th Period(6.7%, 8th period)

=1000* ..595

=$ 595.23

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$344.35 (ReferWN1)+$ 595.23(Refer WN2)

= $939.58

C)We are required to computed the price of the 30-year bond if its yield increases to 6.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate.

hence we say simplify it as follows

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

Since in the given case we have been give a 30 years bond, with coupon/ interest payments for respective years. therefore Company will pay its bondholders 30 identical interest payments of $57($1000*5.70*12/12) at the end of each of the 30 annual periods.

Moreover, maturity of Bond falls on the end of the 30^th year , therefore the single principal payment of $1000 is also payable .

to calculate the price of the bond, the market interest rate is used to discount both the bond's future interest payments and the principal payment occurring on the maturity date.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 6.7%.

Now use the Present value of the ordinary annuity (PVOA) of 6.7% for 30 periods (refer to PVOA table) = 12.926

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*12.79

=$729.03

WN2) Refer Presenr value of 1 Table , here n= 30 & i= 6.7% , hence PV factor =.1429

Present value of Bond's Maturity Amount = $1000 * PVIF OF 30th Period(6.7%, 30th period)

=1000* . .1429

=$ 142.9

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$729.03(ReferWN1)+$ 142.91(Refer WN2)

= $871.94

D)  We are required to computed the price of the 4-year bond if its yield increases to 4.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate/ yield rate

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 4.7%.

Now use the Present value of the ordinary annuity (PVOA) of 4.7% for 4 periods (refer to PVOA table) = 3.57

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*3.57

=$203.49

WN2) Refer Presenr value of 1 Table , here n= 4 & i= 4.7% , hence PV factor =.8321

Present value of Bond's Maturity Amount = $1000 * PVIF OF 4th Period(4.7%, 4th period)

=1000* . 8321

=$832

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$203.49(ReferWN1)+$832(Refer WN2)

= $1035.49

E)

D)  We are required to computed the price of the 8-year bond if its yield increases to 4.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate/ yield rate

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 4.7%.

Now use the Present value of the ordinary annuity (PVOA) of 4.7% for 8 periods (refer to PVOA table) = 6.5423

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*6.5423

=$372.91

WN2) Refer Presenr value of 1 Table , here n= 8 & i= 4.7% , hence PV factor =.6925

Present value of Bond's Maturity Amount = $1000 * PVIF OF 4th Period(4.7%, 8h period)

=1000* .6925

=$692.5

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$372.91(ReferWN1)+$692.5(Refer WN2)

= $1065.41

F) We are required to computed the price of the 30-year bond if its yield increases to 4.70%

the calculation of the price of the bond is done by discounting the bond's future cash flows by the current market interest rate/ yield rate

Price of Bond= PresentValue of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

to calculate the present value of the interest payments of $57 each, we need to discount the interest payments by the market interest rate i.e 4.7%.

Now use the Present value of the ordinary annuity (PVOA) of 4.7% for 30 periods (refer to PVOA table) = 15.9124

WN 1) Present Value of Interest payments = annually payment * PVOA factor

=$57*15.9124

=$907

WN2) Refer Presenr value of 1 Table , here n= 30 & i= 4.7% , hence PV factor =..2521

Present value of Bond's Maturity Amount = $1000 * PVIF OF 4th Period(4.7%, 30TH period)

=1000* .2521

=$252.1

NOW , lets compute

Present Value of Bond= Present Value of the interest payments + present value of the principal amount redeemable on the date of bond maturity.

=$907(ReferWN1)+$252.1 (Refer WN2)

= $1159.12