Question

1. A $1,000 bond has a 7.5 percent coupon and matures after nine years. If current interest rates are 9 percent, what should be the price of the bond? Assume that the bond pays interest annually. Use Appendix B and Appendix D to answer the question. Round your answer to the nearest dollar.

   $  

2. If after five years interest rates are still 9 percent, what should be the price of the bond? Use Appendix B and Appendix D to answer the question. Assume that the bond pays interest annually. Round your answer to the nearest dollar.

   $  

3. Even though interest rates did not change in a and b, why did the price of the bond change?

   The price of the bond with the longer term is _____(less or higher) than the price of the bond with the shorter term as the investors will collect the _____(smaller or higher) interest payments and receive the principal within a longer period of time.

4. Change the interest rate in a and b to 6 percent and rework your answers. Assume that the bond pays interest annually. Round your answers to the nearest dollar.

   Price of the bond (nine years to maturity): $  
   Price of the bond (four years to maturity): $  

   Even though the interest rate is 6 percent in both calculations, why are the bond prices different?

   The price of the bond with the longer term is _____(less or higher) than the price of the bond with the shorter term as the investors will collect the ______(smaller or higher) interest payments for a longer period of time.

Appendix B

$Appendix_B.jpg$

Appendix D

$Appendix_D.jpg$

Answer 1

Sub question (a):

Given,

Face Value (FV)=$1,000, Coupon rate (C)= 7.5%, Term to maturity= 9 year. Current interest rate (r)= 9%

Coupon frequency= Annual. Hence periodical interest payment (I)= FV*C= $1,000*7.5% = $75

Price of the bond is the present value of periodical coupon payments plus PV of Face value discounted at the current interest rate.

Hence price of the bond= Interest (I)*Present Value of Annuity Factor for 9 years+ FV*Present Value Interest Factor for 9 years

Using Appendix B and D given,

Price= $75*5.985 + $1000*0.460 = $448.875 + $460 = $909

Sub question (b):

After 5 years, term to maturity=4 years. Other factors remain unchanged

Hence price of the bond= Interest (I)*Present Value of Annuity Factor for 4 years+ FV*Present Value Interest Factor for 4 years

Using Appendix B and D given,

Price= $75*3.240 + $1000*0.708 = $243+$708 = $951

Sub question (c):

Price of the bond with longer period is less than the price of the bond with shorter term as the investors will collect the smaller interest payments and receive the principal; within a longer period of time.

Sub question (d)

Term to maturity 9 years, interest rate 6%

Price= $75*6.802 + $1000*0.592 = $510.15+$592 = $1,102

Term to maturity 4 years, interest rate 6%

Price=$75*3.465 + $1000* 0.792 = $259.875+$792 = $1,052

Price of the bond with longer period is higher than the price of the bond with shorter term as the investors will collect the higher interest payments for a longer period of time.