Question

Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 10 years remaining to maturity, and have a required rate of return of 15.5 percent.
a. The bond has a 7.2 percent coupon rate. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Fair present value $
b. The bond has a 9.2 percent coupon rate. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Fair present value $
c. The bond has a 15.5 percent coupon rate. (Do not round intermediate calculations.) Fair present value $

Answer 1

Answer:

Explanation:

A)

CR  Semi annually    7.2/2 3.6%

 

Semi Annual Cash-flow 1000*3.6%  36

 

Rate of Return          15.5 7.75%

 

Present value of bond at 7.75% semmi annually return  

Due to series of c/F apply annuity                                 1-(1+0.0775)^-20

Due to one single  c/F apply compound                        1/(1+0.0775)^20

  No of              Cash flows  Discount facto5 @ 7.75% annuity  Present Value

Cashflows                                    P=R*(1-(1+I )^-n) / i  

   20                      36                  9.966011947                        358.7764301

    1                   1000                  0.222651068                222.6510682

                                                    Present values    581.4274982

B)

CR  Semi annually    9.2/2 4.6%

 

Semi Annual Cash-flow 1000*4.6%  46

 

Rate of Return          15.5 7.75%

 

Present value of bond at 7.75% semmi annually return  

  No of              Cash flows  Discount facto5 @ 7.75% annuity  Present Value

Cashflows                                    P=R*(1-(1+I )^-n) / i  

   

    20               46                 9.966011947                        458.4365495

      1                1000           0.222651068                         222.6510682

                                  Present Value                          681.0876177

C)

There is no transaction cost and CR = IRR thats why the present value of the bond will be equal to face value of bond

CR =  15.5%

IRR = 15.5%

Present value of bond at 7.75% semmi annually return  

  No of              Cash flows  Discount facto5 @ 7.75% annuity  Present Value

Cashflows                                    P=R*(1-(1+I )^-n) / i  

  20                77.5               9.939402948                         770.3037285

   1                       1000                0.22472657                         224.7265701  

                                                                                 995.0302985

Difference is due to decimals