Question

In: Finance

9. For the bonds in Questions #9-11, assume semiannual coupons/compounding. A 20-year bond has a coupon...

9. For the bonds in Questions #9-11, assume semiannual coupons/compounding.

A 20-year bond has a coupon rate of 9%, a par value of $1000. If the bond’s YTM is 7%, what is the bond’s price?

10.What is the capital gains yield of the bond in #9?

11.Now suppose the bond in #9 is callable in 10 years with a call price of $1075. What is the bond’s yield to call?

Solutions

Expert Solution

Compute the semi-annual yield, using the equation as shown below:

Semi-annual yield = Annual yield/ 2

                             = 7%/ 2

                              = 3.5%

Hence, the semi-annual yield is 3.5%.

Compute the PVIFA at 3.5% and 40 half years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 0.035)-40}/ 3.5%

             = 21.3550723334

Hence, the PVIFA at 3.5% and 40 half years are 21.3550723334.

Compute the PVIF at 3.5% and 40 half years, using the equation as shown below:

PVIF = 1/ (1 + Rate)Number of periods

              = 1/ (1 + 0.035)40

         = 1/ 3.95925972087

         = 0.25257246821

Hence, the PVIF at 3.5% and 40 half years are 0.25257246821.

Compute the semi-annual interest, using the equation as shown below:

Semi-annual interest = Face value*Coupon rate/2

                                 = $1,000*9%/2

                                = $45

Hence, the semi-annual interest is $45.

Compute the current bond price, using the equation as shown below:

Bond price = (Interest*PVIFA3.5%, 40) + (Face value*PVIF3.5%, 40)

                   = ($45*21.3550723334) + ($1,000*0.25257246821)

                   = $960.978255003 + $252.57246821

                   = $1,213.55072321

Hence, the price of bond is $1,213.55072321.


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