1. Assume that a $1,000 par value bond with a coupon rate of 7.5% (paid semi-ann

Question

1. Assume that a $1,000 par value bond with a coupon rate of 7.5% (paid semi-annually) has 20 years to maturity.

            a. If the current rate of interest on bonds like this is 9%, what will be the price of the bond? What is the price if current interest rates are instead 6%? (2 pts.)

            b. Assume that you buy the bond described above when interest rates are 9%. Five years later, you decided to sell the bond when current interest rates are still 9%. At what price will the bond be selling? Do the same assuming that you buy the bond when interest rates are 6%, and five years later they are still 6%. (2 pts.)

            c. Now assume that you purchase the bond in part a above when interest rates are 9%, and five years later interest rates are 11%. What will be the price of the bond? What percentage gain or loss would you incur in the value of this bond? (2 pts.)

            d. What is the current yield and capital gains yield on this bond under each of the two conditions in part a? (4 pts.)

Explanation / Answer

a)

Semi-annual coupon=1000*0.075/2=37.5

Number of period=20 year*2=40

Semi-annual interest rate=0.09/2=0.045

Price of the bond =37.5*Annuity factor (40 years, r)+1000/(1+r)^40

For interest=9%, Semi-annual interest =4.5%

Price of the bond =37.5*(1/0.045)*(1-(1/(1+0.045)^40)) +1000/(1+0.045)^40=$861.99

For interest=6%, Semi-annual interest =3%

Price of the bond =37.5*(1/0.03)*(1-(1/(1+0.03)^40)) +1000/(1+0.03)^40=$1173.36

b)

5 years later, time remaining till maturity=30 years=60 periods

For interest=9%, Semi-annual interest =4.5%

Price of the bond =37.5*(1/0.045)*(1-(1/(1+0.045)^30)) +1000/(1+0.045)^30=$877.83

Thus the bond will sell at $877.83

For interest=6%, Semi-annual interest =3%

Price of the bond =37.5*(1/0.03)*(1-(1/(1+0.03)^30)) +1000/(1+0.03)^30=$1147

Thus the bond will sell at $1147

c)

5 years later, time remaining till maturity=30 years=60 periods

For interest=11%, Semi-annual interest =5.5%

Price of the bond =37.5*(1/0.055)*(1-(1/(1+0.055)^30)) +1000/(1+0.055)^30=$745.66

Change in the price of the bond= 745.66-861.99=-116.33

Thus there is loss of -$116.33 on the value of the bond

In percentage terms loss %=-116.33/861.99=-13.5%

Thus there is 13.5% loss in the value of the bond

d)

Current yield =Annual Coupon/Price

At 9%, current yield =37.5*2/861.99=8.7%

At 6%, current yield =37.5*2/1173.36=6.4%

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