Question

10. Tom is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds: • Bond A has a 7% annual coupon, matures in 10 years, and has a $1,000 par value. • Bond B has a 9% annual coupon, matures in 11 years, and has a $1,000 par value. • Bond C has an 11% annual coupon, matures in 12 years, and has a $1,000 par value. Each bond has a yield to maturity of 9%.

a) Calculate the price of each of the three bonds.

b) If the yield to maturity for each bond remains at 9%, what will be the price of each bond 5 years from now?

Answer 1

BOND PRICE =C×(1 - (1+YTM)^-n )/YTM + F× (1+YTM)^-n

C = coupon amount (Face value × Coupon rate )

YTM = Yield to maturity

n = no. of years

F = Face value

a) PRICE OF BOND =

A

=70×(1-(1+0.09)^-10)/0.09 + 1,000(1+0.09)^-10

=70×(1 - 0.422)/0.09 + 1,000× 0.422

=70× 0.578/0.09 + 1,000 × 0.422

= 449.56 + 422

=$871.56

B

=90×(1-(1+0.09)^-11)/0.09 + 1,000(1+0.09)^-11

=90×(1 - 0.388)/0.09 + 1,000× 0.388

=90× 0.612/0.09 + 1,000 × 0.388

= 612 + 388

=$1,000

C

=110×(1-(1+0.09)^-12)/0.09 + 1,000(1+0.09)^-12

=110×(1 - 0.356)/0.09 + 1,000× 0.356

=110× 0.644/0.09 + 1,000 × 0.356

= 787.11 + 356

=$1,143.11

b) Price after five years means maturity years(YTM) will be for

Bond A = 10 years - 5 years = 5 years

Bond B = 11 years - 5 years = 6 years

Bond C = 12 years - 5 years = 6 years

A

=70×(1-(1+0.09)^-5)/0.09 + 1,000(1+0.09)^-5

=70×(1 - 0.650)/0.09 + 1,000× 0.650

=70× 0.350/0.09 + 1,000 × 0.650

= 272.22 + 650

=$922.22

B

=90×(1-(1+0.09)^-6)/0.09 + 1,000(1+0.09)^-6

=90×(1 - 0.596)/0.09 + 1,000× 0.596

=90× 0.404/0.09 + 1,000 × 0.596

= 404 + 596

=$1,000

C

=110×(1-(1+0.09)^-7)/0.09 + 1,000(1+0.09)^-7

=110×(1 - 0.547)/0.09 + 1,000× 0.547

=110× 0.453/0.09 + 1,000 × 0.547

= 553.67 + 547

=$1,100.67

Summary

a) Price of bonds

A= $871.56

B=$1,000

C=$1,143.11

b) Price of bond 5 years from now

A=$922.22

B=$1,000

C=$1,100.67