Question

Last year, the yield on AAA-rated corporate bonds averaged approximately 5 percent; one year later, the yield on these same bonds had climbed to about 6 percent because the Reserve Bank of Australia increased interest rates during the year. Assume that BHP Billiton Limited issued a 10-year, 5 percent coupon bond one year ago (on 1 January). On the same date, Rio Tinto Limited issued a 20-year, 5 percent coupon bond. Both bonds pay interest annually. Assume that the market rate on similar risk bonds was 5 percent at the time the bonds were issued.

1. Compute the market value of each bond at the time of the issue.
2. Compute the market value of each bond one year after issue if the market yield for similar risk bonds were 6 percent.

Answer 1

a) Market Value of the bonds at the time of issuance

1. BHP Billiton Ltd

Coupon rate (CR)= 5%

No. of installments (n)= 10 periods

Yield to Maturity (r) = 5%

Face value (fv) = $ 1000 for corporate bonds

Coupon payment (cp) = $1000 * coupon rate

                                                $ 1000 * 5%

                                                $50

Present value of the bond = (CP * (1- (1+r)^-n)) + (FV/(1+r)ⁿ)

                                                = (50* [ 1-(1+0.05)^-10]/0.05) + (1000 (1+0.05)¹⁰)

                                                = 1646.191

2. Rio Tinto Ltd

Coupon rate (CR)= 5%

No. of installments (n)= 20 periods

Yield to Maturity (r) = 5%

Face value (fv) = $ 1000 for corporate bonds

Coupon payment (cp) = $1000 * coupon rate

                                                $ 1000 * 5%

                                                $50

Present value of the bond = (50* [ 1-(1+0.05)^-20]/0.05) + (1000 (1+0.05)²⁰)

                                                     = $ 1404.427

b) Market Value of the bonds 1 year after issuance

1. BHP Billiton Ltd

Coupon rate (CR)= 5%

No. of installments (n)= 9 periods                              (t=10-1)

Yield to Maturity (r) = 6%

Face value (fv) = $ 1000 for corporate bonds

Coupon payment (cp) = $1000 * coupon rate

                                                $ 1000 * 5%

                                                $50

Present value of the bond = (50* [ 1-(1+0.06)^-9]/0.06) + (1000 (1+0.06)⁹)

                                                     = 931.983

2. Rio Tinto Ltd

Coupon rate (CR)= 5%

No. of installments (n)= 19 periods                           (t=20-1)

Yield to Maturity (r) = 6%

Face value (fv) = $ 1000 for corporate bonds

Coupon payment (cp) = $1000 * coupon rate

                                                $ 1000 * 5%

                                                $50

Present value of the bond = (50* [ 1-(1+0.06)^-19]/0.06) + (1000 (1+0.06)1⁹)

                                                     = 888.419

*when YTM increases, value of the bond decreases*