Question

Doisneau 16-year bonds have an annual coupon interest of 9percent, make interest payments on a semiannual basis, and have a$1,000par value. If the bonds are trading with a market's required yield to maturity of 11percent, are these premium or discount bonds? Explain your answer. What is the price of the bonds

Answer 1

The bonds are discount bonds as these are trading at discount offering a coupon rate, 9 % which is lower than prevailing interest rate of 11 %.

Formula for bond price is:

Price of bond = C x [1-{1/ (1+r) ⁿ}/r] +M/ (1+r)ⁿ

M = Face Value = $ 1,000

C= Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

= ($1,000 x 9 %)/2 = $ 90/2 = $ 45

r = Rate of interest = 11 % p.a. or 0.11/2 i.e. 0.055 semiannually

n = No of periods = 16 years x 2 periods = 32

Bond Price = $ 45 x [1-{1/ (1+0.055)³²}/0.055 ] + $ 1,000/ (1+0.055)³²

                    = $ 45 x [1-{1/ (1.055)³²}/0.055 ] + $ 1,000/ (1.055)³²

                    = $ 45 x [1-{1/5.5472623828}/0.055] + $ 1,000/ 5.5472623828

                    = $ 45 x [(1-0.1802691005)/0.055] + $ 180.2691005027

                   = $ 45 x (0.8197308995/0.055) + $ 180.2691005027

                    = $ 45 x 14.9041981727 + $ 180.2691005027

                    = $ 45 x 14.9041981727 + $ 180.2691005027

                    = $ 670.6889177715 + $ 180.2691005027

                     = $ 850.9580182742 or $ 850.96

Price of the bonds is $ 850.96