Question

Doisneau 16​-year bonds have an annual coupon interest of 12 ​percent, make interest payments on a semiannual​ basis, and have a ​$1,000 par value. If the bonds are trading with a​market's required yield to maturity of 13 percent, are these premium or discount​ bonds? Explain your answer. What is the price of the​ bonds?

Answer 1

Doisneau bonds are discount bonds as the coupon rate of 12 % is lower than prevailing interest rate of 13 %.

When a bond sells at a price lower than its par value, is known as discount bond. Market interest rate and bond price are inversely related with each other. If market rate increases, bond price decreases and vice-versa. The bond which offers a lower coupon rate than current market rate, is selling at lower price than its face value.

Let’s compute the price of the bonds.

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/ coupon frequency in a year

                                 = $ 1,000 x 0.12/2 = $ 1,000 x 0.06 = $ 60

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

r = Rate of interest = 13 % p.a. or 0.13/2 = 0.065 semiannually

Price bond = $ 60 x [1-{1/ (1+0.065)³²}/0.065 ] + $ 1,000/ (1+0.065)³²

                    = $ 60 x [1-{1/ (1.065)³²}/0.065 ] + $ 1,000/ (1.065)³²

                    = $ 60 x [1-(1/ 7.50217946127498)/0.065] + $ 1,000/ 7.50217946127498

                    = $ 60 x [(1- 0.133294598611222)/0.065] + $ 133.294598611222

                   = $ 60 x [(0.866705401388778/0.065)] + $ 133.294598611222

                    = $ 60 x 13.3339292521351 + $ 133.294598611222

                   = $ 800.035755128103 + $ 133.294598611222

                    = $ 933.330353739325 or $ 933.33

Price of bonds is $ 933.33 and the bonds are discount bonds selling at a lower price than its par value.