Mullineaux Co issued 11year bonds one year ago at a coupon r

Mullineaux Co. issued 11-year bonds one year ago at a coupon rate of 8.6 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.5 percent, what is the current bond price?

Solution

Formula for Bond Price = C x [1-{1/(1+r)ⁿ}/r ] +M/(1+r)ⁿ

M = Face Value = $1,000 (Assumed)

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

= ($1,000 x 8.6 %)/2 = ($ 1,000 x 0.086)/2 = $ 86/2 = $ 43

r = Rate of interest = 7.5 % or 0.075/2 i.e. 0.0375 semiannually

n = No of periods = (11 – 1) years x 2 periods = 10 x 2 = 20 periods

Bond Price = $ 43 x [1-{1/ (1+0.0375)²⁰}/0.0375 ] + $ 1,000/ (1+0.0375)²⁰

                    = $ 43 x [1-{1/ (1.0375)²⁰}/0.0375 ] + $ 1,000/ (1.0375)²⁰

                = $ 43 x [1-{1/ 2.088151996}/0.0375] + $ 1,000/2.088151996

                = $ 43 x [(1-0.478892342)/0.0375] + $ 478.8923421

                = $ 43 x [0.521107658/0.0375] + $ 478.8923421

                = $ 43 x 13.89620421+ $ 478.8923421

               = $ 597.5367811 + $ 478.8923421

               = $ 1,076.429123 or $ 1,076.43

Current price of bond is $ 1,076.43