Question

A $2,000,000 bond was issued on September 15 2015 with a 5 year maturity. Coupon rate is 5.5% and the present YTM is 5.75% p.a. compounded half-yearly. Interest is paid semi annually. How much is the bond worth on 15 March 2018?

Answer 1

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

M = Face Value = $ 2,000,000

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

= ($ 2,000,000 x 5.5 %)/2 = = ($ 2,000,000 x 0.055)/2 = $ 110,000/2 = $ 55,000

r = Rate of interest = 5.75 % or 0.0575/2 = 0.02875 semiannually

n = No of periods to maturity = 15 Sept 2020 – 15 Mar 2018 = 2.5 years x 2 = 5 periods

Bond Price = $ 55,000 x [1-{1/ (1+0.02875)⁵}/0.02875] + $ 1,000/ (1+0.02875)⁵

                    = $ 55,000 x [1-{1/ (1.02875)⁵}/0.02875] + $ 1,000/ (1.02875)⁵

                = $ 55,000 x [1-{1/ 1.152256697}/0.02875] + $ 2,000,000/1.152256697

                = $ 55,000 x [(1-0.867862172)/ 0.02875] + $ 1,735,724.3438

                = $ 55,000 x [0.132137828/0.02875] + $ 1,735,724.3438

                = $ 55,000 x 4.596098368 + $ 1,735,724.3438

               = $ 252,785.4102 + $ 1,735,724.3438

               = $ 1,988,509.7541 or $ 1,988,509.75

Price of bond on 15 March 2018 is $ 1,988,509.75