Question

An 8% coupon bond matures in 5 years. The face value is $1,000 and has a current yield of 9.1%. What is the bond's current market price?

Answer 1

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 annually

= ($ 1,000 x 8 %)/1 = $ 1,000 x 0.08 = $ 80

[Annual coupon frequency assumed to be one as it is not mentioned}

r = Rate of interest = 9.1 % or 0.091 p.a.

n = No of periods = 5 periods

Bond Price = $ 80 x [1-{1/ (1+0.091)⁵}/0.091] + $ 1,000/ (1+0.091)⁵

                   = $ 80 x [1-{1/ (1.091)⁵}/0.091] + $ 1,000/ (1.091)⁵

                   = $ 80 x [1-(1/1.54569482512645)/0.091] + $ 1,000/1.54569482512645

                  = $ 80 x [(1-0.646958237644479)/0.091] + $ 646.958237644479

                   = $ 80 x [(1-0.646958237644479)/0.091] + $ 646.958237644479

                   = $ 80 x (0.353041762355521/0.091) + $ 646.958237644479

                   = $ 80 x (0.353041762355521/0.091*) + $ 646.958237644479

                   = $ 80 x 3.87957980610462 + $ 646.958237644479

                   = $ 310.366384488370 + $ $ 646.958237644479

                   = $ 957.324622132849 or $ 957.32

Current market price of bond is $ 957.32