Question

You are eyeing an investment in a corporate bond which has a YTM of 14.95%, and a stated rate of interest of 13.04% paid semi-annually, with a maturity of 20 years, and a PAR value of $1,000. What is the price of this bond?

Answer 1

Formula for bond price is:

Bond price = C x 1 – (1+r)-n/r + F/(1+r) n

F = Face value = $ 1,000

Coupon rate =13.04 %

n = Number periods to maturity = 20 years x 2 = 40 periods

C = Periodic coupon payment = Face value x Coupon rate/Annual coupon frequency

                                                = $ 1,000 x 0.1304/2

                                              = $ 1,000 x 0.0652 = $ 65.20

r = Rate of return = 14.95 % or 0.1495/2 = 0.07475 semi annually

Bond price = $ 65.20 x [1 – (1+0.07475)-40]/ 0.07475 + $ 1,000/ (1+0.07475) 40

                   = $ 65.20 x [1 – (1.07475)-40]/ 0.07475 + $ 1,000 x (1.07475) -40

                   = $ 65.20 x [(1 – 0.0559373448954232)/0.07475] + $ 1,000 x 0.0559373448954232

                   = $ 65.20 x (0.9440626551045769/0.07475) + $ 55.9373448954232

                   = $ 65.20 x 12.629600737185 + $ 55.9373448954232

                   = $ 823.44996806446 + $ 55.9373448954232

                   = $ 879.3873129598832 or $ 879.39

Price of the bond is $ 879.39