Question

Ford Motor Company has issued bonds that mature 17 years from now, and pay 7.13% coupon interest. Each bond has $1000 face value, and half the annual coupon is paid each six months. The yield to maturity on these bonds is 11.72%. What is the value of each bond? Explain why these bonds sell at a price that differs from their $1000 face value.

Answer 1

the value of bond = [present value of annuity factor *interest payment] + [present value factor * face value]

now,

present value of annuity factor = [1-(1+r)^(-n)]/r

here,

r = 11.72% per annum =>5.86 % per six months =>0.0586....(since payments are made every six months)

n = 17 years*2 semi annual periods.

=>34 periods.

=>[1- (1.0586)^(-34)]/0.0586

=>0.85575/0.0586

=>14.6032423.

interest payment = $1,000*7.13%*6/12

=>$35.65.

present value factor=1/(1+r)^n

=1/(1.0586)^34

=>0.14424998.

face value =$664.86

now,

value of bond =[14.6032423*$35.65] +[0.14424998*$1,000]

=>$520.605588+144.24998

=>$664.86.

These bonds sells at a price that differs from their $1,000 face value because its yield to maturity is different from its coupon rate.