Question

A public company is offering bonds with a face value of $3,000 and a coupon rate of 14%, paid annually, if you want a yield to maturity of 18.00%, what is the maximum price you will pay for it? Assume that the bond will mature in 10 years and the first payment will be received in one year.

Answer 1

Solution:-

The coupon rate of a 10-year bond is 14% and the face value is $3000.This means the bond will pay $420(=14% of $3000 )for 10 years at the end of 10 Years, the bond will pay the maturity amount $3,000 with the final coupon payment.

Calculate the present value of the bond as follows:

P= Present value of coupon payment + present value of the final payment

=coupon amount[(1+i)^n-1/i(1+i)^n]+Final payment/(1+i)^n

=420[(1+0.1)^10-1/0.1(1+.1)^10]+3000/(1+.1)^10

=420[(1.1)^10-1/0.1(1.1)^10]+3000/(1.1)^10

=420[(2.59-1)/0.1(2.59)]+3000/2.59

=420(1.59/.259)+1158.30

=420(6.14)+1158.30

=2578.38+1158.30

P= 3736.68

Thus, Maximum price to be paid for the bond = $3737 (approx).