Question

Field Industries' outstanding bonds have a 25-year maturity and $1,000 par value. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $950. What is the bond's nominal (annual) coupon interest rate?

Answer 1

The coupon interest rate will be as follows:

= (Coupon payment / Par value) x 2 (Since the bond pays interest semiannually, hence the formula shall be multiplied by 2)

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

r will be as follows:

= 9.25% / 2 (Because the bond pays interest semiannually, hence r is divided by 2)

= 4.625% or 0.04625

n will be as follows:

= 25 x 2 (Because the bond pays interest semiannually, hence n is multiplied by 2)

= 50

$ 950 = Coupon payment x [ [ (1 - 1 / (1 + 0.04625)⁵⁰ ] / 0.04625 ] + $ 1,000 / 1.04625⁵⁰

$ 950 = Coupon payment x 19.3667869 + $ 104.2861057

Coupon payment = ($ 950 - $ 104.2861057) / 19.3667869

Coupon payment = $ 43.66826045

So, the rate will be as follows:

= ($ 43.66826045 / $ 1,000) x 2

= 8.73% Approximately