Question

What is the Coupon Rate of a bond that makes semi-annual coupon payments, has a par value of $1000, sells on the market for $1031.40, has a yield-to-maturity of 6%, and has 8 years remaining until maturity?

Answer 1

The coupon rate will be as follows:

= (Coupon payment / Par value) x 2 (Multiplied by 2 since the payments are on semi annual basis)

Coupon payment is as follows:

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

r will be as follows:

= 6% / 2

= 3% or 0.03

n will be as follows:

= 8 x 2

= 16

$ 1,031.40 = Coupon payment x [ [ (1 - 1 / (1 + 0.03)¹⁶ ] / 0.03 ] + $ 1,000 / 1.03¹⁶

$ 1,031.40 = Coupon payment x 12.56110203 + $ 623.1669392

Coupon payment = ($ 1,031.40 - $ 623.1669392) / 12.56110203

Coupon payment = $ 32.49978066

So, the coupon rate will be:

= ($ 32.49978066 / $ 1,000) x 2

= 6.50% Approximately