Question

Kiss the Sky Enterprises has bonds on the market making annual payments, with 9 years to maturity, and selling for $900. At this price, the bonds yield 8.4 percent. What must the coupon rate be on the bonds? (Note: first find the coupon payment, then the coupon rate. The face value of $1,000 x coupon rate = coupon payment).

Answer 1

$Bond\, price=Coupon\, payment\times \left ( \frac{1-\left ( 1+i \right )^{-n}}{i} \right )+\frac{Face\, value}{\left ( 1+i \right )^{n}}$

$900=Coupon\, payment\times \left ( \frac{1-\left ( 1+0.084 \right )^{-9}}{0.084} \right )+\frac{1,000}{\left ( 1+0.084 \right )^{9}}$

$900=Coupon\, payment\times \left ( \frac{1-0.4838786498}{0.084} \right )+\frac{1,000}{2.066633856}$

$900=Coupon\, payment\times 6.144301788+483.8786498$

$900-483.8786498=Coupon\, payment\times 6.144301788$

$416.1213502=Coupon\, payment\times 6.144301788$

Coupon payment = Face value*Coupon rate

67.72 = 1,000*Coupon rate

0.0677 = Coupon rate

Coupon rate is 6.77%.