Question

Barnes enterprises has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and a price of $967. at this price, the bonds yield 7.9 percent. what must the coupon rate be on the bonds?

Answer 1

Answer: The coupon rate on the bonds is 7.50%.

The current price of a bond is nothing but the discounted value of the coupon payments and the face value at the yield or YTM.

Hence, mathematically the bond's price is given by the formula:

$\mathbf{CMP_{bond} = C*\left ( \frac{1-(1+r)^{-n}}{r} \right) + \frac{FV}{(1+r)^{n}}}$

where,

CMP = Current Market Price of the bond

C    = Coupon in dollars

r      = YTM

n     = number of years to maturity

FV = Face Value

Substituting the values in the equation above we get,

$967 = C*\left ( \frac{1-(1.079)^{-14}}{0.079} \right) + \frac{1000}{(1.079)^{14}}$

Solving further we get,

$967 = C*8.292338915 + \frac{1000}{2.899347199}$

$967 = C*8.292338915 + 344.9052257$

$622.0947743 = C*8.292338915$

\mathbf{C = 75.02042315}

Since the dollar value of coupons is $75.02042315, we can calculate the coupon rate on the bonds as:

$\mathbf{Coupon rate = \frac{Coupon}{Face Value}*100}$

$Coupon rate = \frac{75.02042315}{1000}*100$

$Coupon rate = 0.075020423*100$

$\mathbf{Coupon rate = 7.502042%}$