Question

Merton enterprises has bonds on the market making annual payments, with 13 years to maturity, $1,000 par value, and selling for $825. At this price, the bonds yield 7 percent. What must the coupon rate be on Merton’s bonds

Answer 1

Price of a bond is mathematically represented as: 1 1-- (1 + i)" PEC. - +- м. (1 + i)" where P is price of bond, with periodic coupon C, n periods to maturity, periodic YTM i and face value M.

M = $1000, P = $825, n = 13, i = 7%

$825 = C * \frac{1-\frac{1}{(1 + 0.07)^{13}}}{0.07} + \frac{1000}{(1 + 0.07)^{13}}$

$825 = C * \frac{1-\frac{1}{(1.07)^{13}}}{0.07} + \frac{1000}{(1.07)^{13}}$

$825 = C * \frac{1-\frac{1}{(1.07)^{13}}}{0.07} + 414.9644$

$410.0356 = C * \frac{1-\frac{1}{(1.07)^{13}}}{0.07}$

$410.0356 = C * 8.3577$

C = $49.06

Coupon Rate = $49.06/$1000 = 4.91%