Question

O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $850. What is the bond's nominal (annual) coupon interest rate?
a. 6.27%
b. 6.60%
c. 6.95%
d. 7.32%
e. 7.70%

Answer 1

Answer:

e. 7.70%

Explanation:

With the market alue and the yield to maturity we can solve for the coupon rate:

the bond price is compose of the maturity present valeu and the present value of the coupon payment:

maturity:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  1,000.00

time  50.00 (25 years x 2 payment per year)

rate  0.04625 (9.25% annual /2 = semiannual)

$\frac{1000}{(1 + 0.04625)^{50} } = PV$  

PV   104.2861

The coupon payment should be:

850 - 104.2861 = 745,7139‬

Coupon payment

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,000 x coupon rate / 2 payment per year

time 50

rate 0.04625

$C \times \frac{1-(1+0.04625)^{-50} }{0.04625} = 745,7139‬$

C =  38.505

face value x bond rate / 2 = coupon payment

1,000 x bond rate / 2 = 38.505

bond rate = 0.07701 = 7.70%