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

e. 7.70%

Step-by-step 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:

`(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)

`(1000)/((1 + 0.04625)^(50) ) = PV`

PV 104.2861

The coupon payment should be:

850 - 104.2861 = 745,7139‬

Coupon payment

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

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

time 50

rate 0.04625

`C * (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%