Question

O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal annual, not semiannual yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $700. What is the bond's nominal coupon interest rate?

Answer 1

Solution

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Face value =1000

n=number of periods to maturity=25*2=50

r-intrest rate per period=9.25/2=4.625%

Semi annual Coupon payment=?

Price of bond=700

Putting values in formula

700=Coupon payment*((1-(1/(1+.04625)^50))/.04625)+1000/(1+.04625)^50

Solving we get coupon payment=30.76

Thus annual coupon payment=30.76*2=61.52

Thus the nominal coupon rate=Annual coupon/Face value*100=61.52/1000*100

nominal coupon rate=6.152%

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