Question

O’Brien Ltd.’s outstanding bonds have a $1,000 par value, and they mature in 23 years. Their nominal yield to maturity is 5.50%, they pay interest semiannually, and they sell at a price of $1,230. What is the bond’s nominal (annual) coupon interest rate?

Answer 1

We know that,

Price of bond = Present value of all the semi-annual coupon and face value discounted at semi-annual ytm.

Semi annual ytm = 2.75%

Number of payments = 23*2 = 46

Price = 1230

Face Value = 1000

1230 = Semi annual coupon amount * ( 1/(1+0.0275)^1 + 1/(1+0.0275)^2 +1/(1+0.0275)^3 +1/(1+0.0275)^4 +1/(1+0.0275)^5 +1/(1+0.0275)^6 +1/(1+0.0275)^7 +...................  1/(1+0.0275)^46 ) + 10001/(1+0.0275)^46

Semi annual Coupon Amount = 36.37

Semi annual Coupon Rate = (36.37/1000 )* 1000 = 3.637%

Annual Coupon Rate = 7.274% Answer

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