Semiannual coupon bonds with the same risk (Aaa) and maturity (20 years) as your

Question

Semiannual coupon bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a nominal (not EAR) yield to maturity of 9%. Your company's treasurer is thinking of issuing, at par, some $1,000 par value, 20-year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds. What would the quarterly, dollar interest payment be?

$45.00

$25.00

$22.25

$27.50

$23.00

Explanation / Answer

In order to sell the bond at par, the coupon rate should be equal to YTM

So coupon rate should be equal to 9%

Effective annual rate is given by (1+r/m)^m -1 = EAR

Here r = 0.09 and m= 2(semi annual)

So effective annual rate = (1+0.09/2)^2 -1 = 0.092025

hence The coupon payment (annual) =  0.092025*1000 = 92.025

Hence quarterly payment = 92.025/4 = 23.00625 = $23.00

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