What Coupon Rate Should Alphabet Soup's New Bonds Carry to Sell at Par?

Based on the market price for Alphabet Soup's 7.5% bonds maturing in 10 years selling for $1,013.03, what coupon rate would the new bonds have to carry in order to sell at par when issued? The new bonds would have to carry a coupon rate of 7.5% in order to sell at par when issued.

Understanding Coupon Rate for Bonds

In the world of bonds, the coupon rate is the annual interest payment that the issuer promises to pay the bondholder. It is expressed as a percentage of the bond's face value.

Calculation Process

When a bond sells at par, it means the price is equal to the face value of the bond. In this case, the existing bonds of Alphabet Soup with a coupon rate of 7.5% and a face value of $1,000 are selling for $1,013.03.

To determine the coupon rate for the new bonds, we need to calculate the annual interest payment for the existing bonds. Using the formula:

Annual interest payment = Coupon rate * Face value of bond

For the existing bonds:

Annual interest payment = 7.5% * $1,000 = $75

Since the new bonds need to sell at par, they would also need to carry a coupon rate of 7.5% to match the annual interest payment of $75.

Therefore, the new bonds issued by Alphabet Soup would have to carry a coupon rate of 7.5% in order to sell at par when issued.

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