To determine the coupon rate for the new bonds that will enable them to sell at face value, we need to understand the relationship between coupon rates and bond prices.
When a bond sells at face value, it means that the price of the bond is equal to its face value. In this case, General Matter’s outstanding bond issue sells at a yield to maturity of 7.80%, which implies that its price is equal to its face value.
The coupon rate of the existing bond issue is 9.4%. We can use this information to calculate the price of the bond using the yield to maturity formula:
Bond Price = Coupon Payment / Yield to Maturity + Face Value / (1 + Yield to Maturity)^n
Since the bond is selling at face value, we can substitute the price with the face value:
Face Value = Coupon Payment / Yield to Maturity + Face Value / (1 + Yield to Maturity)^n
To find the coupon rate for the new bonds that will also sell at face value, we need to solve for the coupon payment in this equation.
Face Value – Face Value / (1 + Yield to Maturity)^n = Coupon Payment / Yield to Maturity
Coupon Payment = (Face Value – Face Value / (1 + Yield to Maturity)^n) * Yield to Maturity
Now we can substitute the values into the equation:
Coupon Payment = (Face Value – Face Value / (1 + 7.80%)^n) * 7.80%
To find the coupon rate, we need to divide the coupon payment by the face value and multiply by 100%:
Coupon Rate = (Coupon Payment / Face Value) * 100%
Let’s calculate the coupon rate for the new bonds:
Coupon Rate = ((Face Value – Face Value / (1 + 7.80%)^n) * 7.80% / Face Value) * 100%
Please provide the value of ‘n’ (the number of periods until maturity) and I will calculate the coupon rate for the new bonds.
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